| Title: | Bayesian Network Meta-Analysis with Missing Participants |
|---|---|
| Description: | A comprehensive suite of functions to perform and visualise pairwise and network meta-analysis with aggregate binary or continuous missing participant outcome data. The package covers core Bayesian one-stage models implemented in a systematic review with multiple interventions, including fixed-effect and random-effects network meta-analysis, meta-regression, evaluation of the consistency assumption via the node-splitting approach and the unrelated mean effects model, and sensitivity analysis. Missing participant outcome data are addressed in all models of the package. The robustness to primary analysis results can also be investigated using a novel intuitive index. Methods to evaluate the transitivity assumption quantitatively are provided. The package also offers a rich, user-friendly visualisation toolkit that aids in appraising and interpreting the results thoroughly and preparing the manuscript for journal submission. The visualisation tools comprise the network plot, forest plots, panel of diagnostic plots, heatmaps on the extent of missing participant outcome data in the network, league heatmaps on estimation and prediction, rankograms, Bland-Altman plot, leverage plot, deviance scatterplot, heatmap of robustness, barplot of Kullback-Leibler divergence, heatmap of comparison dissimilarities and dendrogram of comparison clustering. The package also allows the user to export the results to an Excel file at the working directory. |
| Authors: | Loukia Spineli [aut, cre], Chrysostomos Kalyvas [ctb], Katerina Papadimitropoulou [ctb] |
| Maintainer: | Loukia Spineli <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 0.4.0 |
| Built: | 2024-11-20 06:42:56 UTC |
| Source: | CRAN |
An R package for performing Bayesian network meta-analysis while handling missing participant outcome data properly, assessing the robustness of the primary analysis results, and exploring the transitivity assumption.
R-package rnmamod is built upon the WinBUGS program code found in the series of tutorial papers on evidence synthesis methods for decision making (Dias et al., 2013a; Dias et al., 2013b; Dias et al., 2013c) and Dias et al. (2010) that introduces the node-splitting approach. All models comprise Bayesian hierarchical models for one-stage network meta-analysis and they are implemented in JAGS through the R-package R2jags.
rnmamod comprises a suite of core models implemented in a systematic review with multiple interventions:
fixed-effect and random-effects network meta-analysis
(run_model) based on Dias et al. (2013c);
fixed-effect and random-effects network meta-regression
(run_metareg) based on Cooper et al. (2009), and Dias et
al. (2013b);
fixed-effect and random-effects separate pairwise meta-analyses for
comparisons with at least two trials (run_series_meta);
local evaluation of the consistency assumption using the
fixed-effect or random-effects node-splitting approach
(run_nodesplit) based on Dias et al. (2010), and
van Valkenhoef et al. (2016);
global evaluation of the consistency assumption using the
fixed-effect or random-effects unrelated mean effects model
(run_ume) based on Dias et al. (2013a) and Spineli (2021);
comprehensive sensitivity analysis for the impact of aggregate
binary and continuous missing participant outcome data
(run_sensitivity) based on Spineli et al. (2021a);
hierarchical baseline model for the selected reference intervention
(baseline_model) based in Dias et al. (2013d).
rnmamod also includes a rich suite of visualisation tools to aid in the interpretation of the results and preparation of the manuscript for submission:
network plot and description of the evidence base
(netplot and describe_network,
respectively) following the PRISMA statement for systematic reviews with
network meta-analysis (Hutton et al., 2015);
illustration of the R-hat (Gelman and Rubin, 1992) and MCMC error
for all monitored nodes and creation of an HTML file with a panel of
diagnostic plots for each monitored parameter
(mcmc_diagnostics);
heatmap on the proportion of missing participants across the network
(heatmap_missing_network) and across the intervention arms
of each trial in the dataset (heatmap_missing_dataset);
league heatmap with the estimated and predicted summary effects of
all possible pairwise comparisons in the network and integrated SUCRA
(Salanti et al., 2011) or P-scores (Ruecker and Schwarzer, 2015)
(league_heatmap and
league_heatmap_pred, respectively) after performing network
meta-analysis or network meta-regression;
league table for relative and absolute effects for all pairwise
comparisons and interventions when conducting network meta-analysis anew
via the package (league_table_absolute) or using the results
of a published systematic review with network meta-analysis
(league_table_absolute_user);
forest plot with the trial-specific and summary absolute risks when
employing the hierarchical baseline model for the selected reference
intervention (baseline_model) as described in
Dias et al. (2013d);
rankograms with integrated SUCRA values for each intervention in
the network (rankosucra_plot) after performing network
meta-analysis (Salanti et al., 2011);
forest plot with the estimated and predicted summary effects of all
comparisons with a selected intervention (forestplot) as
obtained from the network meta-analysis model, and a forest plot with the
corresponding SUCRA values (Salanti et al., 2011);
tabulation of the estimated regression coefficient(s), the estimated
and predicted summary effects, measures of model fit and estimated
between-trial standard deviation before and after adjusting for a
trial-specific covariate (metareg_plot), and visualisation
of the summary effects and SUCRA values from both models
(forestplot_metareg, and scatterplot_sucra,
respectively–both found in metareg_plot);
tabulation of the estimated direct and indirect effects of the split
nodes and corresponding inconsistency factors, measures of model fit and
estimated between-trial standard deviation after each split node, and
visualisation of these results (nodesplit_plot);
tabulation of the estimated summary effects of all comparisons
observed in the network, measures of model fit and estimated between-trial
standard deviation under the unrelated mean effects model and network
meta-analysis, as well as visualisation of the summary effects from both
models (intervalplot_panel_ume) and the goodness of fit of
each model using a series of complementary plots
(scatterplots_dev (Dias et al., 2013a),
bland_altman_plot (Bland and Altman, 1999), and
leverage_plot (Dias et al., 2010)–all found in
ume_plot);
tabulation of the estimated summary effects and corresponding
between-trial standard deviation for comparisons with at least two trials
under pairwise and network meta-analysis, as well as visualisation of
these results (series_meta_plot);
calculation and visualisation of the robustness index for all
possible comparisons in the network (robustness_index,
robustness_index_user and heatmap_robustness)
(Spineli et al., 2021a);
enhanced balloon plot with the summary effects and between-trial
standard deviation for a selected pairwise comparison under several
scenarios about the missingness parameter (balloon_plot)
(Spineli et al., 2021a);
barplot with the Kullback-Leibler divergence measure from each
informative scenario to the missing-at-random assumption about the
missingness parameter for a selected pairwise comparison
(kld_barplot) (Spineli et al., 2021a).
rnmamod also assists the researcher in assessing the transitivity
assumption quantitatively based on trial dissimilarities for various
trial-level aggregate participant and methodological characteristics
calculated using the Gower's dissimilarity coefficient
(gower_distance and comp_clustering) (Gower,
1971). Results on the clustered comparisons based on hierarchical
agglomerative clustering are illustrated using a dendrogram with integrated
heatmap (dendro_heatmap). The distribution of the
characteristics is presented using violin plots with integrated box
plots and dots, and stacked bar plots across the observed treatment
comparisons (distr_characteristics). Missing data in the
characteristics across the trials and observed comparisons are visualised
using bar plots and tile plot (miss_characteristics).
Missing participant outcome data are addressed in all models of the package after extending the code to incorporate the pattern-mixture model (Spineli et al., 2021b; Spineli, 2019).
Type citation("rnmamod") on how to cite rnmamod.
To report possible bugs and errors, send an email to Loukia Spineli ([email protected]).
The development version of rnmamod is available on GitHub under the GPL-3.0 License.
Loukia M. Spineli
Bland JM, Altman DG. Measuring agreement in method comparison studies. Stat Methods Med Res 1999;8(2):135–60. doi: 10.1177/096228029900800204
Cooper NJ, Sutton AJ, Morris D, Ades AE, Welton NJ. Addressing between-study heterogeneity and inconsistency in mixed treatment comparisons: Application to stroke prevention treatments in individuals with non-rheumatic atrial fibrillation. Stat Med 2009;28(14):1861–81. doi: 10.1002/sim.3594
Dias S, Welton NJ, Sutton AJ, Caldwell DM, Lu G, Ades AE. Evidence synthesis for decision making 4: inconsistency in networks of evidence based on randomized controlled trials. Med Decis Making 2013a;33(5):641–56. doi: 10.1177/0272989X12455847
Dias S, Sutton AJ, Welton NJ, Ades AE. Evidence synthesis for decision making 3: heterogeneity–subgroups, meta-regression, bias, and bias-adjustment. Med Decis Making 2013b;33(5):618–40. doi: 10.1177/0272989X13485157
Dias S, Sutton AJ, Ades AE, Welton NJ. Evidence synthesis for decision making 2: a generalized linear modeling framework for pairwise and network meta-analysis of randomized controlled trials. Med Decis Making 2013c;33(5):607–17. doi: 10.1177/0272989X12458724
Dias S, Welton NJ, Sutton AJ, Ades AE. Evidence synthesis for decision making 5: the baseline natural history model. Med Decis Making 2013d;33(5):657–70. doi: 10.1177/0272989X13485155
Dias S, Welton NJ, Caldwell DM, Ades AE. Checking consistency in mixed treatment comparison meta-analysis. Stat Med 2010;29(7-8):932–44. doi: 10.1002/sim.3767
Gelman, A, Rubin, DB. Inference from iterative simulation using multiple sequences. Stat Sci 1992;7(4):457–72. doi: 10.1214/ss/1177011136
Gower JC. A General Coefficient of Similarity and Some of Its Properties. Biometrics 1971;27(4):857–71. http://dx.doi.org/10.2307/2528823
Hutton B, Salanti G, Caldwell DM, Chaimani A, Schmid CH, Cameron C, et al. The PRISMA extension statement for reporting of systematic reviews incorporating network meta-analyses of health care interventions: checklist and explanations. Ann Intern Med 2015;162(11):777–84. doi: 10.7326/M14-2385
Ruecker G, Schwarzer G. Ranking treatments in frequentist network meta-analysis works without resampling methods. BMC Med Res Methodol 2015;15:58. doi: 10.1186/s12874-015-0060-8
Salanti G, Ades AE, Ioannidis JP. Graphical methods and numerical summaries for presenting results from multiple-treatment meta-analysis: an overview and tutorial. J Clin Epidemiol 2011;64(2):163–71. doi: 10.1016/j.jclinepi.2010.03.016
Spineli LM. A revised framework to evaluate the consistency assumption globally in a network of interventions. Med Decis Making 2021. doi: 10.1177/0272989X211068005
Spineli LM, Kalyvas C, Papadimitropoulou K. Quantifying the robustness of primary analysis results: A case study on missing outcome data in pairwise and network meta-analysis. Res Synth Methods 2021a;12(4):475–90. doi: 10.1002/jrsm.1478
Spineli LM, Kalyvas C, Papadimitropoulou K. Continuous(ly) missing outcome data in network meta-analysis: a one-stage pattern-mixture model approach. Stat Methods Med Res 2021b;30(4):958–75. doi: 10.1177/0962280220983544
Spineli LM. An empirical comparison of Bayesian modelling strategies for missing binary outcome data in network meta-analysis. BMC Med Res Methodol 2019;19(1):86. doi: 10.1186/s12874-019-0731-y
van Valkenhoef G, Dias S, Ades AE, Welton NJ. Automated generation of node-splitting models for assessment of inconsistency in network meta-analysis. Res Synth Methods 2016;7(1):80–93. doi: 10.1002/jrsm.1167
Creates the enhanced balloon plot for the summary effect size and
between-trial standard deviation, tau, under different scenarios
about the missingness parameter for a pair of interventions.
balloon_plot uses the scenarios considered in
run_sensitivity.
balloon_plot(sens, compar, drug_names)balloon_plot(sens, compar, drug_names)
sens |
An object of S3 class |
compar |
A character vector with two elements indicating the pairwise comparison of interest. The first element refers to the 'experimental' and the second element to the 'control' intervention of the comparison. |
drug_names |
A vector of labels with the name of the interventions
in the order they appear in the argument |
For the plot_effect_size of the selected pairwise comparison,
the different colours and sizes of the bubbles reflect the
posterior standard deviation and the posterior mean, respectively.
A colour key appears below the plot. The size of the bubble is proportional
to the corresponding posterior mean.
Crossed bubbles indicate scenarios with conclusive evidence (the
95% credible interval excludes the null value), and filled bubbles
indicate scenarios with inconclusive evidence (the 95% credible interval
includes the null value). The missing-at-random assumption (primary
analysis) is labeled in a white frame.
Both axes illustrate the scenarios as specified in the argument
mean_scenarios of the run_sensitivity:
the x-axis refers to the 'experimental' intervention, and the y-axis refers
to the 'control' intervention.
The same enhanced balloon plot is created for tau (plot_tau).
However, filled bubbles indicate low statistical heterogeneity
(the posterior median of tau is lower than the median of the
prior distribution for the heterogeneity parameter),
and crossed bubbles indicate considerable statistical heterogeneity
(the posterior median of tau exceeds the median of the prior
distribution for the heterogeneity parameter).
balloon_plot can be used only when missing participant
outcome data have been extracted for at least one trial.
Otherwise, the execution of the function will be stopped and an error
message will be printed on the R console.
balloon_plot returns two enhanced balloon plots for one
comparison (see 'Details'):
plot_effect_size |
The enhanced balloon plot for the
summary effect size (according to the argument |
plot_tau |
The enhanced balloon plot for tau. When the
fixed-effect model has been performed in |
Loukia M. Spineli
Spineli LM, Kalyvas C, Papadimitropoulou K. Quantifying the robustness of primary analysis results: A case study on missing outcome data in pairwise and network meta-analysis. Res Synth Methods 2021;12(4):475–490. doi: https://doi.org/10.1002/jrsm.1478
data("pma.taylor2004") # Read results from 'run_sensitivity' (using the default arguments) res_sens <- readRDS(system.file('extdata/res_sens_taylor.rds', package = 'rnmamod')) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "inositol") # Create the enhanced balloon plot for 'inositol versus placebo' balloon_plot(sens = res_sens, compar = c("inositol", "placebo"), drug_names = interv_names)data("pma.taylor2004") # Read results from 'run_sensitivity' (using the default arguments) res_sens <- readRDS(system.file('extdata/res_sens_taylor.rds', package = 'rnmamod')) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "inositol") # Create the enhanced balloon plot for 'inositol versus placebo' balloon_plot(sens = res_sens, compar = c("inositol", "placebo"), drug_names = interv_names)
To process the elements in the argument base_risk of the
run_model function. It also runs the hierarchical baseline
model, separately from the relative effects model as described in
Dias et al. (2018) and Dias et al. (2013b). The output is to be passed to
run_model and run_metareg to obtain the
(unadjusted and adjusted, respectively) absolute risks for each
intervention in the dataset.
baseline_model(base_risk, n_chains, n_iter, n_burnin, n_thin)baseline_model(base_risk, n_chains, n_iter, n_burnin, n_thin)
base_risk |
A scalar, a vector of length three with elements sorted in
ascending order, or a matrix with two columns and number of rows equal to
the number of relevant trials. In the case of a scalar or vector, the
elements should be in the interval (0, 1). For the matrix, the first column
refers to the number of events and the second column to the sample size of
the trials comprising the dataset for the baseline model. See 'Details' in
|
n_chains |
Positive integer specifying the number of chains for the
MCMC sampling; an argument of the |
n_iter |
Positive integer specifying the number of Markov chains for the
MCMC sampling; an argument of the |
n_burnin |
Positive integer specifying the number of iterations to
discard at the beginning of the MCMC sampling; an argument of the
|
n_thin |
Positive integer specifying the thinning rate for the
MCMC sampling; an argument of the |
If base_risk is a matrix, baseline_model creates the
hierarchical baseline model in the JAGS dialect of the BUGS language.
The output of this function (see 'Value') constitutes the
posterior mean and precision of the predicted logit of an event for the
selected reference intervention and it is plugged in the WinBUGS code for
the relative effects model (Dias et al., 2013a) via the
prepare_model function. Following (Dias et al., 2013a), a
uniform prior distribution is assigned on the between-trial standard
deviation with upper and lower limit equal to 0 and 5, respectively.
When base_risk is a matrix, the function also returns a forest plot
with the estimated trial-specific probability of an event and 95% credible
intervals (the random effects) alongside the corresponding observed
probability of an event for the selected reference intervention. A grey
rectangular illustrates the summary mean and 95% credible interval of the
random effects.
When base_risk is a matrix (predicted baseline), the model is
updated until convergence using the autojags
function of the R-package
R2jags with 2 updates and
number of iterations and thinning equal to n_iter and n_thin,
respectively.
When base_risk is scalar (fixed baseline), the function
returns the user-defined baseline for the selected reference intervention
in the logit scale. When base_risk is a vector (random baseline),
the function returns a vector with the calculated logit of an event for the
selected reference intervention and its precision. Finally, when
base_risk is a matrix (predicted baseline), the function returns the
following elements:
ref_base |
A vector with the posterior mean and precision of the
predicted logit of an event for the selected reference intervention.
This vector is be passed to |
figure |
A forest plot on the trial-specific observed and estimated baseline risk. See 'Details'. |
table_baseline |
A table with the posterior and predictive distribution of the summary baseline mean and the posterior distribution of the between-trial standard deviation in baseline. All results are in the logit scale. |
Loukia M. Spineli
Dias S, Ades AE, Welton NJ, Jansen JP, Sutton AJ. Network Meta-Analysis for Decision Making. Chichester (UK): Wiley; 2018.
Dias S, Sutton AJ, Ades AE, Welton NJ. Evidence synthesis for decision making 2: a generalized linear modeling framework for pairwise and network meta-analysis of randomized controlled trials. Med Decis Making 2013a;33(5):607–17. doi: 10.1177/0272989X12458724
Dias S, Welton NJ, Sutton AJ, Ades AE. Evidence synthesis for decision making 5: the baseline natural history model. Med Decis Making 2013b;33(5):657–70. doi: 10.1177/0272989X13485155
prepare_model,
autojags, jags,
run_metareg, run_model
This function facilitates creating the Bland-Altman plot on the posterior mean deviance contribution for two models using only three arguments.
bland_altman_plot(model1, model2, colour)bland_altman_plot(model1, model2, colour)
model1 |
A vector with the numeric values of the target model (for instance, the consistency model). |
model2 |
A vector with the numeric values of the reference model (for instance, the unrelated mean effects model). |
colour |
A string to define the colour of the data points in the plot. |
bland_altman_plot is integrated in ume_plot
to create the Bland-Altman plot on the posterior mean of deviance
under the consistency model (via run_model) and the
unrelated mean effects model (via run_ume).
A uniform scattering of the data points within the 95% limits of agreement and average bias close to 0 indicate that the compared models have a good agreement. Data points positioned above or below the 95% limits of agreement correspond to trials that contribute to the poor fit of the consistency model or unrelated mean effects model, respectively.
bland_altman_plot can be used to compare the following models
regarding deviance contribution:
the consistency model (via run_model) with the
unrelated effect means model (via run_ume);
the network meta-analysis model (via run_model) with
the network meta-analysis model (via run_metareg).
Bland-Altman plot on the posterior mean deviance contribution of the
individual data points under model 1 and model 2.
Each data point corresponds to a trial-arm indicated by a pair of numbers.
The first number refers to the position of the trial in the dataset,
and the second arm refers to the corresponding trial-arm (see 'Arguments'
and 'Value' in data_preparation).
The plot also displays the average bias and the 95% limits of agreement
with horizontal solid black lines.
Loukia M. Spineli
Bland JM, Altman DG. Measuring agreement in method comparison studies. Stat Methods Med Res 1999;8:135–60. doi: 10.1177/096228029900800204
data_preparation, run_metareg,
run_model, run_ume, ume_plot
comp_clustering hosts a toolkit of functions that facilitates
conducting, visualising and evaluating hierarchical agglomerative of
observed comparisons of interventions for a specific network and set of
characteristics that act as effect modifiers. It also calculates the
non-statistical heterogeneity within-comparisons and between-comparisons
using the dissimilarities among all trials of the network.
comp_clustering( input, drug_names, threshold, informative = TRUE, ranged_values = FALSE, optimal_clusters, get_plots = "none", label_size = 4, title_size = 14, axis_title_size = 14, axis_text_size = 14, axis_x_text_angle = 0, legend_text_size = 13, str_wrap_width = 10 )comp_clustering( input, drug_names, threshold, informative = TRUE, ranged_values = FALSE, optimal_clusters, get_plots = "none", label_size = 4, title_size = 14, axis_title_size = 14, axis_text_size = 14, axis_x_text_angle = 0, legend_text_size = 13, str_wrap_width = 10 )
input |
A data-frame in the long arm-based format. Two-arm trials occupy one row in the data-frame. Multi-arm trials occupy as many rows as the number of possible comparisons among the interventions. The first three columns refer to the trial name, first and second arm of the comparison, respectively. The remaining columns refer to summary characteristics. See 'Details' for the specification of the columns. |
drug_names |
A vector of labels with the name of the interventions
in the order they have been defined in the argument |
threshold |
A positive scalar to indicate the cut-off of low dissimilarity of two comparisons. The value must be low. |
informative |
Logical with |
ranged_values |
Whether to use a colour scale when creating the
heatmap of within-comparison and between-comparison dissimilarities
( |
optimal_clusters |
A positive integer for the optimal number of clusters, ideally, decided after inspecting the profile plot with average silhouette widths for a range of clusters, and the dendrogram. The user must define the value. It takes values from two to the number of trials minus one. |
get_plots |
Logical with values |
label_size |
A positive integer for the font size of labels in the
violin plot for the study dissimilarities per comparison and comparison
between comparisons. |
title_size |
A positive integer for the font size of legend title in
the stacked barplot on the percentage studies of each comparison found in
the clusters. |
axis_title_size |
A positive integer for the font size of axis title in
the violin plot for the study dissimilarities per comparison and comparison
between comparisons, and the barplot of percentage trials per comparison
and cluster. |
axis_text_size |
A positive integer for the font size of axis text in
the violin plot for the study dissimilarities per comparison and comparison
between comparisons, the heatmap of comparison dissimilarity, and the
barplot of percentage trials per comparison and cluster.
|
axis_x_text_angle |
A positive integer for the angle of axis text in
the violin plot for the study dissimilarities per comparison and comparison
between comparisons. |
legend_text_size |
A positive integer for the font size of legend text
in the barplot of percentage trials per comparison and cluster.
|
str_wrap_width |
A positive integer for wrapping the axis labels in the
the violin plot for the study dissimilarities per comparison between
comparisons. |
The correct type mode of columns in input must be ensured to use
the function comp_clustering. The first three columns referring to
the trial name, first and second arm of the comparison, respectively, must
be character. The remaining columns referring to the
characteristics must be double or integer depending on
whether the corresponding characteristic refers to a quantitative or
qualitative variable. The type mode of each column is assessed by
comp_clustering using the base function typeof. Note that
comp_clustering invites unordered and ordered variables; for the
latter, add the argument ordered = TRUE in the base function
factor().
The interventions should be sorted in an ascending order of their
identifier number within the trials so that the first intervention column
(second column in input) is the control arm for every pairwise
comparison. This is important to ensure consistency in the intervention
order within the comparisons obtained from the other related functions.
comp_clustering excludes from the dataset the following type of
characteristics: (i) completely missing characteristics and
(ii) characteristics with missing values in all but one studies for at
least one non-single-stufy comparison. Then it proceeds with the clustering
process.
The cophenetic correlation coefficient is calculated using the
cophenetic function alongside the
hclust function for selected linkage methods.
comp_clustering can be used only for a network with at least three
comparisons. Otherwise, the execution of the function will be stopped and
an error message will be printed on the R console.
Initially, comp_clustering prints on the console the following
messages: the number of observed comparisons (and number of single-study
comparisons, if any); the number of dropped characteristics due to many
missing data; the maximum value of the cophenetic correlation coefficient;
and the optimal linkage method selected based on the cophenetic correlation
coefficient. Then, the function returns the following list of elements:
Trials_diss_table |
A lower off-diagonal matrix of 'dist' class with the Gower dissimilarities of all pairs of studies in the network. |
Comparisons_diss_table |
A lower off-diagonal matrix of 'dist' class with the within-comparison dissimilarities at the main diagonal and the between-comparison dissimilarities of all pairs of observed intervention comparisons at the off-diagonal elements. |
Total_dissimilarity |
A data-frame on the observed comparisons and comparisons between comparisons, alongside the corresponding within-comparison and between-comparisons dissimilarity. The data-frame has been sorted in decreasing within each dissimilarity 'type'. |
Types_used |
A data-frame with type mode (i.e., double or integer) of each characteristic. |
Total_missing |
The percentage of missing cases in the dataset, calculated as the ratio of total missing cases to the product of the number of studies with the number of characteristics. |
Cluster_comp |
A data-frame on the studies and the cluster they
belong (based on the argument |
Table_average_silhouette_width |
A data-frame with the average silhouette width for a range of 2 to P-1 trials, with P being the number trials. |
Table_cophenetic_coefficient |
A data-frame on the cophenetic correlation coefficient for eight linkage methods (Ward's two versions, single, complete, average, Mcquitty, median and centroid). The data-frame has been sorted in decreasing order of the cophenetic correlation coefficient. |
Optimal_link |
The optimal linkage method (ward.D, ward.D2, single, complete, average, mcquitty, median, or centroid) based on the cophenetic correlation coefficient. |
If get_plots = FALSE only the list of elements mentioned above is
returned. If get_plots = TRUE, comp_clustering returns a
series of plots in addition to the list of elements mentioned above:
Within_comparison_dissimilarity |
A violin plot with integrated box plots and dots on the study dissimilarities per observed comparison (x-axis). Violins are sorted in descending order of the within-comparison dissimilarities (blue point). |
Between_comparison_dissimilarity |
A violin plot with integrated box plots and dots on the study dissimilarities per comparison between comparisons (x-axis). Violins are sorted in descending order of the between-comparison dissimilarities (blue point). |
Dissimilarity_heatmap |
A heatmap on within-comparison and
between-comparison dissimilarities when ( |
Profile_plot |
A profile plot on the average silhouette width for a range of 2 to P-1 clusters, with P being the number of trials. The candidate optimal number of clusters is indicated with a red point directly on the line. |
Silhouette_width_plot |
A silhouette plot illustrating the silhouette
width for each trial, with the trials sorted in decreasing order within the
cluster they belong. This output is obtained by calling the
|
Barplot_comparisons_cluster |
As stacked barplot on the percentage
trials of each comparison found in the clusters (based on the argument
|
Loukia M. Spineli
Gower J. General Coefficient of Similarity and Some of Its Properties. Biometrics 1971;27(4):857–71. doi: 10.2307/2528823
Sokal R, Rohlf F. The Comparison of Dendrograms by Objective Methods. Int Assoc Plant Taxon 1962;11(2):33–40. doi: 10.2307/1217208
Handl J, Knowles J, Kell DB. Computational cluster validation in post-genomic data analysis. Biometrics 2005;21(15):3201–120. doi: 10.1093/bioinformatics/bti517
Rousseeuw PJ. Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. J Comput Appl Math 1987;20:53–65.
cophenetic,
hclust, internal_measures_plot,
silhouette,
str_wrap
# Fictional dataset data_set <- data.frame(Trial_name = as.character(1:7), arm1 = c("1", "1", "1", "1", "1", "2", "2"), arm2 = c("2", "2", "2", "3", "3", "3", "3"), sample = c(140, 145, 150, 40, 45, 75, 80), age = c(18, 18, 18, 48, 48, 35, 35), blinding = factor(c("yes", "yes", "yes", "no", "no", "no", "no"))) # Obtain comparison dissimilarities (informative = TRUE) comp_clustering(input = data_set, drug_names = c("A", "B", "C"), threshold = 0.13, # General research setting informative = TRUE, get_plots = TRUE)# Fictional dataset data_set <- data.frame(Trial_name = as.character(1:7), arm1 = c("1", "1", "1", "1", "1", "2", "2"), arm2 = c("2", "2", "2", "3", "3", "3", "3"), sample = c(140, 145, 150, 40, 45, 75, 80), age = c(18, 18, 18, 48, 48, 35, 35), blinding = factor(c("yes", "yes", "yes", "no", "no", "no", "no"))) # Obtain comparison dissimilarities (informative = TRUE) comp_clustering(input = data_set, drug_names = c("A", "B", "C"), threshold = 0.13, # General research setting informative = TRUE, get_plots = TRUE)
data_preparation prepares the dataset in the proper format for
R2jags and returns a list of elements that run_model inherits
via the argument data.
data_preparation(data, measure)data_preparation(data, measure)
data |
A data-frame of the one-trial-per-row format with arm-level data.
See 'Format' in |
measure |
Character string indicating the effect measure. For a binary
outcome, the following can be considered: |
data_preparation prepares the data for the Bayesian analysis
(See 'Format' in run_model). data_preparation
creates the pseudo-data-frames m_new, I, and m_pseudo
that have the same dimensions with the element N. m_new takes
the zero value for the observed trial-arms with unreported missing
participant outcome data (i.e., m equals NA for the
corresponding trial-arms), the same value with m for the observed
trial-arms with reported missing participant outcome data, and NA
for the unobserved trial-arms. I is a dummy data-frame and takes the
value one for the observed trial-arms with reported missing participant
outcome data, the zero value for the observed trial-arms with unreported
missing participant outcome data (i.e., m_new equals zero for the
corresponding trial-arms), and NA for the unobserved trial-arms.
Thus, I indicates whether missing participant outcome data have been
collected for the observed trial-arms. If the user has not defined the
element m in data_preparation, m_new and I
take the zero value for all observed trial-arms to indicate that no missing
participant outcome data have been collected for the analysed outcome.
I and m_new are used from the following functions of the
package: run_model, run_metareg,
prepare_model, run_nodesplit,
prepare_nodesplit, run_ume,
prepare_ume, and run_sensitivity.
Lastly, m_pseudo is a variant of m_new: it takes the value -1
for the observed trial-arms with unreported missing participant outcome
data (i.e., m equals NA for the corresponding trial-arms),
the same value with m for the observed trial-arms with reported
missing participant outcome data, and NA for the unobserved
trial-arms. It is used in function heatmap_missing_network to
calculate and illustrate the percentage of missing participant outcome data
across the observed comparisons and interventions of the network and the
function heatmap_missing_dataset to illustrate the trial-arms
with unreported missing participant outcome data. All pseudo-data-frames
aim to retain the trials without information on missing participant outcome
data.
Furthermore, data_preparation sorts the interventions across
the arms of each trial in an ascending order and correspondingly the
remaining elements in data (See 'Format' in
run_model). data_preparation considers the first
column in t as being the control arm for every trial. Thus,
this sorting ensures that interventions with a lower identifier are
consistently treated as the control arm in each trial. This case is
relevant in non-star-shaped networks.
A list of data-frames on the following elements to be passed
to run_model:
pseudo_m |
A pseudo-data-frame with values -1 and m for the corresponding trial-arms with unreported and reported missing participant outcome data, respectively (see 'Details'). |
m |
The number of missing participant outcome data in each trial-arm (see 'Details'). |
N |
The number of randomised participants in each trial-arm. |
t |
The intervention identifier in each trial-arm. |
I |
A pseudo-data-frame that indicates whether missing participant outcome data have been reported or not for each observed trial-arm (see 'Details'). |
measure |
The effect measure for the analysed outcome. |
y0 |
The observed mean value of the outcome in each trial-arm, when the outcome is continuous. |
se0 |
The observed standard deviation of the outcome in each trial-arm, when the outcome is continuous. |
r |
The number of observed events of the outcome in each trial-arm, when the outcome is binary. |
Loukia M. Spineli
heatmap_missing_dataset,
heatmap_missing_network,
R2jags,
run_metareg, run_model,
run_nodesplit, run_sensitivity,
run_ume, prepare_model,
prepare_nodesplit, prepare_ume
dendro_heatmap creates a dendrogram alongside the heatmap of
Gower dissimilarities among the trials in the network for a specific
linkage method and number of clusters.
dendro_heatmap(input, label_size = 12, axis_text_size = 10)dendro_heatmap(input, label_size = 12, axis_text_size = 10)
input |
An object of S3 class |
label_size |
A positive integer for the font size of the heatmap
elements. |
axis_text_size |
A positive integer for the font size of row and column
names of the heatmap. |
dendro_heatmap uses the heatmaply
function of the R-package
heatmaply to create a
cluster heatmap for a selected linkage method and number of clusters. The
function uses different colours to indicate the clusters directly on the
dendrogram, specified using the R-package
dendextend. The names
of the leaves refer to the trials and corresponding pairwise comparison.
@details
The function inherits the linkage method and number of optimal clusters by
the comp_clustering function.
Remember: when using the comp_clustering function, inspect
the average silhouette width for a wide range of clusters to decide on the
optimal number of clusters.
Loukia M. Spineli
# Fictional dataset data_set <- data.frame(Trial_name = as.character(1:7), arm1 = c("1", "1", "1", "1", "1", "2", "2"), arm2 = c("2", "2", "2", "3", "3", "3", "3"), sample = c(140, 145, 150, 40, 45, 75, 80), age = c(18, 18, 18, 48, 48, 35, 35), blinding = factor(c("yes", "yes", "yes", "no", "no", "no", "no"))) # Apply hierarchical clustering (informative = FALSE) hier <- comp_clustering(input = data_set, drug_names = c("A", "B", "C"), threshold = 0.13, # General research setting informative = FALSE, optimal_clusters = 3, get_plots = TRUE) # Create the dendrogram with integrated heatmap dendro_heatmap(hier)# Fictional dataset data_set <- data.frame(Trial_name = as.character(1:7), arm1 = c("1", "1", "1", "1", "1", "2", "2"), arm2 = c("2", "2", "2", "3", "3", "3", "3"), sample = c(140, 145, 150, 40, 45, 75, 80), age = c(18, 18, 18, 48, 48, 35, 35), blinding = factor(c("yes", "yes", "yes", "no", "no", "no", "no"))) # Apply hierarchical clustering (informative = FALSE) hier <- comp_clustering(input = data_set, drug_names = c("A", "B", "C"), threshold = 0.13, # General research setting informative = FALSE, optimal_clusters = 3, get_plots = TRUE) # Create the dendrogram with integrated heatmap dendro_heatmap(hier)
Calculates the necessary elements to describe the evidence base for an outcome across the network, the interventions, and observed comparisons.
describe_network(data, drug_names, measure, save_xls)describe_network(data, drug_names, measure, save_xls)
data |
A data-frame of a one-trial-per-row format containing arm-level
data of each trial. See 'Format' in |
drug_names |
A vector of labels with the name of the interventions in
the order they appear in the argument |
measure |
Character string indicating the effect measure. For a binary
outcome, the following can be considered: |
save_xls |
Logical to indicate whether to export the tabulated results
to an 'xlsx' file (via the |
describe_network calls data_preparation to
facilitate the calculations.
Furthermore, describe_network exports the data-frames to separate
'xlsx' files (via the write_xlsx function
of the R-package
writexl) at the working
directory of the user.
describe_network returns the following data-frames that describe the
evidence base:
network_description |
The number of: interventions, possible comparisons, direct and indirect comparisons, number of trials in total, number of two-arm and multi-arm trials, number of randomised participants, and proportion of participants completing the trial (completers). When the outcome is binary, the number of trials with at least one zero event, and the number of trials with all zero events are also presented. |
table_interventions |
For each intervention, the number of trials, number of randomised participants, and proportion of completers. When the outcome is binary, the data-frame presents also the corresponding proportion of total observed events, the minimum, median and maximum proportion of observed events across the corresponding trials. |
table_comparisons |
Identical structure to |
Loukia M. Spineli
data_preparation, run_model
write_xlsx
distr_characteristics uses violin and bar plots to visualise the
distribution of each characteristic in the dataset either per comparison
or cluster of comparisons.
distr_characteristics( input, drug_names, rename_char = NULL, cluster = NULL, label_size = 4, title_size = 14, axis_title_size = 14, axis_text_size = 14, axis_x_text_angle = 0, legend_text_size = 13 )distr_characteristics( input, drug_names, rename_char = NULL, cluster = NULL, label_size = 4, title_size = 14, axis_title_size = 14, axis_text_size = 14, axis_x_text_angle = 0, legend_text_size = 13 )
input |
A data-frame in the long arm-based format. Two-arm trials occupy one row in the data-frame. Multi-arm trials occupy as many rows as the number of possible comparisons among the interventions. The first three columns refer to the trial name, first and second arm of the comparison (their identifier number), respectively. The remaining columns refer to summary characteristics. See 'Details' for specifying the columns. |
drug_names |
A vector of labels with the name of the interventions
in the order they appear in the argument |
rename_char |
A list of two elements: (i) a numeric vector with the
position of the characteristics in |
cluster |
An object of S3 class |
label_size |
A positive integer for the font size of labels in the
plots. |
title_size |
A positive integer for the font size of legend title in
the plots. |
axis_title_size |
A positive integer for the font size of axis title in
the plots. |
axis_text_size |
A positive integer for the font size of axis text in
the plots. |
axis_x_text_angle |
A positive integer for the angle of axis text in
the plots. |
legend_text_size |
A positive integer for the font size of legend text
in the plots. |
The correct type mode of columns in input must be ensured to use
the function distr_characteristics. The first three columns
referring to the trial name, first and second arm of the comparison,
respectively, must be character. The remaining columns referring
to the characteristics must be double or integer
depending on whether the corresponding characteristic refers to a
quantitative or qualitative variable. The type mode of each column is
assessed by distr_characteristics using the base function
typeof.
The interventions should be sorted in an ascending order of their
identifier number within the trials so that the first treatment column
(second column in input) is the control arm for every pairwise
comparison. This is important to ensure consistency in the order of
interventions within the comparisons obtained from the other related
functions.
distr_characteristics returns a list of plots using the proper plot
(violin or bar plot) for each characteristic. The size of the dots in the
violin plot (with amalgamated box plots and dots) are proportional to the
total sample size of the study: the large the sample size of the study, the
larger the size of the corresponding point.
Loukia M. Spineli
# Fictional dataset set.seed(13022024) data_set <- data.frame(Trial_name = as.character(1:(5 + 7 +2)), arm1 = rep(c("1", "2"), c(5 + 7, 2)), arm2 = rep(c("2", "3"), c(5, 7 + 2)), sample = as.numeric(sample(50:300, 5 + 7 + 2)), age = as.numeric(sample(18:50, 5 + 7 + 2)), blinding = factor(rep(c("yes", "no", "yes"), c(5, 7, 2)))) distr_characteristics(input = data_set, drug_names = c("A", "B", "C"))# Fictional dataset set.seed(13022024) data_set <- data.frame(Trial_name = as.character(1:(5 + 7 +2)), arm1 = rep(c("1", "2"), c(5 + 7, 2)), arm2 = rep(c("2", "3"), c(5, 7 + 2)), sample = as.numeric(sample(50:300, 5 + 7 + 2)), age = as.numeric(sample(18:50, 5 + 7 + 2)), blinding = factor(rep(c("yes", "no", "yes"), c(5, 7, 2)))) distr_characteristics(input = data_set, drug_names = c("A", "B", "C"))
Provides a forest plot with the posterior median and 95% credible and prediction intervals for comparisons with the selected intervention (comparator) in the network, and a forest plot with the corresponding SUCRA values.
forestplot(full, compar, drug_names)forestplot(full, compar, drug_names)
full |
|
compar |
A character to indicate the comparator intervention. It must be
any name found in |
drug_names |
A vector of labels with the name of the interventions in
the order they appear in the argument |
The y-axis of the forest plot on effect sizes displays the
labels of the interventions in the network; the selected intervention that
comprises the compar argument is annotated in the plot with the
label 'Comparator intervention'.
For each comparison with the selected intervention, the 95% credible and
prediction intervals are displayed as overlapping lines in different
colours. The corresponding numerical results are displayed above each line:
95% credible intervals are found in parentheses, and 95% predictive
intervals are found in brackets. Odds ratios, relative risks, and ratio of
means are reported in the original scale after exponentiation of the
logarithmic scale.
The y-axis for the forest plot on SUCRA values displays the labels of the interventions in the network. The corresponding numerical results are displayed above each line. Three coloured rectangles appear in the forest plot: a red rectangle for SUCRA values up to 50%, a yellow rectangular for SUCRA values between 50% and 80%, and a green rectangle for SUCRA values over 80%. Interventions falling at the green area are considered as the highest ranked interventions, whilst interventions falling at the red area are considered as the lowest ranked interventions.
In both plots, the interventions are sorted in descending order of their SUCRA values.
forestplot can be used only for a network of interventions.
Otherwise, the execution of the function will be stopped and an error
message will be printed on the R console.
A panel of two forest plots: (1) a forest plot on the effect estimates and predictions of comparisons with the selected intervention in the network, and (2) a forest plot on the posterior mean and 95% credible interval of SUCRA values of the interventions (Salanti et al., 2011).
Loukia M. Spineli
Salanti G, Ades AE, Ioannidis JP. Graphical methods and numerical summaries for presenting results from multiple-treatment meta-analysis: an overview and tutorial. J Clin Epidemiol 2011;64(2):163–71. doi: 10.1016/j.jclinepi.2010.03.016
data("nma.liu2013") # Show the first six trials of the dataset (one-trial-per-row format) head(nma.liu2013) # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_liu.rds', package = 'rnmamod')) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "pramipexole", "serotonin-norepinephrine reuptake inhibitor", "serotonin reuptake inhibitor", "tricyclic antidepressant", "pergolide") # Create the forest plot forestplot(full = res, compar = "placebo", drug_names = interv_names)data("nma.liu2013") # Show the first six trials of the dataset (one-trial-per-row format) head(nma.liu2013) # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_liu.rds', package = 'rnmamod')) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "pramipexole", "serotonin-norepinephrine reuptake inhibitor", "serotonin reuptake inhibitor", "tricyclic antidepressant", "pergolide") # Create the forest plot forestplot(full = res, compar = "placebo", drug_names = interv_names)
Provides a forest plot with the posterior median and 95% credible and prediction intervals for comparisons with the selected intervention (comparator) in the network under the network meta-analysis and network meta-regression for a specified level or value of the investigated covariate, and a forest plot with the corresponding SUCRA values.
forestplot_metareg(full, reg, compar, cov_value, drug_names)forestplot_metareg(full, reg, compar, cov_value, drug_names)
full |
|
reg |
An object of S3 class |
compar |
A character to indicate the comparator intervention. It must
be any name found in |
cov_value |
A list of two elements in the following order: a number
for the covariate value of interest (see 'Arguments' in
|
drug_names |
A vector of labels with the name of the interventions in
the order they appear in the argument |
The y-axis of the forest plot on effect sizes displays the
labels of the interventions in the network; the selected intervention that
comprises the compar argument is annotated in the plot with the
label 'Comparator intervention'.
For each comparison with the selected intervention, the 95% credible and
prediction intervals are displayed as overlapping lines. Black lines refer
to estimation under both analyses. Green and red lines refer to prediction
under network meta-analysis and network meta-regression, respectively. The
corresponding numerical results are displayed above each line:
95% credible intervals are found in parentheses, and 95% predictive
intervals are found in brackets. Odds ratios, relative risks, and ratio of
means are reported in the original scale after exponentiation of the
logarithmic scale.
The y-axis for the forest plot on SUCRA values displays the labels of the interventions in the network. The corresponding numerical results are displayed above each line. Three coloured rectangles appear in the forest plot: a red rectangle for SUCRA values up to 50%, a yellow rectangular for SUCRA values between 50% and 80%, and a green rectangle for SUCRA values over 80%. Interventions falling at the green area are considered as the highest ranked interventions, whilst interventions falling at the red area are considered as the lowest ranked interventions.
In both plots, the interventions are sorted in the descending order of their SUCRA values based on the network meta-analysis.
To obtain the posterior distribution of SUCRAs under the network meta-regression for a specified level or value of the investigated covariate, a two-step procedured is followed. First, the posterior median and standard deviation of the basic parameters and corresponding beta coefficients are considered to calculate the meadin and standard deviation of the basic parameters at the selected level or value of the investigated covariate: d + beta * cov_value. Then, these calculated values are fed into the BUGS code to get the posterior distribution of SUCRA. The progress of the simulation appears on the R console.
forestplot_metareg is integrated in metareg_plot.
forestplot_metareg can be used only for a network of interventions.
In the case of two interventions, the execution of the function will be
stopped and an error message will be printed on the R console.
A panel of two forest plots: (1) a forest plot on the effect estimates and predictions of comparisons with the selected intervention in the network under the network meta-analysis and network meta-regression for a specified level or value of the investigated covariate, and (2) a forest plot on the posterior mean and 95% credible interval of SUCRA values of the interventions (Salanti et al., 2011).
Loukia M. Spineli
Salanti G, Ades AE, Ioannidis JP. Graphical methods and numerical summaries for presenting results from multiple-treatment meta-analysis: an overview and tutorial. J Clin Epidemiol 2011;64(2):163–71. doi:10.1016/j.jclinepi.2010.03.016
metareg_plot, run_metareg,
run_model
gower_distance calculate the Gower's dissimilarity coefficient for
all pairs of trials included in a network of interventions, considering
several characteristics measured at trial level.
It takes values from 0 to 1, with 0 implying complete similarity and 1
complete dissimilarity.
gower_distance(input)gower_distance(input)
input |
A data-frame in the long arm-based format. Two-arm trials occupy one row in the data-frame. Multi-arm trials occupy as many rows as the number of possible comparisons among the interventions. The first two columns refer to the trial name, and the pairwise comparison, respectively. The remaining columns refer to summary characteristics. See 'Details' for the specification of the columns. |
The correct type mode of columns in input must be ensured to use
the function gower_distance. The first two columns referring to
the trial name, and pairwise comparison, respectively, must
be character. The remaining columns referring to the
characteristics must be double or integer depending on
whether the corresponding characteristic refers to a quantitative or
qualitative variable. The type mode of each column is assessed by
gower_distance using the base function typeof. Note that
gower_distance invites unordered and ordered variables; for the
latter, add the argument ordered = TRUE in the base function
factor().
gower_distance is integrated in the function
comp_clustering.
gower_distance returns the following list of elements:
Dissimilarity_table |
A lower off-diagonal matrix of 'dist' class with the dissimilarities of all pairs of trials. |
Types_used |
A data-frame with type mode (i.e., double or integer) of each characteristic. |
Total_missing |
The percentage of missing cases in the comparison, calculated as the ratio of total missing cases to the product of the number of studies with the number of characteristics. |
Loukia M. Spineli
Gower J. General Coefficient of Similarity and Some of Its Properties. Biometrics 1971;27(4):857–71. doi: 10.2307/2528823
Illustrates the proportion of missing participants and the associated risk of bias in each arm of every trial in the dataset.
heatmap_missing_dataset(data, trial_names, drug_names)heatmap_missing_dataset(data, trial_names, drug_names)
data |
A data-frame of a one-trial-per-row format containing arm-level
data of each trial. See 'Format' in |
trial_names |
A vector of labels with the name of the trials in the
order they appear in the argument |
drug_names |
A vector of labels with the name of the interventions in
the order they appear in the argument |
When the number of missing participants has not been extracted for any arm of the trials, the execution of the function will be stopped and an error message will be printed on the R console.
When there are more than 80 trials, the value on the proportion of missing participants will not appear on the heatmap. This is because the number on the cells will not be distinguishable.
A heatmap presenting the proportion of missing participants in each trial-arm of the dataset. The columns and the rows of the heatmap correspond to the interventions and trials, respectively. The 'five-and-twenty' rule of Sackett and colleagues (1997) is used to characterise the proportion of missing participants as being associated with low (up to 5%), moderate (more than 5% and up to 20%), and high risk of bias (more than 20%). Low, moderate, and high risk of bias due to missing participants are indicated using green, orange, and red colour, respectively. The function is also applicable for a pairwise meta-analysis. If missing participants have not been reported for a trial-arm, the corresponding cell is indicated in grey.
Loukia M. Spineli
Sackett DL, Richardson WS, Rosenberg WM, Haynes RB. Evidence-based medicine: how to practice and teach EBM. New York: Churchill Livingstone 1997. ISBN: 0-443-05686-2.
data("nma.schwingshackl2014") # Return the first six trials of the dataset head(nma.schwingshackl2014) # The names of the interventions in the order they appear in the dataset interv_names <- c("aerobic", "resistance", "combined training") # Create the heatmap heatmap_missing_dataset(data = nma.schwingshackl2014, trial_names = nma.schwingshackl2014$study, drug_names = interv_names)data("nma.schwingshackl2014") # Return the first six trials of the dataset head(nma.schwingshackl2014) # The names of the interventions in the order they appear in the dataset interv_names <- c("aerobic", "resistance", "combined training") # Create the heatmap heatmap_missing_dataset(data = nma.schwingshackl2014, trial_names = nma.schwingshackl2014$study, drug_names = interv_names)
Illustrates the distribution of missing participants and the associated risk of bias for each intervention and observed comparison in the network.
heatmap_missing_network(data, drug_names)heatmap_missing_network(data, drug_names)
data |
A data-frame of a one-trial-per-row format containing arm-level
data of each trial. See 'Format' in |
drug_names |
A vector of labels with the name of the interventions in
the order they appear in the argument |
A heatmap with the proportion of missing participants in each intervention and observed comparison in the network. Each cell annotates the median, minimum and maximum (the latter two in parenthesis) proportion of missing participants across the corresponding trials. The proportion of missing participants in each intervention and observed comparison are depicted in the main diagonal and lower off-diagonal with white and black colour, respectively. The pairwise comparisons are read from left to right.
The 'five-and-twenty' rule of Sackett and colleagues (1997) is used to characterise the median proportion of missing participants as being associated with low (up to 5%), moderate (more than 5% and up to 20%), and high risk of bias (more than 20%). Low, moderate, and high risk of bias associated with missing participants is indicated using green, orange, and red colour, respectively. If missing participants have not been reported for an intervention or comparison, the corresponding cell is indicated in grey.
The summary statistics (median, minimum and maximum) for each intervention (main diagonal; white font) result from calculating the proportion of missing participants in each arm of every trial and then summarising across the corresponding trial-arms. Similarly, the summary statistics for each observed comparison (lower off-diagonal; black font) result from calculating the proportion of total missing participants in each trial and then summarising across the corresponding trials.
heatmap_missing_network can be used only for a network of
interventions. Otherwise, the execution of the function will be stopped and
an error message will be printed on the R console. Likewise, when the
number of missing participants has not been extracted for any arm of the
trials.
Loukia M. Spineli
Sackett DL, Richardson WS, Rosenberg WM, Haynes RB. Evidence-based medicine: how to practice and teach EBM. New York: Churchill Livingstone 1997. ISBN: 0-443-05686-2.
data("nma.stowe2011") # Return the first six trials of the dataset head(nma.stowe2011) # The names of the interventions in the order they appear in the dataset interv_names <- c("PBO+LD", "DA+LD", "COMTI+LD", "MAOBI+LD") # Create the heatmap heatmap_missing_network(data = nma.stowe2011, drug_names = interv_names)data("nma.stowe2011") # Return the first six trials of the dataset head(nma.stowe2011) # The names of the interventions in the order they appear in the dataset interv_names <- c("PBO+LD", "DA+LD", "COMTI+LD", "MAOBI+LD") # Create the heatmap heatmap_missing_network(data = nma.stowe2011, drug_names = interv_names)
Facilitates the detection of comparisons that are associated with a lack of robustness in the context of a sensitivity analysis.
heatmap_robustness(robust, drug_names)heatmap_robustness(robust, drug_names)
robust |
An object of S3 class |
drug_names |
A vector of labels with the name of the interventions in
the order they appear in the argument |
The heatmap illustrates the robustness index for each possible
pairwise comparison in the network. The pairwise comparisons are read from
left to right. Comparisons highlighted with green or red colour imply
robust or frail conclusions for the primary analysis, respectively.
This corresponds to robustness index below or at least the selected
threshold of robustness. heatmap_robustness inherits the threshold
of robustness selected in the robustness_index or
robustness_index_user function.
The robustness index of each pairwise comparison also appears in the
corresponding cell.
When there is at least one comparison with frail conclusions, the primary
analysis results may be questionable for the whole network
(Spineli et al., 2021).
heatmap_robustness is not restricted to the sensitivity
analysis concerning the impact of missing participant outcome data.
heatmap_robustness can be used only for a network of interventions.
Otherwise, the execution of the function will be stopped and an
error message will be printed on the R console.
heatmap_robustness first prints on the R console a message on
the threshold of robustness determined by the user in
robustness_index and robustness_index_user.
Then, it returns a lower triangular heatmap matrix with the robustness
index value of all possible pairwise comparisons.
Loukia M. Spineli
Spineli LM, Kalyvas C, Papadimitropoulou K. Quantifying the robustness of primary analysis results: A case study on missing outcome data in pairwise and network meta-analysis. Res Synth Methods 2021;12(4):475–90. doi: 10.1002/jrsm.1478
robustness_index, robustness_index_user,
run_model
data("nma.baker2009") # Read results from 'run_sensitivity' (using the default arguments) res_sens <- readRDS(system.file('extdata/res_sens_baker.rds', package = 'rnmamod')) # Calculate the robustness index robust <- robustness_index(sens = res_sens, threshold = 0.28) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "budesonide", "budesonide plus formoterol", "fluticasone", "fluticasone plus salmeterol", "formoterol", "salmeterol", "tiotropium") # Create the heatmap of robustness heatmap_robustness(robust = robust, drug_names = interv_names)data("nma.baker2009") # Read results from 'run_sensitivity' (using the default arguments) res_sens <- readRDS(system.file('extdata/res_sens_baker.rds', package = 'rnmamod')) # Calculate the robustness index robust <- robustness_index(sens = res_sens, threshold = 0.28) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "budesonide", "budesonide plus formoterol", "fluticasone", "fluticasone plus salmeterol", "formoterol", "salmeterol", "tiotropium") # Create the heatmap of robustness heatmap_robustness(robust = robust, drug_names = interv_names)
Generates the prior distribution (weakly informative or empirically-based)
for the heterogeneity parameter.
run_model inherits heterogeneity_param_prior via the
argument heter_prior.
heterogeneity_param_prior(measure, model, heter_prior)heterogeneity_param_prior(measure, model, heter_prior)
measure |
Character string indicating the effect measure. For a binary
outcome, the following can be considered: |
model |
Character string indicating the analysis model with values
|
heter_prior |
A list of three elements with the following order:
1) a character string indicating the distribution with
(currently available) values |
The names of the (current) prior distributions follow the JAGS syntax.
The mean and precision of "lognormal" and "logt" should align
with the values proposed by Turner et al. (2015) and Rhodes et al. (2015)
for the corresponding empirically-based prior distributions when
measure is "OR" or "SMD", respectively.
The users may refer to Dias et al. (2013) to determine the minimum and
maximum value of the uniform distribution, and to Friede et al. (2017)
to determine the mean and precision of the half-normal distribution.
When model is "FE", heterogeneity_param_prior
is ignored in run_model.
A value to be passed to run_model.
Loukia M. Spineli
Dias S, Sutton AJ, Ades AE, Welton NJ. Evidence synthesis for decision making 2: a generalized linear modeling framework for pairwise and network meta-analysis of randomized controlled trials. Med Decis Making 2013;33(5):607–17. doi: 10.1177/0272989X12458724
Friede T, Roever C, Wandel S, Neuenschwander B. Meta-analysis of two studies in the presence of heterogeneity with applications in rare diseases. Biom J 2017;59(4):658–71. doi: 10.1002/bimj.201500236
Rhodes KM, Turner RM, Higgins JP. Predictive distributions were developed for the extent of heterogeneity in meta-analyses of continuous outcome data. J Clin Epidemiol 2015;68(1):52–60. doi: 10.1016/j.jclinepi.2014.08.012
Turner RM, Jackson D, Wei Y, Thompson SG, Higgins JP. Predictive distributions for between-study heterogeneity and simple methods for their application in Bayesian meta-analysis. Stat Med 2015;34(6):984–98. doi: 10.1002/sim.6381
Detects the frail comparisons in multi-arm trials, that is, comparisons between non-baseline interventions not investigated in any two-arm trial in the network (Spineli, 2021). The 'original' model of Dias et al. (2013) omits the frail comparisons from the estimation process of the unrelated mean effects model. Consequently, their posterior distribution coincides with the prior distribution yielding implausible posterior standard deviations.
improved_ume(t, N, ns, na)improved_ume(t, N, ns, na)
t |
A data-frame of the one-trial-per-row format containing the
intervention identifier in each arm of every trial (see 'Details' below,
and 'Format' in |
N |
A data-frame of the one-trial-per-row format containing the number
of participants randomised to the assigned intervention in each arm of
every trial (see 'Details' below, and 'Format' in |
ns |
A scale parameter on the number trials. |
na |
A vector of length equal to |
improved_ume is integrated in run_ume and
calls the output of data_preparation after sorting the
rows so that multi-arm trials appear at the bottom of the dataset.
When there are no multi-arm trials or no frail comparisons in the network,
improved_ume returns only the element obs_comp
(see, 'Value').
The output of improved_ume is a list of elements that are
inherited by run_ume:
nbase_multi |
A scalar parameter on the number of frail comparisons. |
t1_bn |
A vector with numeric values referring to the first arm of each frail comparison. |
t2_bn |
A vector with numeric values referring to the second arm of each frail comparison. |
ref_base |
A scalar referring to the reference intervention for the subnetwork of interventions in frail comparisons. |
base |
A vector with numeric values referring to the baseline intervention of the multi-arm trials that contain the frail comparisons. |
obs_comp |
A data-frame that indicates how many two-arm and multi-arm trials have included each pairwise comparison observed in the network. |
Loukia M. Spineli
Dias S, Welton NJ, Sutton AJ, Caldwell DM, Lu G, Ades AE. Evidence synthesis for decision making 4: inconsistency in networks of evidence based on randomized controlled trials. Med Decis Making 2013;33(5):641–56. doi: 10.1177/0272989X12455847
Spineli LM. A revised framework to evaluate the consistency assumption globally in a network of interventions. Med Decis Making 2021. doi: 10.1177/0272989X211068005
data_preparation, run_model,
run_ume
internal_measures_plot currently prepares the table with the results
of the average silhouette width for a range of clusters, and visualises the
results using a profile plot.
internal_measures_plot( input, optimal_link, label_size = 4, axis_title_size = 14, axis_text_size = 14 )internal_measures_plot( input, optimal_link, label_size = 4, axis_title_size = 14, axis_text_size = 14 )
input |
An object of 'dist' class. It is a lower off-diagonal matrix with the dissimilarities of all pairs of comparisons. |
optimal_link |
A character string with values |
label_size |
A positive integer for the font size of labels in the
profile plot with the average silhouette width per candidate cluster.
|
axis_title_size |
A positive integer for the font size of axis title in
the profile plot with the average silhouette width per candidate cluster.
|
axis_text_size |
A positive integer for the font size of axis text in
the profile plot with the average silhouette width per candidate cluster.
|
internal_measures_plot also calls the function
comp_clustering to define the argument optimal_link to
create the silhouette plot for the selected number of clusters.
internal_measures_plot calls the
silhouette function in the R-package
cluster to obtain the
results on average silhouette for each candidate cluster.
internal_measures_plot is integrated in the function
comp_clustering.
internal_measures_plot currently returns the following list of
elements:
Table_internal_measures |
A data-frame of the average silhouette width for a range of 2 to P-1 clusters, with P being the number of trials |
Internal_measures_panel |
A profile plot on the average silhouette width for a range of 2 to P-1 clusters, with P being the number of trials The candidate optimal number of clusters is indicated with a red point directly on the line. |
Loukia M. Spineli
Handl J, Knowles J, Kell DB. Computational cluster validation in post-genomic data analysis. Biometrics 2005;21(15):3201–120. doi: 10.1093/bioinformatics/bti517
Rousseeuw PJ. Silhouettes: A graphical aid to the interpretation and validation of cluster analysis. J Comput Appl Math 1987;20:53–65.
Creates a panel of interval plots on the summary effect sizes under the consistency model and the unrelated mean effects model. The number of interval plots equals the number of pairwise comparisons observed in the network.
intervalplot_panel_ume(full, ume, drug_names)intervalplot_panel_ume(full, ume, drug_names)
full |
|
ume |
|
drug_names |
A vector of labels with the name of the interventions in
the order they appear in the argument |
intervalplot_panel_ume is integrated in the
ume_plot function. The consistency model and the unrelated
mean effects model are abbreviated in the y-axis as 'NMA model' and
'UME model', respectively. The intervals are highlighted with green, when
the corresponding summary effect sizes do not cross the vertical line of no
difference, and red otherwise. Grey panels refer to the frail comparisons
as detected by the improved_ume function (see 'Details' in
improved_ume).
For a binary outcome, when measure is "RR" (relative risk) or "RD"
(risk difference) in run_model, intervalplot_panel_ume
currently presents the results in the odds ratio scale.
A panel of interval plots on the posterior mean and 95% credible interval of the summary effect size under the consistency model and the improved unrelated mean effects model (Spineli, 2021) of all pairwise comparisons observed in the network.
Loukia M. Spineli
Spineli LM. A revised framework to evaluate the consistency assumption globally in a network of interventions. Med Decis Making 2021. doi: 10.1177/0272989X211068005
improved_ume run_model,
run_ume, ume_plot
Produces a barplot with the Kullback-Leibler divergence measure
from each re-analysis to the primary analysis for a pairwise
comparison. Currently, kld_barplot is used concerning the impact of
missing participant outcome data.
kld_barplot(robust, compar, drug_names)kld_barplot(robust, compar, drug_names)
robust |
An object of S3 class |
compar |
A character vector with two elements that indicates the pairwise comparison of interest. The first element refers to the 'experimental' intervention and the second element refers to the 'control' intervention of the comparison. |
drug_names |
A vector of labels with the name of the interventions in
the order they appear in the argument |
kld_barplot uses the scenarios inherited by
robustness_index via the run_sensitivity
function. The scenarios for the missingness parameter (see 'Details' in
run_sensitivity) in the compared interventions are split to
Extreme, Sceptical, and Optimistic following the
classification of Spineli et al. (2021). In each class, bars will green,
orange, and red colour refer to scenarios without distance, less distant,
and more distant from the primary analysis
(the missing-at-random assumption).
kld_barplot can be used only when missing participant outcome
data have been extracted for at least one trial. Otherwise, the execution
of the function will be stopped and an error message will be printed on
the R console.
kld_barplot returns a panel of barplots on the
Kullback-Leibler divergence measure for each re-analysis.
Loukia M. Spineli
Kullback S, Leibler RA. On information and sufficiency. Ann Math Stat 1951;22(1):79–86. doi: 10.1214/aoms/1177729694
Spineli LM, Kalyvas C, Papadimitropoulou K. Quantifying the robustness of primary analysis results: A case study on missing outcome data in pairwise and network meta-analysis. Res Synth Methods 2021;12(4):475–90. doi: 10.1002/jrsm.1478
robustness_index, run_model,
run_sensitivity
data("pma.taylor2004") # Read results from 'run_sensitivity' (using the default arguments) res_sens <- readRDS(system.file('extdata/res_sens_taylor.rds', package = 'rnmamod')) # Calculate the robustness index robust <- robustness_index(sens = res_sens, threshold = 0.17) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "inositol") # Create the barplot for the comparison 'inositol versus placebo' kld_barplot(robust = robust, compar = c("inositol", "placebo"), drug_names = interv_names)data("pma.taylor2004") # Read results from 'run_sensitivity' (using the default arguments) res_sens <- readRDS(system.file('extdata/res_sens_taylor.rds', package = 'rnmamod')) # Calculate the robustness index robust <- robustness_index(sens = res_sens, threshold = 0.17) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "inositol") # Create the barplot for the comparison 'inositol versus placebo' kld_barplot(robust = robust, compar = c("inositol", "placebo"), drug_names = interv_names)
For one outcome, it creates a heatmap of the estimated effect measure for
all possible comparisons of interventions in the network.
For two outcomes, the heatmap illustrates these two outcomes for the same
effect measure in the upper and lower off-diagonals for all
possible comparisons of interventions in the network.
The function can also be used to illustrate the results of two different
models on the same outcome and effect measure.
league_heatmap can be used for a random-effects or fixed-effect
network meta-analysis, network meta-regression, and series of pairwise
meta-analyses.
league_heatmap( full1, full2 = NULL, cov_value = NULL, drug_names1, drug_names2 = NULL, name1 = NULL, name2 = NULL, show = NULL )league_heatmap( full1, full2 = NULL, cov_value = NULL, drug_names1, drug_names2 = NULL, name1 = NULL, name2 = NULL, show = NULL )
full1 |
An object of S3 class |
full2 |
An object of S3 class |
cov_value |
A list of two elements in the following order: a number for the covariate value of interest and a character for the name of the covariate. See also 'Details'. |
drug_names1 |
A vector of labels with the name of the interventions in
the order they appear in the argument |
drug_names2 |
A vector of labels with the name of the interventions in
the order they appear in the argument |
name1 |
The text for the title of the results that refer to
the outcome or model under |
name2 |
The text for the title of the results that refer to
the outcome or model under |
show |
A vector of at least three character strings that refer to the
names of the interventions exactly as defined in |
heatmap_league offers the following options to display
one estimated effect measure for all (or some) pairwise comparisons:
one outcome, with results in the lower triangle referring to comparisons in the opposite direction after converting negative values into positive values (in absolute or logarithmic scale), and vice versa. Comparisons between interventions should be read from left to right. Therefore, each cell refers to the corresponding row-defining intervention against the column-defining intervention. Results that indicate strong evidence in favour of the row-defining intervention (i.e. the respective 95% credible interval does not include the null value) are indicated in bold. A message is printed on the R console on how to read the heatmap;
two outcomes for the same model, namely, network meta-analysis (via
run_model) or network meta-regression (via
run_metareg).
When one of the outcomes includes more interventions, the argument
full1 should be considered for that outcome.
Comparisons between interventions should be read as follows: for the upper
diagonal, each cell refers to the corresponding row-defining intervention
against the column-defining intervention, and for the lower diagonal, each
cell refers to the corresponding column-defining intervention against the
row-defining intervention. Results that indicate strong evidence (i.e. the
respective 95% credible interval does not include the null value) are
indicated in bold. A message is printed on the R console on how to read
the heatmap;
two models for the same outcome, namely, network meta-analysis versus network meta-regression, or network meta-analysis versus series of pairwise meta-analyses. The instructions to read the heatmap are in line with the previous point. A message is printed on the R console on how to read the heatmap.
For a beneficial outcome, red favours the first intervention of the comparison, and blue favours the second intervention. For a harmful outcome, blue favours the first intervention of the comparison, and red favours the second intervention. The larger the treatment effect, the darker the colour shade.
The function displays the effect measure as inherited by the argument
full1. For binary outcome, it can display the odds ratio,
relative risk, and risk difference. See 'Details' in
run_model for the relative risk, and risk difference.
For continuous outcome, it can display the mean difference, standardised
mean difference, and ratio of means. Odds ratios, relative risk and ratio
of means are reported in the original scale after exponentiation of the
logarithmic scale.
The rows and columns of the heatmap display the names of
interventions sorted by decreasing order from the best to the worst
based on their SUCRA value (Salanti et al., 2011) for the outcome or model
under the argument full1. The off-diagonals contain the posterior
median and 95% credible interval of the effect measure (according to the
argument measure as inherited in the argument full1) of the
corresponding comparisons.
The main diagonal contains the posterior mean of SUCRA of the corresponding
interventions when the arguments full1 refers to the
run_model function. When the arguments full1
refers to the run_metareg function, the p-score
(Ruecker and Schwarzer, 2015) is calculated for each intervention while
taking into account the covariate value in the argument cov_value.
P-score is the 'frequentist analogue to SUCRA'
(Ruecker and Schwarzer, 2015).
In the case of network meta-regression, when the covariate is binary,
specify in the second element of cov_value the name of the level
for which the heatmap will be created.
league_heatmap can be used only for a network of interventions.
In the case of two interventions, the execution of the function will be
stopped and an error message will be printed on the R console.
A heatmap of the league table showing the posterior median and 95% credible interval of the comparisons in the off-diagonals, and the posterior mean of the SUCRA values in the diagonal.
Loukia M. Spineli, Chrysostomos Kalyvas, Katerina Papadimitropoulou
Ruecker G, Schwarzer G. Ranking treatments in frequentist network meta-analysis works without resampling methods. BMC Med Res Methodol 2015;15:58. doi: 10.1186/s12874-015-0060-8
Salanti G, Ades AE, Ioannidis JP. Graphical methods and numerical summaries for presenting results from multiple-treatment meta-analysis: an overview and tutorial. J Clin Epidemiol 2011;64(2):163–71. doi: 10.1016/j.jclinepi.2010.03.016
run_metareg, run_model,
run_series_meta
data("nma.liu2013") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_liu.rds', package = 'rnmamod')) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "pramipexole", "serotonin-norepinephrine reuptake inhibitor", "serotonin reuptake inhibitor", "tricyclic antidepressant", "pergolide") # Create the league heatmap league_heatmap(full1 = res, drug_names1 = interv_names)data("nma.liu2013") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_liu.rds', package = 'rnmamod')) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "pramipexole", "serotonin-norepinephrine reuptake inhibitor", "serotonin reuptake inhibitor", "tricyclic antidepressant", "pergolide") # Create the league heatmap league_heatmap(full1 = res, drug_names1 = interv_names)
For one outcome, it creates a heatmap with the predicted effect measure for
all possible comparisons of interventions in the network.
For two outcomes, the heatmap illustrates these two outcomes for the same
effect measure in the upper and lower off-diagonals for all possible
comparisons of interventions in the network.
league_heatmap_pred can be used only for a random-effects
network meta-analysis and network meta-regression.
league_heatmap_pred( full1, full2 = NULL, cov_value = NULL, drug_names1, drug_names2 = NULL, name1 = NULL, name2 = NULL, show = NULL )league_heatmap_pred( full1, full2 = NULL, cov_value = NULL, drug_names1, drug_names2 = NULL, name1 = NULL, name2 = NULL, show = NULL )
full1 |
An object of S3 class |
full2 |
An object of S3 class |
cov_value |
A list of two elements in the following order: a number for the covariate value of interest and a character for the name of the covariate. See also 'Details'. |
drug_names1 |
A vector of labels with the name of the interventions in
the order they appear in the argument |
drug_names2 |
A vector of labels with the name of the interventions in
the order they appear in the argument |
name1 |
The text for the title of the results that refer to
the outcome or model under |
name2 |
The text for the title of the results that refer to
the outcome or model under |
show |
A vector of at least three character strings that refer to the
names of the interventions exactly as defined in |
heatmap_league offers the following options to display
one estimated effect measure for all (or some) pairwise comparisons:
one outcome, with results in the lower triangle referring to comparisons in the opposite direction after converting negative values into positive values (in absolute or logarithmic scale), and vice versa. Darker shades of red and green correspond to larger treatment effects in the upper and lower triangle, respectively, for a beneficial outcome, and vice versa for a harmful outcome. Comparisons between interventions should be read from left to right. Therefore, each cell refers to the corresponding row-defining intervention against the column-defining intervention. Results that indicate strong evidence in favour of the row-defining intervention (i.e. the respective 95% prediction interval does not include the null value) are indicated in bold. A message is printed on the R console on how to read the heatmap;
two outcomes for the same model, namely, network meta-analysis (via
run_model) or network meta-regression (via
run_metareg).
When one of the outcomes includes more interventions, the argument
full1 should be considered for that outcome.
Comparisons between interventions should be read as follows: for the upper
diagonal, each cell refers to the corresponding row-defining intervention
against the column-defining intervention, and for the lower diagonal, each
cell refers to the corresponding column-defining intervention against the
row-defining intervention. Results that indicate strong evidence (i.e. the
respective 95% prediction interval does not include the null value) are
indicated in bold. A message is printed on the R console on how to read
the heatmap;
two models for the same outcome, namely, network meta-analysis versus network meta-regression. The instructions to read the heatmap are in line with the previous point. A message is printed on the R console on how to read the heatmap.
The function displays the effect measure as inherited by the argument
full1. For binary outcome, it can display the odds ratio,
relative risk, and risk difference. See 'Details' in
run_model for the relative risk, and risk difference.
For continuous outcome, it can display the mean difference, standardised
mean difference, and ratio of means. Odds ratios, relative risk and ratio
of means are reported in the original scale after exponentiation of the
logarithmic scale.
The rows and columns of the heatmap display the names of interventions
which are sorted by decreasing order from the best to the worst based on
their SUCRA value (Salanti et al., 2011) for the outcome or model under the
argument full1. The off-diagonals contain the posterior median and
95% prediction interval of the effect measure (according to the argument
measure as inherited in the argument full1) of the
corresponding comparisons.
The main diagonal contains the SUCRA values of the corresponding
interventions when the argument full1 refers to the
run_model function.
When the argument full1 refers to the run_metareg
function, the p-score (Ruecker and Schwarzer, 2015) is calculated for each
intervention while taking into account the covariate value in
the argument cov_value. P-score is the 'frequentist analogue to
SUCRA' (Ruecker and Schwarzer, 2015).
In the case of network meta-regression, when the covariate is binary,
specify in the second element of cov_value the name of the level for
which the heatmap will be created.
league_heatmap_pred can be used only for a network of interventions.
In the case of two interventions, the execution of the function will be
stopped and an error message will be printed on the R console. Similarly,
when the function is executed for a fixed-effect network meta-analysis or
network meta-regression.
A league heatmap of the posterior median and 95% prediction interval
of the effect measure (according to the argument measure defined in
run_model) for all possible comparisons in the off-diagonals,
and the posterior mean of the SUCRA values in the diagonal.
Loukia M. Spineli, Chrysostomos Kalyvas, Katerina Papadimitropoulou
Ruecker G, Schwarzer G. Ranking treatments in frequentist network meta-analysis works without resampling methods. BMC Med Res Methodol 2015;15:58. doi: 10.1186/s12874-015-0060-8
Salanti G, Ades AE, Ioannidis JP. Graphical methods and numerical summaries for presenting results from multiple-treatment meta-analysis: an overview and tutorial. J Clin Epidemiol 2011;64(2):163–71. doi: 10.1016/j.jclinepi.2010.03.016
data("nma.liu2013") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_liu.rds', package = 'rnmamod')) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "pramipexole", "serotonin-norepinephrine reuptake inhibitor", "serotonin reuptake inhibitor", "tricyclic antidepressant", "pergolide") # Create the league heatmap league_heatmap_pred(full1 = res, drug_names1 = interv_names)data("nma.liu2013") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_liu.rds', package = 'rnmamod')) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "pramipexole", "serotonin-norepinephrine reuptake inhibitor", "serotonin reuptake inhibitor", "tricyclic antidepressant", "pergolide") # Create the league heatmap league_heatmap_pred(full1 = res, drug_names1 = interv_names)
Provides a league table of the estimated odds ratio, and risk difference
per 1000 participants for all possible comparisons of interventions in the
network. The main diagonal of the table presents the absolute risk for each
intervention in the network. league_table_absolute can be used for a
random-effects or fixed-effect network meta-analysis. This function should
be used when the user has access to the raw trial-level data
(one-trial-per-row format with arm-level data).
league_table_absolute is applied for one binary outcome only.
league_table_absolute(full, drug_names, show = NULL)league_table_absolute(full, drug_names, show = NULL)
full |
|
drug_names |
A vector of labels with the name of the interventions in
the order they appear in the argument |
show |
A vector of at least three character strings that refer to the
names of the interventions exactly as defined in |
The user must define the argument measure = "RD" in
run_model; otherwise, the function will be stopped and an
error message will be printed in the R console.
The rows and columns of the league table display the names of the interventions sorted by decreasing order from the best to the worst based on their SUCRA value (Salanti et al., 2011) for the odds ratio. The upper off-diagonals contain the posterior median and 95% credible interval of the odds ratio, the lower off-diagonals contain the posterior median and 95% credible interval of the risk difference (per 1000 participants), and the main diagonal comprises the posterior median and 95% credible interval of the absolute risks (per 1000 participants) of the corresponding interventions. The reference intervention of the network (which the baseline risk has been selected for) is indicated in the main diagonal with a black, thick frame.
Comparisons between interventions should be read from left to right. Results that indicate strong evidence in favor of the row-defining intervention (i.e. the respective 95% credible interval does not include the null value) are indicated in bold.
To obtain unique absolute risks for each intervention, the network
meta-analysis model has been extended to incorporate the transitive risks
framework, namely, an intervention has the same absolute risk regardless of
the comparator intervention(s) in a trial (Spineli et al., 2017).
The absolute risks are a function of the odds ratio (the base-case
effect measure for a binary outcome) and the selected baseline risk for the
reference intervention (Appendix in Dias et al., 2013). See 'Arguments' in
run_model. We advocate using the odds ratio as an effect
measure for its desired mathematical properties. Then, the risk difference
can be obtained as a function of the absolute risks of the corresponding
interventions in the comparison of interest.
league_table_absolute can be used only for a network of
interventions. In the case of two interventions, the execution of the
function will be stopped and an error message will be printed in the R
console.
A league table showing the posterior estimate and 95% credible interval of the odds ratio (upper off-diagonals), risk difference per 1000 participants (lower off-diagonals), and absolute risks per 1000 participants (main diagonal).
Loukia M. Spineli
Salanti G, Ades AE, Ioannidis JP. Graphical methods and numerical summaries for presenting results from multiple-treatment meta-analysis: an overview and tutorial. J Clin Epidemiol 2011;64(2):163–71. doi: 10.1016/j.jclinepi.2010.03.016
Spineli LM, Brignardello-Petersen R, Heen AF, Achille F, Brandt L, Guyatt GH, et al. Obtaining absolute effect estimates to facilitate shared decision making in the context of multiple-treatment comparisons. Abstracts of the Global Evidence Summit, Cape Town, South Africa. Cochrane Database of Systematic Reviews 2017;9(Suppl 1):1891.
In line with league_table_absolute, provides a league table
of the estimated odds ratio, and risk difference per 1000 participants for
all possible comparisons of interventions in the network.
The main diagonal of the table presents the absolute risk for each
intervention in the network. league_table_absolute_user requires
users to input the summary effect and 95% credible or confidence interval
of the basic parameters in the reported effect measure. This function
should be used when the user has access to the results of a published
systematic review rather than the raw trial-level data. In the latter case,
the user should consider the function league_table_absolute.
league_table_absolute_user is applied for one binary outcome only.
league_table_absolute_user( data, measure, base_risk, drug_names, show = NULL, save_xls )league_table_absolute_user( data, measure, base_risk, drug_names, show = NULL, save_xls )
data |
A data-frame with the summary effects of comparisons with the
reference intervention of the network, known as basic parameters. The
data-frame has |
measure |
Character string indicating the effect measure of |
base_risk |
A number in the interval (0, 1) that indicates the baseline risk for the selected reference intervention. |
drug_names |
A vector of labels with the name of the interventions in
the order they appear in the argument |
show |
A vector of at least three character strings that refer to the
names of the interventions exactly as defined in |
save_xls |
Logical to indicate whether to export the tabulated results
to an 'xlsx' file (via the |
When the published results are reported in the relative risk scale
(i.e., measure = "RR"), the function calculates odds ratios and risk
differences (point estimate and 95% confidence interval) for all possible
pairwise comparisons in the network based on the obtained absolute risks
and the selected baseline risk. Likewise, when the published results are in
the odds ratio or risk difference scale (i.e., measure = "OR" or
measure = "RD", respectively), the function calculates risk
differences or odds ratios (point estimate and 95% confidence interval),
respectively, for all possible pairwise comparisons in the network based on
the obtained absolute risks and the selected baseline risk.
The rows and columns of the league table display the names of the
interventions sorted by decreasing order from the best to the worst
based on the ranking measure in the fourth column of the argument
data. The upper off-diagonals contain the estimate and 95%
confidence interval of the odds ratio, the lower off-diagonals contain the
estimate and 95% confidence interval of the risk difference (per 1000
participants), and the main diagonal comprises the absolute risks and their
95% confidence interval (per 1000 participants) of the corresponding
non-reference interventions. The reference intervention of the network
(which the baseline risk has been selected for) is indicated in the main
diagonal with a black, thick frame.
Comparisons between interventions should be read from left to right. Results that indicate strong evidence in favour of the row-defining intervention (i.e. the respective 95% confidence interval does not include the null value) are indicated in bold.
Furthermore, league_table_absolute_user exports
table_relative_absolute_effect, a table with the relative and
absolute effects of the basic parameters, as an 'xlsx' file (via the
write_xlsx function) to the working
directory of the user.
To obtain unique absolute risks for each intervention, we have considered the transitive risks framework, namely, an intervention has the same absolute risk regardless of the comparator intervention(s) in a trial (Spineli et al., 2017).
league_table_absolute_user can be used only for a network of
interventions. In the case of two interventions, the execution of the
function will be stopped and an error message will be printed in the R
console.
A league table showing the estimate and 95% confidence interval of the odds ratio (upper off-diagonals), risk difference per 1000 participants (lower off-diagonals), and absolute risks per 1000 participants (main diagonal).
Loukia M. Spineli
Ruecker G, Schwarzer G. Ranking treatments in frequentist network meta-analysis works without resampling methods. BMC Med Res Methodol 2015;15:58. doi: 10.1186/s12874-015-0060-8
Salanti G, Ades AE, Ioannidis JP. Graphical methods and numerical summaries for presenting results from multiple-treatment meta-analysis: an overview and tutorial. J Clin Epidemiol 2011;64(2):163–71. doi: 10.1016/j.jclinepi.2010.03.016
Spineli LM, Brignardello-Petersen R, Heen AF, Achille F, Brandt L, Guyatt GH, et al. Obtaining absolute effect estimates to facilitate shared decision making in the context of multiple-treatment comparisons. Abstracts of the Global Evidence Summit, Cape Town, South Africa. Cochrane Database of Systematic Reviews 2017;9(Suppl 1):1891.
league_table_absolute,
write_xlsx
Plots the leverage against the square root of the posterior mean of residual deviance of the trial-arms under the model of interest.
leverage_plot(net, drug_names, title)leverage_plot(net, drug_names, title)
net |
An object of S3 class |
drug_names |
A vector of labels with the name of the interventions in
the order they appear in the argument |
title |
A title to indicate the model (consistency model, network meta-regression or unrelated mean effects model). |
leverage_plot is integrated in the ume_plot
function to create the leverage plot for the consistency model and the
unrelated mean effects model. These plots appear side-by-side in the output
of ume_plot. Dias et al. (2010) used leverage plots to
investigate the fit of the consistency and inconsistency models–the
latter through the node-splitting approach.
A scatterplot of the leverage against the square root of the
posterior mean of residual deviance of the trial-arms under the model of
interest. The green, yellow, and red curves correspond to the parabola
with = 1, 2, and 3, respectively. The data points
correspond to trial-arms. Data points found outside the yellow parabola are
linked with a pair of numbers. The first number refers to the position
of the trial in the dataset, and the second number refers to the
corresponding trial-arm (see 'Arguments' and 'Value' in
data_preparation). These trial-arms contribute more than
1 to the deviance information criterion and, hence, the model's poor fit.
Loukia M. Spineli
Dias S, Welton NJ, Caldwell DM, Ades AE. Checking consistency in mixed treatment comparison meta-analysis. Stat Med 2010;29(7-8):932–44. doi: 10.1002/sim.3767
data_preparation, run_metareg,
run_model, run_ume, ume_plot
Evaluates whether convergence has been achieved for the monitored parameters of the Bayesian models. The Gelman-Rubin convergence diagnostic, the Markov Chain Monte Carl (MCMC) error and relevant diagnostic plots are applied.
mcmc_diagnostics(net, par = NULL)mcmc_diagnostics(net, par = NULL)
net |
An object of S3 class |
par |
A vector of at least one character string that refers to the
monitored parameters in |
For each monitored parameter, mcmc_diagnostics considers the
R-hat and MCMC error and compares them with the thresholds 1.1 and 5% of
the posterior standard deviation (the rule of thumb), respectively.
Convergence is achieved for the monitored parameter, when the R-hat is
below the corresponding threshold. Visual inspection of the trace plots
and posterior density of the monitored parameters should also be considered
when drawing conclusions about convergence.
mcmc_diagnostics considers the following monitored parameters:
EM |
The estimated summary effect measure. |
EM_pred |
The predicted summary effect measure. |
delta |
The estimated trial-specific effect measure. |
tau |
The between-trial standard deviation. |
direct |
The direct estimate of the split node (see 'Value' in
|
indirect |
The indirect estimate of the split node
(see 'Value' in |
diff |
The inconsistency factor of the split node (see 'Value' in
|
phi |
The informative missingness parameter. |
beta |
The regression coefficient. |
For each monitored parameter mentioned above, mcmc_diagnostics also
returns a barplot on the ratio of MCMC error to the posterior standard
deviation and a barplot on the Gelman-Rubin R diagnostic. Bars that
correspond to a ratio less than 5% are indicated in green (the
corresponding parameters have been estimated accurately); otherwise, the
bars are indicated in red (inaccurate estimation). Furthermore, bars that
correspond to an R value less than 1.10 are indicated in green (the
corresponding parameters have been converged); otherwise, the bars are
indicated in red (convergence is not achieved).
mcmc_diagnostics returns histograms than barplots for EM when
run_sensitivity is considered.
mcmc_diagnostics also uses the
mcmcplot function of the R-package
mcmcplots to create an
HTML file with a panel of diagnostic plots (trace, density, and
autocorrelation) for each monitored parameter.
Loukia M. Spineli
Gelman, A, Rubin, DB. Inference from iterative simulation using multiple sequences. Stat Sci 1992;7(4):457–72. doi: 10.1214/ss/1177011136
mcmcplot,
run_metareg, run_model,
run_nodesplit, run_sensitivity,
run_series_meta, run_ume
data("nma.baker2009") # Read results from 'run_nodesplit' (using the default arguments) res <- readRDS(system.file('extdata/node_baker.rds', package = 'rnmamod')) # Check convergence based on R-hat mcmc_diagnostics(net = res, par = c("tau", "EM[2,1]", "EM.pred[2,1]"))data("nma.baker2009") # Read results from 'run_nodesplit' (using the default arguments) res <- readRDS(system.file('extdata/node_baker.rds', package = 'rnmamod')) # Check convergence based on R-hat mcmc_diagnostics(net = res, par = c("tau", "EM[2,1]", "EM.pred[2,1]"))
Illustrates the effect estimates, predictions and regression coefficients of comparisons with a specified comparator intervention for a selected covariate value and also exports these results to an Excel file.
metareg_plot(full, reg, compar, cov_value, drug_names, save_xls)metareg_plot(full, reg, compar, cov_value, drug_names, save_xls)
full |
|
reg |
An object of S3 class |
compar |
A character to indicate the comparator intervention. It must be
any name found in |
cov_value |
A list of two elements in the following order: a number
for the covariate value of interest (see 'Arguments' in
|
drug_names |
A vector of labels with the name of the interventions in
the order they appear in the argument |
save_xls |
Logical to indicate whether to export the tabulated results
to an 'xlsx' file (via the |
The deviance information criterion (DIC) of the network meta-analysis model is compared with the DIC of the network meta-regression model. If the difference in DIC exceeds 5, the network meta-regression model is preferred; if the difference in DIC is less than -5, the network meta-analysis model is preferred; otherwise, there is little to choose between the compared models.
When the covariate is binary, specify in the second element of
cov_value the name of the level for which the output will be
created.
Furthermore, metareg_plot exports all tabulated results to separate
'xlsx' files (via the write_xlsx function
of the R-package
writexl) to the working
directory of the user.
metareg_plot can be used only for a network of interventions. In the
case of two interventions, the execution of the function will be stopped
and an error message will be printed on the R console.
metareg_plot prints on the R console a message on the most
parsimonious model (if any) based on the DIC (in red text). Furthermore,
the function returns the following list of elements:
table_estimates |
The posterior median, and 95% credible interval
of the summary effect measure (according to the argument |
table_predictions |
The posterior median, and 95% prediction
interval of the summary effect measure (according to the argument
|
table_model_assessment |
The DIC, total residual deviance,
number of effective parameters, and the posterior median and 95% credible
interval of between-trial standard deviation (tau) under each model
(Spiegelhalter et al., 2002). When a fixed-effect model has been
performed, |
table_regression_coeffients |
The posterior median and 95%
credible interval of the regression coefficient(s) (according to the
argument |
interval_plot |
A forest plot on the estimated and predicted effect
sizes of comparisons with the selected comparator intervention under
network meta-analysis and network meta-regression based on the specified
|
sucra_scatterplot |
A scatterplot of the SUCRA values from the
network meta-analysis against the SUCRA values from the network
meta-regression based on the specified |
Loukia M. Spineli
Salanti G, Ades AE, Ioannidis JP. Graphical methods and numerical summaries for presenting results from multiple-treatment meta-analysis: an overview and tutorial. J Clin Epidemiol 2011;64(2):163–71. doi: 10.1016/j.jclinepi.2010.03.016
Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A. Bayesian measures of model complexity and fit. J R Stat Soc B 2002;64(4):583–616. doi: 10.1111/1467-9868.00353
forestplot_metareg, run_metareg,
run_model, scatterplot_sucra,
write_xlsx
data("nma.baker2009") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_baker.rds', package = 'rnmamod')) # Read results from 'run_metareg' (exchangeable structure) reg <- readRDS(system.file('extdata/reg_baker.rds', package = 'rnmamod')) # Publication year as the covariate pub_year <- c(1996, 1998, 1999, 2000, 2000, 2001, rep(2002, 5), 2003, 2003, rep(2005, 4), 2006, 2006, 2007, 2007) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "budesonide", "budesonide plus formoterol", "fluticasone", "fluticasone plus salmeterol", "formoterol", "salmeterol", "tiotropium") # Plot the results from both models for all comparisons with salmeterol and # publication year 2000 metareg_plot(full = res, reg = reg, compar = "salmeterol", cov_value = list(2000, "publication year"), drug_names = interv_names)data("nma.baker2009") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_baker.rds', package = 'rnmamod')) # Read results from 'run_metareg' (exchangeable structure) reg <- readRDS(system.file('extdata/reg_baker.rds', package = 'rnmamod')) # Publication year as the covariate pub_year <- c(1996, 1998, 1999, 2000, 2000, 2001, rep(2002, 5), 2003, 2003, rep(2005, 4), 2006, 2006, 2007, 2007) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "budesonide", "budesonide plus formoterol", "fluticasone", "fluticasone plus salmeterol", "formoterol", "salmeterol", "tiotropium") # Plot the results from both models for all comparisons with salmeterol and # publication year 2000 metareg_plot(full = res, reg = reg, compar = "salmeterol", cov_value = list(2000, "publication year"), drug_names = interv_names)
miss_characteristics hosts a set of visualisation tools to assess
the size and pattern of missing characteristics values in the dataset.
miss_characteristics( input, drug_names, rename_char = NULL, label_size = 4, axis_title_size = 14, axis_text_size = 14, axis_x_text_angle = 0, legend_text_size = 14, legend_title_size = 14, strip_text_size = 14, strip_text_angle = 0 )miss_characteristics( input, drug_names, rename_char = NULL, label_size = 4, axis_title_size = 14, axis_text_size = 14, axis_x_text_angle = 0, legend_text_size = 14, legend_title_size = 14, strip_text_size = 14, strip_text_angle = 0 )
input |
A data-frame in the long arm-based format. Two-arm trials occupy one row in the data-frame. Multi-arm trials occupy as many rows as the number of possible comparisons among the interventions. The first two columns refer to the trial name, and the pairwise comparison, respectively. The remaining columns refer to summary characteristics. See 'Details' for the specification of the columns. |
drug_names |
A vector of labels with the name of the interventions
in the order they appear in the argument |
rename_char |
A list of two elements: (i) a numeric vector with the
position of the characteristics in |
label_size |
A positive integer for the font size of labels in the
plots. |
axis_title_size |
A positive integer for the font size of axis titles in
the plots. |
axis_text_size |
A positive integer for the font size of axis text in
the plots. |
axis_x_text_angle |
A positive integer for the angle of axis text in
plots related to missing data. |
legend_text_size |
A positive integer for the font size of legend text
in the plots. |
legend_title_size |
A positive integer for the font size of legend title
in the plots. |
strip_text_size |
A positive integer for the font size of strip text
in the plots. |
strip_text_angle |
A positive integer for the angle of strip text
in the plots. |
The correct type mode of columns in input must be ensured to use
the function miss_characteristics. The first two columns referring
to the trial name, and pairwise comparison, respectively, must be
character. The remaining columns referring to the characteristics
must be double or integer depending on whether the
corresponding characteristic refers to a quantitative or qualitative
variable. The type mode of each column is assessed by
miss_characteristics using the base function typeof.
The interventions should be sorted in an ascending order of their
identifier number within the trials so that the first treatment column
(second column in input) is the control arm for every pairwise
comparison. This is important to ensure consistency in the order of
interventions within the comparisons obtained from the other related
functions.
miss_characteristics returns the following list of elements:
Barplot_missing_combined |
A panel of barplots on the percentage of missing and observed cases for each comparison and characteristic. |
Barplot_missing_characteristics |
A barplot on the percentage of missing and observed cases for each comparison. |
Tileplot_missing |
A plot that illustrates the position of missing cases for each trial, comparison and characteristic. |
Loukia M. Spineli
# Fictional dataset set.seed(13022024) data_set <- data.frame(Trial_name = as.character(1:(5 + 7 +2)), arm1 = rep(c("1", "2"), c(5 + 7, 2)), arm2 = rep(c("2", "3"), c(5, 7 + 2)), sample = as.numeric(sample(c(50:300), 5 + 7 + 2)), age = as.numeric(sample(c(18:50), 5 + 7 + 2)), blinding = factor(rep(c("yes", "no", "yes"), c(5, 7, 2)))) data_set$age[data_set$age < 30] <- NA miss_characteristics(input = data_set, drug_names = c("A", "B", "C"))# Fictional dataset set.seed(13022024) data_set <- data.frame(Trial_name = as.character(1:(5 + 7 +2)), arm1 = rep(c("1", "2"), c(5 + 7, 2)), arm2 = rep(c("2", "3"), c(5, 7 + 2)), sample = as.numeric(sample(c(50:300), 5 + 7 + 2)), age = as.numeric(sample(c(18:50), 5 + 7 + 2)), blinding = factor(rep(c("yes", "no", "yes"), c(5, 7, 2)))) data_set$age[data_set$age < 30] <- NA miss_characteristics(input = data_set, drug_names = c("A", "B", "C"))
Generates the mean value of the normal distribution of the missingness
parameter in the proper format depending on the assumed structure of the
missingness parameter. run_model inherits
missingness_param_prior through the argument mean_misspar
(see 'Argument' in run_model).
missingness_param_prior(assumption, mean_misspar)missingness_param_prior(assumption, mean_misspar)
assumption |
Character string indicating the structure of the
informative missingness parameter.
Set |
mean_misspar |
A numeric value or a vector of two numeric values for the
mean of the normal distribution of the informative missingness parameter
(see 'Details'). The default argument is 0 and corresponds to the
missing-at-random assumption for |
run_model considers the informative missingness odds
ratio in the logarithmic scale for binary outcome data (Spineli, 2019a;
Turner et al., 2015; White et al., 2008), the informative missingness
difference of means when measure is "MD" or "SMD",
and the informative missingness ratio of means in the logarithmic scale
when measure is "ROM" (Spineli et al., 2021;
Mavridis et al., 2015).
When assumption is trial-specific (i.e., "IDE-TRIAL" or
"HIE-TRIAL"), or independent (i.e., "IND-CORR" or
"IND-UNCORR"), only one numeric value can be assigned to
mean_misspar because the same missingness scenario is applied to all
trials and trial-arms of the dataset, respectively. When assumption
is "IDE-ARM" or "HIE-ARM", a maximum of two
different or identical numeric values can be assigned as a vector to
mean_misspars: the first value refers to the experimental arm,
and the second value refers to the control arm of a trial.
In the case of a network, the first value is considered for all
non-reference interventions and the second value is considered for the
reference intervention of the network (see 'Argument' ref in
run_model). This is necessary to ensure transitivity in the
assumptions for the missingness parameter across the comparisons in the
network (Spineli, 2019b).
Currently, there are no empirically-based prior distributions for the
informative missingness parameters. The users may refer to
Mavridis et al. (2015) and Spineli (2019) to determine mean_misspar
for an informative missingness parameter.
A scalar or numeric vector to be passed to run_model.
Loukia M. Spineli
Mavridis D, White IR, Higgins JP, Cipriani A, Salanti G. Allowing for uncertainty due to missing continuous outcome data in pairwise and network meta-analysis. Stat Med 2015;34(5):721–41. doi: 10.1002/sim.6365
Spineli LM, Kalyvas C, Papadimitropoulou K. Continuous(ly) missing outcome data in network meta-analysis: a one-stage pattern-mixture model approach. Stat Methods Med Res 2021;30(4):958–75. doi: 10.1177/0962280220983544
Spineli LM. An empirical comparison of Bayesian modelling strategies for missing binary outcome data in network meta-analysis. BMC Med Res Methodol 2019a;19(1):86. doi: 10.1186/s12874-019-0731-y
Spineli LM. Modeling missing binary outcome data while preserving transitivity assumption yielded more credible network meta-analysis results. J Clin Epidemiol 2019b;105:19–26. doi: 10.1016/j.jclinepi.2018.09.002
Turner NL, Dias S, Ades AE, Welton NJ. A Bayesian framework to account for uncertainty due to missing binary outcome data in pairwise meta-analysis. Stat Med 2015;34(12):2062–80. doi: 10.1002/sim.6475
White IR, Higgins JP, Wood AM. Allowing for uncertainty due to missing data in meta-analysis–part 1: two-stage methods. Stat Med 2008;27(5):711–27. doi: 10.1002/sim.3008
Illustrates the network plot for one outcome.
netplot( data, drug_names, show_multi = FALSE, multi_frame = -16, alpha_multi_color = 0.1, layout = igraph::layout_in_circle, node_color = "tomato", node_frame_color = "black", node_frame_width = 1, node_shape = "circle", node_label_color = "black", node_label_font = 1, node_label_cex = 1, node_label_dist = 0, edge_color = "grey50", edge_arrow_size = 0.5, edge_lty = 1, edge_label = NULL, edge_label_color = "black", edge_label_font = 1, edge_label_cex = 2, edge_curved = 0, direction = FALSE, ... )netplot( data, drug_names, show_multi = FALSE, multi_frame = -16, alpha_multi_color = 0.1, layout = igraph::layout_in_circle, node_color = "tomato", node_frame_color = "black", node_frame_width = 1, node_shape = "circle", node_label_color = "black", node_label_font = 1, node_label_cex = 1, node_label_dist = 0, edge_color = "grey50", edge_arrow_size = 0.5, edge_lty = 1, edge_label = NULL, edge_label_color = "black", edge_label_font = 1, edge_label_cex = 2, edge_curved = 0, direction = FALSE, ... )
data |
A data-frame of a one-trial-per-row format containing arm-level
data of each trial. See 'Format' in |
drug_names |
A vector of labels with the name of the interventions
(nodes) in the order they appear in the argument |
show_multi |
Logical to indicate whether to colour the closed-loops
informed by multi-arm trials. The default is |
multi_frame |
A numeric scalar to determine the size of the border
around the closed-loops formed by multi-arm trials. The default is -16.
|
alpha_multi_color |
A numerical scalar with range from 0 to 1 to
determine the opacity of |
layout |
The layout specification. The default is
|
node_color |
A character or vector of characters (with length equal to
the number of nodes) to indicate the colour of the nodes. The default is
|
node_frame_color |
A character to indicate the colour of the frame
around the nodes. The default is |
node_frame_width |
A numerical scalar to indicate the width of the frame
around the nodes. The default is 1. |
node_shape |
A character to indicate the shape of the nodes. The default
is |
node_label_color |
A character to indicate the color of the node labels.
The default is |
node_label_font |
A numerical scalar to indicate the font of the node
labels. The default is 1. |
node_label_cex |
A numerical scalar to indicate the font size of the
node labels. The default is 1. |
node_label_dist |
A numerical scale between 0 and 1 to indicate the
position of the node labels relative to the node center. The default is 0,
where the label is centered. |
edge_color |
A character or vector of characters (with length equal to
the number of edges) to indicate the colour of the edges. The default is
|
edge_arrow_size |
A numerical scalar between 0 and 1 to indicate the
arrow size. The default is 0.5. |
edge_lty |
A numerical scalar, discrete with values from 0 to 6 to
indicate the line type of the edges. The default is 1 (solid).
|
edge_label |
A vector of number of characters with length equal to the
number of edges to present the edge label. The default is
|
edge_label_color |
A character to indicate the color of the edge labels.
The default is |
edge_label_font |
A numerical scalar to indicate the font of the edge
labels. The default is 1. |
edge_label_cex |
A numerical scalar to indicate the font size of the
edge labels. The default is 2. |
edge_curved |
A numerical scalar with range from 0 to 1 that indicates
the edge curvature. The default is 0 (no curvature). |
direction |
Logical to draw (TRUE) or not (FALSE) arrow for each edge
according to each direction. The default is |
... |
Further graphical arguments of the
|
The edge thickness is proportional to the number of trials investigating the corresponding comparison. The node size is weighted by the total sample size of the corresponding intervention.
The user can control many of the arguments found in the
plot.igraph function of the
R-package igraph), such
as the colour of the nodes and edges, the node and edge label size, and so
on.
A network plot with coloured closed-loops informed by multi-arm trials. Each node indicates an intervention and each edge an observed pairwise comparison.
Loukia M. Spineli
data("nma.bottomley2011") # Return the first six trials of the dataset head(nma.bottomley2011) # The names of the interventions in the order they appear in the dataset interv_names <- c("betamethasone dipropionate", "betamethasone valerate", "calcipotriol", "calcipotriol plus polytar", "capasal", "two-compound formulation gel", "placebo") # Create the network plot netplot(data = nma.bottomley2011, drug_names = interv_names, edge_label_cex = 1)data("nma.bottomley2011") # Return the first six trials of the dataset head(nma.bottomley2011) # The names of the interventions in the order they appear in the dataset interv_names <- c("betamethasone dipropionate", "betamethasone valerate", "calcipotriol", "calcipotriol plus polytar", "capasal", "two-compound formulation gel", "placebo") # Create the network plot netplot(data = nma.bottomley2011, drug_names = interv_names, edge_label_cex = 1)
A dataset of 21 trials comparing seven pharmacologic interventions with each other and placebo in patients with chronic obstructive pulmonary disease (COPD). The exacerbation of COPD is the analysed binary outcome.
data(nma.baker2009)data(nma.baker2009)
A data-frame with 21 rows of arm-based data and 17 columns (maximum number of 4 arms).
The interventions have been coded as follows: 1, placebo; 2, budesonide; 3, budesonide plus formoterol; 4, fluticasone; 5, fluticasone plus salmeterol; 6, formoterol; 7, salmeterol; and 8, tiotropium.
Baker WL, Baker EL, Coleman CI. Pharmacologic treatments for chronic obstructive pulmonary disease: a mixed-treatment comparison meta-analysis. Pharmacotherapy 2009;29(8):891–905. doi: 10.1592/phco.29.8.891
A dataset of 9 trials comparing six pharmacologic interventions with each other and placebo for moderately severe scalp psoriasis. The analysed binary outcome is the investigator's global assessment response at 4 weeks.
data(nma.bottomley2011)data(nma.bottomley2011)
A data frame with 9 rows of arm-based data and 17 columns (maximum number of 4 arms).
The interventions have been coded as follows: 1, betamethasone dipropionate; 2, betamethasone valerate; 3, calcipotriol; 4, calcipotriol plus polytar; 5, capasal; 6, two-compound formulation gel; and 7, placebo.
Bottomley JM, Taylor RS, Ryttov J. The effectiveness of two-compound formulation calcipotriol and betamethasone dipropionate gel in the treatment of moderately severe scalp psoriasis: a systematic review of direct and indirect evidence. Curr Med Res Opin 2011;27(1):251–68. doi: 10.1185/03007995.2010.541022
A dataset of 16 trials comparing seven oral antithrombotics with each other and placebo in patients with atrial fibrillation. The analysed binary outcome is prevention of a stroke episode.
data(nma.dogliotti2014)data(nma.dogliotti2014)
A data frame with 16 rows of arm-based data and 13 columns (maximum number of 3 arms).
The interventions have been coded as follows: 1, placebo; 2, aspirin; 3, aspirin plus clopidogrel; 4, dabigatran 110 mg; 5, dabigatran 150 mg; 6, rivaroxaban; 7, vitamin K antagonist; and 8, apixaban
Dogliotti A, Paolasso E, Giugliano RP. Current and new oral antithrombotics in non-valvular atrial fibrillation: a network meta-analysis of 79808 patients. Heart 2014;100(5):396–405. doi: 10.1136/heartjnl-2013-304347
A dataset of 11 trials comparing the effectiveness of five antidepressants and placebo in Parkinson's disease. The analysed binary outcome is the number of patients with a reduction of at least 50/ the baseline score.
data(nma.liu2013)data(nma.liu2013)
A data frame with 11 rows of arm-based data and 13 columns (maximum number of 3 arms).
The interventions have been coded as follows: 1, placebo; 2, pramipexole; 3, serotonin-norepinephrine reuptake inhibitor; 4, selective serotonin reuptake inhibitor; 5, tricyclic antidepressant; and 6, pergolide.
Liu J, Dong J, Wang L, Yan P, Sun S. Comparative efficacy and acceptability of antidepressants in Parkinson's disease: a network meta-analysis. PLoS One 2013;8(10):e76651. doi: 10.1371/journal.pone.0076651
A dataset of 14 trials comparing three different training modalities (a triangle network) for patients with type 2 diabetes. The analysed continuous outcome is change from baseline in HbA1c levels.
data(nma.schwingshackl2014)data(nma.schwingshackl2014)
A data frame with 14 rows of arm-based data and 16 columns (maximum number of 3 arms).
The interventions have been coded as follows: 1, aerobic; 2, resistance; and 3, combined training;
Schwingshackl L, Missbach B, Dias S, et al. M Impact of different training modalities on glycaemic control and blood lipids in patients with type 2 diabetes: a systematic review and network meta-analysis. Diabetologia 2014;57(9):1789–97. doi: 10.1007/s00125-014-3303-z
A dataset of 29 trials comparing three antiparkinsonian interventions with placebo (a star-shaped network) in patients with later Parkinson's disease. The analysed continuous outcome is the change from baseline of patient off-time reduction.
data(nma.stowe2011)data(nma.stowe2011)
A data frame with 29 rows of arm-based data and 11 columns (maximum number of 2 arms).
The interventions have been coded as follows: 1, placebo plus levodopa (PBO+LD); 2, dopamine agonist plus levodopa (DA+LD); 3, catechol-O-methyl transferase inhibitors plus levodopa (COMBI+LD); and 4, monoamine oxidase type B inhibitors plus levodopa (MAOBI+LD).
Stowe R, Ives N, Clarke CE, et al. Meta-analysis of the comparative efficacy and safety of adjuvant treatment to levodopa in later Parkinson's disease. Mov Disord 2011;26(4):587–98. doi: 10.1002/mds.23517
nodesplit_plot hosts a toolkit of functions that
facilitates the comparison of the consistency model
(via run_model) with the node-splitting approach
(via run_nodesplit) regarding the posterior summaries of the
direct and indirect effects and inconsistency factor of the split
nodes, the between-trial standard deviation and model assessment
parameters (Spiegelhalter et al., 2002) after each split node in the
network.
nodesplit_plot(full, node, drug_names, save_xls)nodesplit_plot(full, node, drug_names, save_xls)
full |
|
node |
An object of S3 class |
drug_names |
A vector of labels with the name of the interventions in
the order they appear in the argument |
save_xls |
Logical to indicate whether to export the tabulated results
to an 'xlsx' file (via the |
intervalplot_inconsistency_factor includes as many interval
plots as the number of split nodes in the network. Each interval plot
illustrates the posterior median and 95% credible interval of the direct and
indirect effect of the split nodes and the corresponding inconsistency
factor.
The line that corresponds to the inconsistency factor is highlighted with
green, when it does not cross the vertical line of no difference (between
the direct and indirect effect), and red otherwise. If there are more than
30 split nodes, the function presents the interval plots on split nodes
with conclusive inconsistency factor (green intervals) or those with
an opposite sign in the direct and indirect effects.
intervalplot_tau is an interval plot on the median and 95% credible
interval of tau after each split node. The lines that correspond to
the split nodes are sorted in ascending order of the deviance information
criterion (DIC) which appears at the top of each line.
The estimated median and 95% credible intervals of tau under the
consistency model appear in the interval plot as a solid and two dotted
parallel blue lines, respectively. The different levels of heterogeneity
appear as green, yellow, orange, and red rectangulars to indicate a low,
reasonable, fairly high, and fairly extreme heterogeneity, respectively,
following the classification of Spiegelhalter et al. (2004).
When a fixed-effect model has been performed, nodesplit_plot does
not return the intervalplot_tau.
table_model_assessment also includes the column
DIC-based better fit that indicates the preferred model in terms of
parsimony for each split node. Therefore, the DIC of the model after each
split node is compared with the DIC of the consistency model
(Dias et al., 2010). If the difference in DIC exceeds 5, the consistency
model is preferred; if the difference in DIC is less than -5, the model
after the split node is preferred; otherwise, there is little to choose
between the compared models.
For a binary outcome, when measure is "RR" (relative risk) or "RD"
(risk difference) in run_model, nodesplit_plot
currently presents the results in the odds ratio scale. This is because,
the odds ratio is used as the 'best-case' effect measure in
run_model. Then, relative risk, and risk difference are
obtained as a function of the odds ratio and the selected baseline risk
(See 'Details' in run_model).
The split nodes have been automatically selected via the
mtc.nodesplit.comparisons
function of the R-package
gemtc.
See 'Details' in run_nodesplit.
Furthermore, nodesplit_plot exports both data-frames to separate
'xlsx' files (via the write_xlsx function
of the R-package
writexl) to the working
directory of the user.
nodesplit_plot can be used only for a network of interventions and
when there is at least one split node. Otherwise, the execution of the
function will be stopped and an error message will be printed on the R
console.
nodesplit_plot returns the following list of elements:
table_effect_size |
A data-frame with the posterior median, posterior standard deviation and 95% credible interval of the direct and indirect effect and the inconsistency factor of each split node. |
table_model_assessment |
A data-frame with the model assessment parameters (DIC, posterior mean of total residual deviance, and number of effective parameters), the posterior median, posterior standard deviation and 95% credible interval of tau under the consistency model and after each split node. See 'Details'. |
intervalplot_inconsistency_factor |
A panel of interval plots on the direct and indirect effect of the split nodes and the corresponding inconsistency factor. See 'Details'. |
intervalplot_tau |
An interval plot on tau after each split node. See 'Details'. |
Loukia M. Spineli
Dias S, Welton NJ, Caldwell DM, Ades AE. Checking consistency in mixed treatment comparison meta-analysis. Stat Med 2010;29(7-8):932–44. doi: 10.1002/sim.3767
Spiegelhalter DJ, Abrams KR, Myles JP. Bayesian approaches to clinical trials and health-care evaluation. John Wiley and Sons, Chichester, 2004.
Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A. Bayesian measures of model complexity and fit. J R Stat Soc B 2002;64(4):583–616. doi: 10.1111/1467-9868.00353
mtc.nodesplit.comparisons,
run_model, run_nodesplit,
write_xlsx
data("nma.baker2009") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_baker.rds', package = 'rnmamod')) # Read results from 'run_nodesplit' (using the default arguments) node <- readRDS(system.file('extdata/node_baker.rds', package = 'rnmamod')) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "budesonide", "budesonide plus formoterol", "fluticasone", "fluticasone plus salmeterol", "formoterol", "salmeterol", "tiotropium") # Plot the results from both models nodesplit_plot(full = res, node = node, drug_names = interv_names)data("nma.baker2009") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_baker.rds', package = 'rnmamod')) # Read results from 'run_nodesplit' (using the default arguments) node <- readRDS(system.file('extdata/node_baker.rds', package = 'rnmamod')) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "budesonide", "budesonide plus formoterol", "fluticasone", "fluticasone plus salmeterol", "formoterol", "salmeterol", "tiotropium") # Plot the results from both models nodesplit_plot(full = res, node = node, drug_names = interv_names)
A pairwise meta-analysis of 4 trials comparing paroxetine with placebo for depressive disorders in children and adolescents. The analysed binary outcome is remission or response as defined in the trials.
data(pma.hetrick2012)data(pma.hetrick2012)
A data frame with 4 rows of arm-based data and 9 columns.
The interventions have been coded as follows: 1, placebo; 2, paroxetine.
Hetrick SE, McKenzie JE, Cox GR, Simmons MB, Merry SN. Newer generation antidepressants for depressive disorders in children and adolescents. Cochrane Database Syst Rev 2012;11(11):CD004851. doi: 10.1002/14651858.CD004851.pub3
A pairwise meta-analysis of 4 trials comparing inositol with glucose (placebo) for depressive episode. The analysed continuous outcome is the resolution of a depressive episode using the Hamilton Depression Rating Scale.
data(pma.taylor2004)data(pma.taylor2004)
A data frame with 4 rows of arm-based data and 11 columns.
The interventions have been coded as follows: 1, placebo; 2, inositol.
Taylor MJ, Wilder H, Bhagwagar Z, Geddes J. Inositol for depressive disorders. Cochrane Database Syst Rev 2004;2004(2):CD004049. doi: 10.1002/14651858.CD004049.pub2
The WinBUGS code, as written by Dias et al. (2013) to run a one-stage Bayesian network meta-analysis, extended to incorporate the pattern-mixture model for binary or continuous missing participant outcome data (Spineli et al., 2021; Spineli, 2019). The model has been also extended to incorporate a trial-level covariate to apply meta-regression (Cooper et al., 2009). In the case of two interventions, the code boils down to a one-stage Bayesian pairwise meta-analysis with pattern-mixture model (Turner et al., 2015; Spineli et al, 2021).
prepare_model(measure, model, covar_assumption, assumption)prepare_model(measure, model, covar_assumption, assumption)
measure |
Character string indicating the effect measure. For a binary
outcome, the following can be considered: |
model |
Character string indicating the analysis model with values
|
covar_assumption |
Character string indicating the structure of the
intervention-by-covariate interaction, as described in
Cooper et al., (2009). Set |
assumption |
Character string indicating the structure of the
informative missingness parameter. Set |
prepare_model creates the model in the JAGS dialect
of the BUGS language. The output of this function constitutes the argument
model.file of the jags function (in the
R-package R2jags) via the
textConnection function.
An R character vector object to be passed to run_model
and run_metareg through the
textConnection function as the argument
object.
Loukia M. Spineli
Cooper NJ, Sutton AJ, Morris D, Ades AE, Welton NJ. Addressing between-study heterogeneity and inconsistency in mixed treatment comparisons: Application to stroke prevention treatments in individuals with non-rheumatic atrial fibrillation. Stat Med 2009;28(14):1861–81. doi: 10.1002/sim.3594
Dias S, Sutton AJ, Ades AE, Welton NJ. Evidence synthesis for decision making 2: a generalized linear modeling framework for pairwise and network meta-analysis of randomized controlled trials. Med Decis Making 2013;33(5):607–17. doi: 10.1177/0272989X12458724
Spineli LM, Kalyvas C, Papadimitropoulou K. Continuous(ly) missing outcome data in network meta-analysis: a one-stage pattern-mixture model approach. Stat Methods Med Res 2021;30(4):958–75. doi: 10.1177/0962280220983544
Spineli LM. An empirical comparison of Bayesian modelling strategies for missing binary outcome data in network meta-analysis. BMC Med Res Methodol 2019;19(1):86. doi: 10.1186/s12874-019-0731-y
Turner NL, Dias S, Ades AE, Welton NJ. A Bayesian framework to account for uncertainty due to missing binary outcome data in pairwise meta-analysis. Stat Med 2015;34(12):2062–80. doi: 10.1002/sim.6475
run_metareg, run_model,
jags,
textConnection
The WinBUGS code, as written by Dias et al. (2010) to run a one-stage Bayesian node-splitting model, extended to incorporate the pattern-mixture model for binary or continuous missing participant outcome data (Spineli et al., 2021; Spineli, 2019).
prepare_nodesplit(measure, model, assumption)prepare_nodesplit(measure, model, assumption)
measure |
Character string indicating the effect measure. For a binary
outcome, the following can be considered: |
model |
Character string indicating the analysis model with values
|
assumption |
Character string indicating the structure of the
informative missingness parameter. Set |
This functions creates the model in the JAGS dialect of the BUGS
language. The output of this function constitutes the argument
model.file of jags (in the R-package
R2jags) via the
textConnection function.
prepare_nodesplit inherits measure, model, and
assumption from the run_model function. For a binary
outcome, when measure is "RR" (relative risk) or "RD"
(risk difference) in run_model, prepare_nodesplit
currently considers the WinBUGS code for the odds ratio.
The split nodes have been automatically selected via the
mtc.nodesplit.comparisons
function of the R-package
gemtc.
See 'Details' in run_nodesplit.
An R character vector object to be passed to
run_nodesplit through the
textConnection function as the argument
object.
Loukia M. Spineli
Dias S, Welton NJ, Caldwell DM, Ades AE. Checking consistency in mixed treatment comparison meta-analysis. Stat Med 2010;29(7-8):932–44. doi: 10.1002/sim.3767
Spineli LM, Kalyvas C, Papadimitropoulou K. Continuous(ly) missing outcome data in network meta-analysis: a one-stage pattern-mixture model approach. Stat Methods Med Res 2021;30(4):958–75. doi: 10.1177/0962280220983544
Spineli LM. An empirical comparison of Bayesian modelling strategies for missing binary outcome data in network meta-analysis. BMC Med Res Methodol 2019;19(1):86. doi: 10.1186/s12874-019-0731-y
jags,
run_model,
mtc.nodesplit.comparisons,
run_nodesplit,
textConnection
The WinBUGS code, as proposed by Dias et al. (2013) to run a one-stage Bayesian unrelated mean effects model, refined (Spineli, 2021), and extended to incorporate the pattern-mixture model for binary or continuous missing participant outcome data (Spineli et al., 2021; Spineli, 2019).
prepare_ume(measure, model, assumption, connected)prepare_ume(measure, model, assumption, connected)
measure |
Character string indicating the effect measure with values
|
model |
Character string indicating the analysis model with values
|
assumption |
Character string indicating the structure of the
informative missingness parameter. Set |
connected |
An integer equal to one or larger that indicates the number of subnetworks. |
This functions creates the model in the JAGS dialect of the BUGS
language. The output of this function constitutes the argument
model.file of jags (in the R-package
R2jags) via the
textConnection function.
prepare_ume inherits measure, model, and
assumption from the run_model function. For a binary
outcome, when measure is "RR" (relative risk) or "RD"
(risk difference) in run_model, prepare_ume
currently considers the WinBUGS code for the odds ratio.
An R character vector object to be passed to run_ume
through the textConnection function as
the argument object.
Loukia M. Spineli
Dias S, Welton NJ, Sutton AJ, Caldwell DM, Lu G, Ades AE. Evidence synthesis for decision making 4: inconsistency in networks of evidence based on randomized controlled trials. Med Decis Making 2013;33(5):641–56. doi: 10.1177/0272989X12455847
Spineli LM. A revised framework to evaluate the consistency assumption globally in a network of interventions. Med Decis Making 2021. doi: 10.1177/0272989X211068005
Spineli LM, Kalyvas C, Papadimitropoulou K. Continuous(ly) missing outcome data in network meta-analysis: a one-stage pattern-mixture model approach. Stat Methods Med Res 2021;30(4):958–75. doi: 10.1177/0962280220983544
Spineli LM. An empirical comparison of Bayesian modelling strategies for missing binary outcome data in network meta-analysis. BMC Med Res Methodol 2019;19(1):86. doi: 10.1186/s12874-019-0731-y
jags, run_model,
run_ume, textConnection
It returns a panel of rankograms with integrated SUCRA curves for each intervention in the network. The function can illustrate the results of a single or two outcomes simultaneously.
rankosucra_plot( full1, full2 = NULL, drug_names1, drug_names2 = NULL, name1 = NULL, name2 = NULL )rankosucra_plot( full1, full2 = NULL, drug_names1, drug_names2 = NULL, name1 = NULL, name2 = NULL )
full1 |
An object of S3 class |
full2 |
An object of S3 class |
drug_names1 |
A vector of labels with the name of the interventions in
the order they appear in the argument |
drug_names2 |
A vector of labels with the name of the interventions in
the order they appear in the argument |
name1 |
The text for the title of the results that refer to
the outcome under |
name2 |
The text for the title of the results that refer to
the outcome under |
Interventions are sorted in the descending order of their SUCRA
value. The SUCRA value expressed in percentage appears on the top left
corner of each panel. In the case of two outcomes, the SUCRA values of the
outcome under the argument full1 are considered to sort the
interventions from the best to the worst.
When a second outcome is also considered, different colours are used to
draw the corresponding SUCRA curves and the rankograms: green for the
outcome under full1, and red for the outcome under full2.
rankosucra_plot can be used only for a network of interventions.
Otherwise, the execution of the function will be stopped and an error
message will be printed on the R console.
A panel of rankograms (yellowish bars) with integrated reddish SUCRA curves for each intervention in the network (Salanti et al., 2011). The x-axis of each panel refers to the ranking, and the y-axis refers to the ranking probability expressed in percentage.
Loukia M. Spineli, Chrysostomos Kalyvas, Katerina Papadimitropoulou
Salanti G, Ades AE, Ioannidis JP. Graphical methods and numerical summaries for presenting results from multiple-treatment meta-analysis: an overview and tutorial. J Clin Epidemiol 2011;64(2):163–71. doi: 10.1016/j.jclinepi.2010.03.016
data("nma.liu2013") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_liu.rds', package = 'rnmamod')) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "pramipexole", "serotonin-norepinephrine reuptake inhibitor", "serotonin reuptake inhibitor", "tricyclic antidepressant", "pergolide") # Create the integrated rankograms and SUCRA curves rankosucra_plot(full1 = res, drug_names1 = interv_names)data("nma.liu2013") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_liu.rds', package = 'rnmamod')) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "pramipexole", "serotonin-norepinephrine reuptake inhibitor", "serotonin reuptake inhibitor", "tricyclic antidepressant", "pergolide") # Create the integrated rankograms and SUCRA curves rankosucra_plot(full1 = res, drug_names1 = interv_names)
Calculates the robustness index, a novel index that quantifies the overall divergence of the sensitivity analysis results from the primary analysis results. The robustness index considers objective decision rules to infer the presence or lack of robustness of the primary analysis results when conducting a sensitivity analysis (Spineli et al., 2021).
robustness_index(sens, threshold)robustness_index(sens, threshold)
sens |
An object of S3 class |
threshold |
A number indicating the threshold of robustness, that is, the minimally allowed deviation between the primary analysis and re-analysis results. See 'Details' below. |
Thresholds of robustness have been proposed only for the odds ratio
and standardised mean difference (Spineli et al., 2021).
The user may consider the values 0.28 and 0.17 in the argument
threshold for the odds ratio and standardised mean difference effect
measures (the default values), respectively, or consider other plausible
values. When the argument threshold has not been defined,
robustness_index considers the default values 0.28 and 0.17 as
threshold for robustness for binary and continuous outcome, respectively,
regardless of the effect measure (the default thresholds may not be proper
choices for other effect measures; hence, use these threshold with great
caution in this case). Spineli et al. (2021) offers a discussion on
specifying the threshold of robustness.
In the case of binary outcome, robustness_index considers the
results in the odds ratio scale to calculate the robustness index.
This is because, the odds ratio is used as the 'best-case' effect measure
in run_model. Then, relative risk, and risk difference are
functions of the odds ratio and the selected baseline risk (See 'Details'
in run_model).
In the case of missing participant outcome data, the primary analysis is
considered to be the middle of the numbers in the argument
mean_scenarios of run_sensitivity (see 'Arguments'
and 'Details' in run_sensitivity).
In robust, the value "robust" appears when
robust_index is less than threshold; otherwise, the value
"frail" appears.
In the case of missing participant outcome data, robustness_index
can be used only when missing participant outcome data have been
extracted for at least one trial. Otherwise, the execution of the function
will be stopped and an error message will be printed in the R console.
robustness_index prints on the R console a message in green
text on the threshold of robustness determined by the user.
Then, the function returns the following list of elements:
robust_index |
A numeric scalar or vector on the robustness
index values. In the case of a pairwise meta-analysis,
|
robust |
A character or character vector (of same length with
|
kld |
A vector or matrix on the Kullback-Leibler divergence
(KLD) measure in the summary effect size from a subsequent re-analysis to
the primary analysis. In the case of a pairwise meta-analysis, |
threshold |
The threshold used to be inherited by the
|
scenarios |
The scenarios considered to be inherited by the
|
Loukia M. Spineli
Kullback S, Leibler RA. On information and sufficiency. Ann Math Stat 1951;22(1):79–86. doi: 10.1214/aoms/1177729694
Spineli LM, Kalyvas C, Papadimitropoulou K. Quantifying the robustness of primary analysis results: A case study on missing outcome data in pairwise and network meta-analysis. Res Synth Methods 2021;12(4):475–90. doi: 10.1002/jrsm.1478
heatmap_robustness, kld_barplot,
run_model, run_sensitivity
data("nma.baker2009") # Read results from 'run_sensitivity' (using the default arguments) res_sens <- readRDS(system.file('extdata/res_sens_baker.rds', package = 'rnmamod')) # Calculate the robustness index robustness_index(sens = res_sens, threshold = 0.28)data("nma.baker2009") # Read results from 'run_sensitivity' (using the default arguments) res_sens <- readRDS(system.file('extdata/res_sens_baker.rds', package = 'rnmamod')) # Calculate the robustness index robustness_index(sens = res_sens, threshold = 0.28)
Calculates the robustness index for a sensitivity analysis (Spineli et al., 2021) performed using the results of the analysis performed via the R-package netmeta or metafor. The user defines the input and the function returns the robustness index.
robustness_index_user(sens, pkg, attribute, threshold)robustness_index_user(sens, pkg, attribute, threshold)
sens |
A list of R objects of class
|
pkg |
Character string indicating the R-package with values
|
attribute |
This is relevant only for
netmeta. A vector of
at least two characters with values |
threshold |
A number indicating the threshold of robustness, that is,
the minimally allowed deviation between the primary analysis (the first
element in |
Thresholds of robustness have been proposed only for the odds ratio
and standardised mean difference (Spineli et al., 2021).
The user may consider the values 0.28 and 0.17 in the argument
threshold for the odds ratio and standardised mean difference effect
measures (the default values), respectively, or consider other plausible
values. When the argument threshold has not been defined,
robustness_index considers the default values 0.28 and 0.17 as
threshold for robustness for binary and continuous outcome, respectively,
regardless of the effect measure (the default thresholds may not be proper
choices for other effect measures; hence, use these threshold with great
caution in this case). Spineli et al. (2021) offers a discussion on
specifying the threshold of robustness.
When other effect measure is used (other than odds ratio or standardised
mean difference) or the elements in sens refer to different effect
measures, the execution of the function will be stopped and an error
message will be printed in the R console.
In robust, the value "robust" appears when the calculated
robust_index is less than threshold; otherwise, the value
"frail" appears.
robustness_index_user prints on the R console a message in
red text on the threshold of robustness determined by the user.
Then, the function returns the following list of elements:
robust_index |
A numeric scalar or vector on the robustness
index values. In the case of a pairwise meta-analysis,
|
robust |
A character or character vector (of same length with
|
kld |
A vector or matrix on the Kullback-Leibler divergence
(KLD) measure in the summary effect size from a subsequent re-analysis to
the primary analysis. In the case of a pairwise meta-analysis, |
attribute |
The attributes considered. |
threshold |
The threshold used to be inherited by the
|
Loukia M. Spineli
Kullback S, Leibler RA. On information and sufficiency. Ann Math Stat 1951;22(1):79–86. doi: 10.1214/aoms/1177729694
Spineli LM, Kalyvas C, Papadimitropoulou K. Quantifying the robustness of primary analysis results: A case study on missing outcome data in pairwise and network meta-analysis. Res Synth Methods 2021;12(4):475–90. doi: 10.1002/jrsm.1478
rma,
rma.glmm,
rma.mh, rma.mv,
rma.peto,
rma.uni,
netmeta,
netmetabin,
heatmap_robustness
## Not run: library(netmeta) data(Baker2009) # Transform from arm-based to contrast-based format p1 <- pairwise(treatment, exac, total, studlab = paste(study, year), data = Baker2009, sm = "OR") # Conduct standard network meta-analysis net1 <- netmeta(p1, ref = "Placebo") # Calculate the robustness index (random-effects versus fixed-effect) robustness_index_user(sens = list(net1, net1), pkg = "netmeta", attribute = c("TE.random", "TE.common"), threshold = 0.28) ## End(Not run)## Not run: library(netmeta) data(Baker2009) # Transform from arm-based to contrast-based format p1 <- pairwise(treatment, exac, total, studlab = paste(study, year), data = Baker2009, sm = "OR") # Conduct standard network meta-analysis net1 <- netmeta(p1, ref = "Placebo") # Calculate the robustness index (random-effects versus fixed-effect) robustness_index_user(sens = list(net1, net1), pkg = "netmeta", attribute = c("TE.random", "TE.common"), threshold = 0.28) ## End(Not run)
Performs a one-stage pairwise or network meta-regression while addressing aggregate binary or continuous missing participant outcome data via the pattern-mixture model.
run_metareg( full, covariate, covar_assumption, n_chains, n_iter, n_burnin, n_thin, inits = NULL )run_metareg( full, covariate, covar_assumption, n_chains, n_iter, n_burnin, n_thin, inits = NULL )
full |
|
covariate |
A numeric vector or matrix for a trial-specific covariate that is a potential effect modifier. See 'Details'. |
covar_assumption |
Character string indicating the structure of the
intervention-by-covariate interaction, as described in
Cooper et al. (2009). Set |
n_chains |
Positive integer specifying the number of chains for the
MCMC sampling; an argument of the |
n_iter |
Positive integer specifying the number of Markov chains for the
MCMC sampling; an argument of the |
n_burnin |
Positive integer specifying the number of iterations to
discard at the beginning of the MCMC sampling; an argument of the
|
n_thin |
Positive integer specifying the thinning rate for the
MCMC sampling; an argument of the |
inits |
A list with the initial values for the parameters; an argument
of the |
run_metareg inherits the arguments data,
measure, model, assumption, heter_prior,
mean_misspar, var_misspar, D, ref,
indic, and base_risk from run_model
(now contained in the argument full). This prevents specifying a
different Bayesian model from that considered in run_model.
Therefore, the user needs first to apply run_model, and then
use run_metareg (see 'Examples').
The model runs in JAGS and the progress of the simulation appears on
the R console. The output of run_metareg is used as an S3 object by
other functions of the package to be processed further and provide an
end-user-ready output. The model is updated until convergence using the
autojags function of the R-package
R2jags with 2 updates and
number of iterations and thinning equal to n_iter and n_thin,
respectively.
The models described in Spineli et al. (2021), and Spineli (2019) have been extended to incorporate one study-level covariate variable following the assumptions of Cooper et al. (2009) for the structure of the intervention-by-covariate interaction. The covariate can be either a numeric vector or matrix with columns equal to the maximum number of arms in the dataset.
A list of R2jags outputs on the summaries of the posterior distribution, and the Gelman-Rubin convergence diagnostic (Gelman et al., 1992) for the following monitored parameters for a fixed-effect pairwise meta-analysis:
EM |
The estimated summary effect measure (according to the argument
|
beta_all |
The estimated regression coefficient for all possible
pairwise comparisons according to the argument |
dev_o |
The deviance contribution of each trial-arm based on the observed outcome. |
hat_par |
The fitted outcome at each trial-arm. |
phi |
The informative missingness parameter. |
For a fixed-effect network meta-analysis, the output additionally includes:
SUCRA |
The surface under the cumulative ranking (SUCRA) curve for each intervention. |
effectiveneness |
The ranking probability of each intervention for every rank. |
For a random-effects pairwise meta-analysis, the output additionally includes the following elements:
EM_pred |
The predicted summary effect measure (according to the
argument |
delta |
The estimated trial-specific effect measure (according to the
argument |
tau |
The between-trial standard deviation. |
In network meta-analysis, EM and EM_pred refer to all
possible pairwise comparisons of interventions in the network. Furthermore,
tau is typically assumed to be common for all observed comparisons
in the network.
For a multi-arm trial, we estimate a total T-1 of delta for
comparisons with the baseline intervention of the trial (found in the first
column of the element t), with T being the number of
interventions in the trial.
Furthermore, the output includes the following elements:
abs_risk |
The adjusted absolute risks for each intervention. This
appears only when |
leverage_o |
The leverage for the observed outcome at each trial-arm. |
sign_dev_o |
The sign of the difference between observed and fitted outcome at each trial-arm. |
model_assessment |
A data-frame on the measures of model assessment: deviance information criterion, number of effective parameters, and total residual deviance. |
jagsfit |
An object of S3 class |
The run_metareg function also returns the arguments data,
measure, model, assumption, covariate,
covar_assumption, n_chains, n_iter, n_burnin,
and n_thin to be inherited by other relevant functions of the
package.
Loukia M. Spineli
Cooper NJ, Sutton AJ, Morris D, Ades AE, Welton NJ. Addressing between-study heterogeneity and inconsistency in mixed treatment comparisons: Application to stroke prevention treatments in individuals with non-rheumatic atrial fibrillation. Stat Med 2009;28(14):1861–81. doi: 10.1002/sim.3594
Gelman A, Rubin DB. Inference from iterative simulation using multiple sequences. Stat Sci 1992;7(4):457–72. doi: 10.1214/ss/1177011136
Spineli LM, Kalyvas C, Papadimitropoulou K. Continuous(ly) missing outcome data in network meta-analysis: a one-stage pattern-mixture model approach. Stat Methods Med Res 2021;30(4):958–75. doi: 10.1177/0962280220983544
Spineli LM. An empirical comparison of Bayesian modelling strategies for missing binary outcome data in network meta-analysis. BMC Med Res Methodol 2019;19(1):86. doi: 10.1186/s12874-019-0731-y
data("nma.baker2009") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_baker.rds', package = 'rnmamod')) # Publication year pub_year <- c(1996, 1998, 1999, 2000, 2000, 2001, rep(2002, 5), 2003, 2003, rep(2005, 4), 2006, 2006, 2007, 2007) # Perform a random-effects network meta-regression (exchangeable structure) # Note: Ideally, set 'n_iter' to 10000 and 'n_burnin' to 1000 run_metareg(full = res, covariate = pub_year, covar_assumption = "exchangeable", n_chains = 3, n_iter = 1000, n_burnin = 100, n_thin = 1)data("nma.baker2009") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_baker.rds', package = 'rnmamod')) # Publication year pub_year <- c(1996, 1998, 1999, 2000, 2000, 2001, rep(2002, 5), 2003, 2003, rep(2005, 4), 2006, 2006, 2007, 2007) # Perform a random-effects network meta-regression (exchangeable structure) # Note: Ideally, set 'n_iter' to 10000 and 'n_burnin' to 1000 run_metareg(full = res, covariate = pub_year, covar_assumption = "exchangeable", n_chains = 3, n_iter = 1000, n_burnin = 100, n_thin = 1)
Performs a one-stage pairwise or network meta-analysis while addressing aggregate binary or continuous missing participant outcome data via the pattern-mixture model.
run_model( data, measure, model, assumption, heter_prior, mean_misspar, var_misspar, D, ref, base_risk, n_chains, n_iter, n_burnin, n_thin, inits = NULL )run_model( data, measure, model, assumption, heter_prior, mean_misspar, var_misspar, D, ref, base_risk, n_chains, n_iter, n_burnin, n_thin, inits = NULL )
data |
A data-frame of the one-trial-per-row format with arm-level data. See 'Format' for the specification of the columns. |
measure |
Character string indicating the effect measure. For a binary
outcome, the following can be considered: |
model |
Character string indicating the analysis model with values
|
assumption |
Character string indicating the structure of the
informative missingness parameter.
Set |
heter_prior |
A list of three elements with the following order:
1) a character string indicating the distribution with
(currently available) values |
mean_misspar |
A scalar or numeric vector of two numeric values for the
mean of the normal distribution of the informative missingness parameter
(see 'Details'). The default argument is 0 and corresponds to the
missing-at-random assumption.
See also 'Details' in |
var_misspar |
A positive non-zero number for the variance of the
normal distribution of the informative missingness parameter.
When the |
D |
A binary number for the direction of the outcome.
Set |
ref |
An integer specifying the reference intervention. The number
should match the intervention identifier under element t in
|
base_risk |
A scalar, a vector of length three with elements sorted in
ascending order, or a matrix with two columns and number of rows equal to
the number of relevant trials. In the case of a scalar or vector, the
elements should be in the interval (0, 1) (see 'Details'). If
|
n_chains |
Positive integer specifying the number of chains for the
MCMC sampling; an argument of the |
n_iter |
Positive integer specifying the number of Markov chains for the
MCMC sampling; an argument of the |
n_burnin |
Positive integer specifying the number of iterations to
discard at the beginning of the MCMC sampling; an argument of the
|
n_thin |
Positive integer specifying the thinning rate for the
MCMC sampling; an argument of the |
inits |
A list with the initial values for the parameters; an argument
of the |
The columns of the data-frame in the argument data refer
to the following elements for a continuous outcome:
| t | An intervention identifier in each arm. |
| y | The observed mean value of the outcome in each arm. |
| sd | The observed standard deviation of the outcome in each arm. |
| m | The number of missing participant outcome data in each arm. |
| n | The number of randomised participants in each arm. |
For a binary outcome, the columns of the data-frame in the argument
data refer to the following elements:
| t | An intervention identifier in each arm. |
| r | The observed number of events of the outcome in each arm. |
| m | The number of missing participant outcome data in each arm. |
| n | The number of randomised participants in each arm. |
The number of rows in data equals the number of collected trials.
Each element appears in data as many times as the maximum number of
interventions compared in a trial of the dataset.
In pairwise meta-analysis, the maximum number of arms is inherently two.
The same holds for a network meta-analysis without multi-arm trials.
In the case of network meta-analysis with multi-arm trials, the maximum
number of arms exceeds two. See 'Examples' that illustrates the structure
of data for a network with a maximum number of four arms.
It is not a prerequisite of run_model that the multi-arm trials
appear at the bottom of the dataset.
The model runs in JAGS and the progress of the simulation
appears on the R console. The output of run_model is used as an S3
object by other functions of the package to be processed further and
provide an end-user-ready output.
The data_preparation function is called to prepare the data
for the Bayesian analysis. data_preparation creates the
pseudo-data-frames m_new, and I, that have the same
dimensions with the element N. m_new takes the zero
value for the observed trial-arms with unreported missing participant
outcome data (i.e., m equals NA for the corresponding
trial-arms), the same value with m for the observed trial-arms with
reported missing participant outcome data, and NA for the unobserved
trial-arms. I is a dummy pseudo-data-frame and takes the value one
for the observed trial-arms with reported missing participant outcome data,
the zero value for the observed trial-arms with unreported missing
participant outcome data (i.e., m_new equals zero for the
corresponding trial-arms), and NA for the unobserved trial-arms.
Thus, I indicates whether missing participant outcome data have been
collected for the observed trial-arms. If the user has not defined the
element m in data, m_new and I take the zero
value for all observed trial-arms to indicate that no missing participant
outcome data have been collected for the analysed outcome. See 'Details' in
data_preparation.
Furthermore, data_preparation sorts the interventions across
the arms of each trial in an ascending order and correspondingly the
remaining elements in data (see 'Format').
data_preparation considers the first column in t as
being the control arm for every trial. Thus, this sorting ensures that
interventions with a lower identifier are consistently treated as the
control arm in each trial. This case is relevant in non-star-shaped
networks.
The model is updated until convergence using the
autojags function of the R-package
R2jags with 2 updates and
number of iterations and thinning equal to n_iter and n_thin,
respectively.
To perform a Bayesian pairwise or network meta-analysis, the
prepare_model function is called which contains the WinBUGS
code as written by Dias et al. (2013a) for binomial and normal likelihood to
analyse aggregate binary and continuous outcome data, respectively.
prepare_model uses the consistency model (as described in
Lu and Ades (2006)) to estimate all possible comparisons in the network.
It also accounts for the multi-arm trials by assigning conditional
univariate normal distributions on the underlying trial-specific effect
size of comparisons with the baseline arm of the multi-arm trial
(Dias et al., 2013a).
The code of Dias et al. (2013a) has been extended to incorporate the
pattern-mixture model to adjust the underlying outcome in each arm of
every trial for missing participant outcome data (Spineli et al., 2021;
Spineli, 2019a; Turner et al., 2015). The assumptions about the
missingness parameter are specified using the arguments mean_misspar
and var_misspar. Specifically, run_model considers the
informative missingness odds ratio in the logarithmic scale for binary
outcome data (Spineli, 2019a; Turner et al., 2015; White et al., 2008), the
informative missingness difference of means when measure is
"MD" or "SMD", and the informative missingness ratio of means
in the logarithmic scale when measure is "ROM"
(Spineli et al., 2021; Mavridis et al., 2015).
When assumption is trial-specific (i.e., "IDE-TRIAL" or
"HIE-TRIAL"), or independent (i.e., "IND-CORR" or
"IND-UNCORR"), only one numeric value can be assigned to
mean_misspar because the same missingness scenario is applied to all
trials and trial-arms of the dataset, respectively. When assumption
is "IDE-ARM" or "HIE-ARM", a maximum of two
different or identical numeric values can be assigned as a
vector to mean_misspars: the first value refers to the experimental
arm, and the second value refers to the control arm of a trial.
In the case of a network, the first value is considered for all
non-reference interventions and the second value is considered for the
reference intervention of the network (i.e., the intervention with
identifier equal to ref). This is necessary to ensure transitivity
in the assumptions for the missingness parameter across the network
(Spineli, 2019b).
When there is at least one trial-arm with unreported missing participant
outcome data (i.e., m equals NA for the corresponding
trial-arms) or when missing participant outcome data have not been
collected for the analysed outcome (i.e., m is missing in
data), run_model assigns the assumption "IND-UNCORR"
to assumption.
Currently, there are no empirically-based prior distributions for the
informative missingness parameters. The user may refer to Spineli (2019),
Turner et al. (2015), Mavridis et al. (2015), and White et al. (2008) to
determine mean_misspar and select a proper value for
var_misspar.
The scalar base_risk refers to a fixed baseline risk for the
selected reference intervention (as specified with ref).
When base_risk is a three-element vector, it refers to a random
baseline risk and the elements should be sorted in ascending order as they
refer to the lower bound, mean value, and upper bound of the 95%
confidence interval for the baseline risk for the selected reference
intervention. The baseline_model function is called to
calculate the mean and variance of the approximately normal distribution of
the logit of an event for ref using these three elements
(Dias et al., 2018). When base_risk is a matrix, it refers to the
predicted baseline risk with first column being the number of events, and
second column being the sample size of the corresponding trials on the
selected reference intervention. Then the baseline_model
function is called that contains the WinBUGS code as written by Dias et al.
(2013b) for the hierarchical baseline model. The posterior mean and
precision of the predictive distribution of the logit of an event
for the selected reference intervention are plugged in the WinBUGS code for
the relative effects model (via the prepare_model function).
The matrix base_risk should not comprise the trials in data
that include the ref, unless justified (Dias et al., 2018).
To obtain unique absolute risks for each intervention, the network
meta-analysis model has been extended to incorporate the transitive risks
framework, namely, an intervention has the same absolute risk regardless of
the comparator intervention(s) in a trial (Spineli et al., 2017).
The absolute risks are a function of the odds ratio (the base-case
effect measure for a binary outcome) and the selected baseline risk for the
reference intervention (ref) (Appendix in Dias et al., 2013a).
We advocate using the odds ratio as an effect measure for its desired
mathematical properties. Then, the relative risk and risk difference can be
obtained as a function of the absolute risks of the corresponding
interventions in the comparison of interest. Hence, regardless of the
selected measure for a binary outcome, run_model performs
pairwise or network meta-analysis based on the odds ratio.
A list of R2jags output on the summaries of the posterior distribution, and the Gelman-Rubin convergence diagnostic (Gelman et al., 1992) of the following monitored parameters for a fixed-effect pairwise meta-analysis:
EM |
The estimated summary effect measure (according to the argument
|
EM_LOR |
The estimated summary odd ratio in the logarithmic scale when
|
dev_o |
The deviance contribution of each trial-arm based on the observed outcome. |
hat_par |
The fitted outcome at each trial-arm. |
phi |
The informative missingness parameter. |
For a fixed-effect network meta-analysis, the output additionally includes:
SUCRA |
The surface under the cumulative ranking curve for each intervention. |
SUCRA_LOR |
The surface under the cumulative ranking curve for each
intervention under the odds ratio effect measure when |
effectiveneness |
The ranking probability of each intervention for every rank. |
For a random-effects pairwise meta-analysis, the output additionally includes the following elements:
EM_pred |
The predicted summary effect measure (according to the
argument |
EM_pred_LOR |
The predicted summary odds ratio in the logarithmic
scale when |
delta |
The estimated trial-specific effect measure (according to the
argument |
tau |
The between-trial standard deviation. |
In network meta-analysis, EM and EM_pred refer to all
possible pairwise comparisons of interventions in the network. Furthermore,
tau is typically assumed to be common for all observed comparisons
in the network. For a multi-arm trial, we estimate a total of T-1
delta for comparisons with the baseline intervention of the trial
(found in the first column of the element t), with T being
the number of interventions in the trial.
Furthermore, the output includes the following elements:
leverage_o |
The leverage for the observed outcome at each trial-arm. |
sign_dev_o |
The sign of the difference between observed and fitted outcome at each trial-arm. |
model_assessment |
A data-frame on the measures of model assessment: deviance information criterion, number of effective parameters, and total residual deviance. |
indic |
The sign of basic parameters in relation to the reference
intervention as specified in argument |
jagsfit |
An object of S3 class |
The run_model function also returns the arguments data,
measure, model, assumption, heter_prior,
mean_misspar, var_misspar, D, ref,
base_risk, n_chains, n_iter, n_burnin,
and n_thin as specified by the user to be inherited by other
functions of the package.
Loukia M. Spineli
Cooper NJ, Sutton AJ, Morris D, Ades AE, Welton NJ. Addressing between-study heterogeneity and inconsistency in mixed treatment comparisons: Application to stroke prevention treatments in individuals with non-rheumatic atrial fibrillation. Stat Med 2009;28(14):1861–81. doi: 10.1002/sim.3594
Dias S, Ades AE, Welton NJ, Jansen JP, Sutton AJ. Network Meta-Analysis for Decision Making. Chichester (UK): Wiley; 2018.
Dias S, Sutton AJ, Ades AE, Welton NJ. Evidence synthesis for decision making 2: a generalized linear modeling framework for pairwise and network meta-analysis of randomized controlled trials. Med Decis Making 2013a;33(5):607–17. doi: 10.1177/0272989X12458724
Dias S, Welton NJ, Sutton AJ, Ades AE. Evidence synthesis for decision making 5: the baseline natural history model. Med Decis Making 2013b;33(5):657–70. doi: 10.1177/0272989X13485155
Gelman A, Rubin DB. Inference from iterative simulation using multiple sequences. Stat Sci 1992;7(4):457–72. doi: 10.1214/ss/1177011136
Lu G, Ades AE. Assessing evidence inconsistency in mixed treatment comparisons. J Am Stat Assoc 2006;101:447–59. doi: 10.1198/016214505000001302
Mavridis D, White IR, Higgins JP, Cipriani A, Salanti G. Allowing for uncertainty due to missing continuous outcome data in pairwise and network meta-analysis. Stat Med 2015;34(5):721–41. doi: 10.1002/sim.6365
Spineli LM, Kalyvas C, Papadimitropoulou K. Continuous(ly) missing outcome data in network meta-analysis: a one-stage pattern-mixture model approach. Stat Methods Med Res 2021;30(4):958–75. doi: 10.1177/0962280220983544
Spineli LM. An empirical comparison of Bayesian modelling strategies for missing binary outcome data in network meta-analysis. BMC Med Res Methodol 2019a;19(1):86. doi: 10.1186/s12874-019-0731-y
Spineli LM. Modeling missing binary outcome data while preserving transitivity assumption yielded more credible network meta-analysis results. J Clin Epidemiol 2019b;105:19–26. doi: 10.1016/j.jclinepi.2018.09.002
Spineli LM, Brignardello-Petersen R, Heen AF, Achille F, Brandt L, Guyatt GH, et al. Obtaining absolute effect estimates to facilitate shared decision making in the context of multiple-treatment comparisons. Abstracts of the Global Evidence Summit, Cape Town, South Africa. Cochrane Database of Systematic Reviews 2017;9(Suppl 1):18911.
Turner NL, Dias S, Ades AE, Welton NJ. A Bayesian framework to account for uncertainty due to missing binary outcome data in pairwise meta-analysis. Stat Med 2015;34(12):2062–80. doi: 10.1002/sim.6475
White IR, Higgins JP, Wood AM. Allowing for uncertainty due to missing data in meta-analysis–part 1: two-stage methods. Stat Med 2008;27(5):711–27. doi: 10.1002/sim.3008
autojags,
baseline_model, data_preparation,
heterogeneity_param_prior,
jags,
missingness_param_prior, prepare_model
data("nma.baker2009") # Show the first six trials of the dataset head(nma.baker2009) # Perform a random-effects network meta-analysis # Note: Ideally, set 'n_iter' to 10000 and 'n_burnin' to 1000 run_model(data = nma.baker2009, measure = "OR", model = "RE", assumption = "IDE-ARM", heter_prior = list("halfnormal", 0, 1), mean_misspar = c(0, 0), var_misspar = 1, D = 0, ref = 1, n_chains = 3, n_iter = 1000, n_burnin = 100, n_thin = 1)data("nma.baker2009") # Show the first six trials of the dataset head(nma.baker2009) # Perform a random-effects network meta-analysis # Note: Ideally, set 'n_iter' to 10000 and 'n_burnin' to 1000 run_model(data = nma.baker2009, measure = "OR", model = "RE", assumption = "IDE-ARM", heter_prior = list("halfnormal", 0, 1), mean_misspar = c(0, 0), var_misspar = 1, D = 0, ref = 1, n_chains = 3, n_iter = 1000, n_burnin = 100, n_thin = 1)
Performs the Bayesian node-splitting approach of Dias et al. (2010) extended to address aggregate binary and continuous missing participant outcome data via the pattern-mixture model (Spineli et al., 2021; Spineli, 2019). This model offers a local evaluation of the plausibility of the consistency assumption in the network (Dias et al., 2010).
run_nodesplit(full, n_chains, n_iter, n_burnin, n_thin, inits = NULL)run_nodesplit(full, n_chains, n_iter, n_burnin, n_thin, inits = NULL)
full |
|
n_chains |
Positive integer specifying the number of chains for the
MCMC sampling; an argument of the |
n_iter |
Positive integer specifying the number of Markov chains for the
MCMC sampling; an argument of the |
n_burnin |
Positive integer specifying the number of iterations to
discard at the beginning of the MCMC sampling; an argument of the
|
n_thin |
Positive integer specifying the thinning rate for the
MCMC sampling; an argument of the |
inits |
A list with the initial values for the parameters; an argument
of the |
run_nodesplit inherits the arguments data,
measure, model, assumption, heter_prior,
mean_misspar, var_misspar, ref, and indic from
run_model (now contained in the argument full).
This prevents specifying a different Bayesian model from that considered
in run_model. Therefore, the user needs first to apply
run_model, and then use run_nodesplit
(see 'Examples').
For a binary outcome, when measure is "RR" (relative risk) or "RD"
(risk difference) in run_model, run_nodesplit
currently performs node-splitting using the odds ratio as effect measure
for being the base-case effect measure in run_model
for a binary outcome (see also 'Details' in run_model).
To perform the Bayesian node-splitting approach, the
prepare_nodesplit function is called which contains the
WinBUGS code as written by Dias et al. (2010) for binomial and normal
likelihood to analyse binary and continuous outcome data, respectively.
prepare_nodesplit has been extended to incorporate the
pattern-mixture model with informative missingness parameters for binary
and continuous outcome data (see 'Details' in run_model).
run_nodesplit runs the Bayesian node-splitting approach in
JAGS. The progress of the simulation appears on the R console. The
number of times run_nodesplit is used appears on the R console as a
text in red and it equals the number of split nodes (see 'Examples').
If there are no split nodes in the network, the execution of the function
will be stopped and an error message will be printed on the R console.
The model is updated until convergence using the
autojags function of the R-package
R2jags with 2 updates and
number of iterations and thinning equal to n_iter and n_thin,
respectively.
run_nodesplit uses the
mtc.nodesplit.comparisons
function of the R-package
gemtc
to obtain automatically the nodes to split based on the decision rule of
van Valkenhoef et al. (2016).
run_nodesplit uses the option (1) in van Valkenhoef et al. (2016)
to parameterise multi-arm trials that contain the node-to-split.
In contrast,
mtc.nodesplit.comparisons
uses the option (3) in van Valkenhoef et al. (2016).
Option (1) keeps the baseline arm of the node-to-split in the corresponding
multi-arms. Option (3) excludes both arms of the node-to-split from the
corresponding multi-arm trials.
The output of run_nodesplit is not end-user-ready.
The nodesplit_plot function inherits the output of
run_nodesplit as an S3 object and processes it further to provide an
end-user-ready output.
run_nodesplit can be used only for a network of interventions.
In the case of two interventions, the execution of the function will
be stopped and an error message will be printed on the R console.
An R2jags output on the summaries of the posterior distribution, and the Gelman-Rubin convergence diagnostic of the following monitored parameters:
direct |
The summary effect measure (according to the argument
|
indirect |
The indirect summary effect measure (according to the
argument |
diff |
The inconsistency parameter for each split node defined as the difference between the direct and indirect effect of the corresponding split node. |
tau |
The between-trial standard deviation after each split node, when the random-effects model has been specified. |
Furthermore, the output includes the following element:
model_assessment |
A data-frame on the measures of model assessment after each split node: deviance information criterion, total residual deviance, and number of effective parameters. |
Loukia M. Spineli
Dias S, Welton NJ, Caldwell DM, Ades AE. Checking consistency in mixed treatment comparison meta-analysis. Stat Med 2010;29(7-8):932–44. doi: 10.1002/sim.3767
Gelman A, Rubin DB. Inference from iterative simulation using multiple sequences. Stat Sci 1992;7(4):457–72. doi: 10.1214/ss/1177011136
Spineli LM, Kalyvas C, Papadimitropoulou K. Continuous(ly) missing outcome data in network meta-analysis: a one-stage pattern-mixture model approach. Stat Methods Med Res 2021;30(4):958–75. doi: 10.1177/0962280220983544
Spineli LM. An empirical comparison of Bayesian modelling strategies for missing binary outcome data in network meta-analysis. BMC Med Res Methodol 2019;19(1):86. doi: 10.1186/s12874-019-0731-y
van Valkenhoef G, Dias S, Ades AE, Welton NJ. Automated generation of node-splitting models for assessment of inconsistency in network meta-analysis. Res Synth Methods 2016;7(1):80–93. doi: 10.1002/jrsm.1167
autojags,
jags,
mtc.nodesplit.comparisons,
nodesplit_plot, prepare_nodesplit,
run_model
data("nma.baker2009") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_baker.rds', package = 'rnmamod')) # Run random-effects node-splitting approach # Note: Ideally, set 'n_iter' to 10000 and 'n_burnin' to 1000 run_nodesplit(full = res, n_chains = 3, n_iter = 1000, n_burnin = 100, n_thin = 1)data("nma.baker2009") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_baker.rds', package = 'rnmamod')) # Run random-effects node-splitting approach # Note: Ideally, set 'n_iter' to 10000 and 'n_burnin' to 1000 run_nodesplit(full = res, n_chains = 3, n_iter = 1000, n_burnin = 100, n_thin = 1)
Performs a sensitivity analysis by applying pairwise meta-analysis or network meta-analysis for a series of different scenarios about the informative missingness parameter.
run_sensitivity( full, assumption, mean_scenarios, var_misspar, n_chains, n_iter, n_burnin, n_thin, inits = NULL )run_sensitivity( full, assumption, mean_scenarios, var_misspar, n_chains, n_iter, n_burnin, n_thin, inits = NULL )
full |
|
assumption |
Character string indicating the structure of the
informative missingness parameter. Set |
mean_scenarios |
A vector with numeric values for the mean of the normal distribution of the informative missingness parameter (see 'Details'). The vector should have a length equal to 5 or larger. The missing-at-random (MAR) assumption should be the median of the vector, so that the same number of informative scenarios appear before and after the MAR. The default scenarios are c(-log(3), -log(2), log(0.9999), log(2), log(3)) and c(-2, -1, 0, 1, 2) for binary and continuous outcome data, respectively. |
var_misspar |
A positive non-zero number for the variance of the normal
distribution of the informative missingness parameter. When the
|
n_chains |
Integer specifying the number of chains for the MCMC
sampling; an argument of the |
n_iter |
Integer specifying the number of Markov chains for the MCMC
sampling; an argument of the |
n_burnin |
Integer specifying the number of iterations to discard at the
beginning of the MCMC sampling; an argument of the
|
n_thin |
Integer specifying the thinning rate for the MCMC sampling; an
argument of the |
inits |
A list with the initial values for the parameters; an argument
of the |
The model runs in JAGS and the progress of the simulation
appears on the R console. The number of times run_sensitivity is
used appears on the R console as a text in red and it equals the
number of scenarios defined as the square of the length of the
vector specified in mean_scenarios (see 'Examples').
The output of run_sensitivity is used as an S3 object by other
functions of the package to be processed further and provide an
end-user-ready output.
In the case of pairwise meta-analysis, EM and tau are
estimated as many times as the number of scenarios considered.
In the case of network meta-analysis, each possible pairwise comparison is
estimated as many times as the number of scenarios considered.
The informative missingness parameter is assumed to differ only across the
interventions of the dataset. Therefore, the user can specify the
informative missingness parameter to be arm-specific and identical
(assumption = "IDE-ARM"), or arm-specific and
hierarchical (assumption = "HIE-ARM") (Spineli et al., 2021).
The length of the vector specified in argument mean_scenarios should
be equal to or more than 5 (a positive odd integer) to allow for an
adequate number of scenarios. It is important that the number
corresponding to the MAR assumption is the middle of the numbers in the
vector specified in argument mean_scenarios. The MAR
assumption constitutes the primary analysis.
Under the informative missingness difference of means parameter (relevant
for the raw and standardised mean diffenre), the MAR assumption equals 0.
Under the informative missingness odds ratio parameter (IMOR; relevant for
the odds ratio) and the informative missingness ratio of means (IMRoM;
relevant for the ratio of means) parameter, the MAR assumption equals 1;
however, both parameters are analysed in the logarithmic scale. We advise
using the value 0.999 rather than 1 in mean_scenarios
for the IMOR and IMRoM parameters; otherwise, the execution of the function
will be stopped and the error 'Invalid parent values' will be printed on
the R console.
Currently, there are no empirically-based prior distributions for the
informative missingness parameters. The users may refer to Spineli (2019),
Mavridis et al. (2015), Turner et al. (2015), and White et al. (2008) to
determine mean_scenarios for an informative missingness mechanism
and select a proper value for var_misspar.
run_sensitivity inherits the arguments data,
measure, model, heter_prior, D, indic,
base_risk, and ref from run_model
(now contained in the argument full). This prevents specifying a
different Bayesian model from that considered in the primary analysis
(via run_model)–an exception in the assumption
argument as it is restricted to only two character strings. Therefore, the
user needs first to apply run_model, and then use
run_sensitivity (see 'Examples').
The run_sensitivity function also returns the arguments
measure, scenarios, D, heter, n_chains,
n_iter, n_burnin, and n_thin as specified by the user
to be inherited by other relevant functions of the package.
The model is updated until convergence using the
autojags function of the R-package
R2jags with 2 updates and
number of iterations and thinning equal to n_iter and n_thin,
respectively.
run_sensitivity can be used only when missing participant
outcome data have been extracted for at least one trial. Otherwise, the
execution of the function will be stopped and an error message will be
printed on the R console.
A list of R2jags outputs on the summaries of the posterior distribution, and the Gelman-Rubin convergence diagnostic (Gelman et al., 1992) of the following monitored parameters for a random-effects pairwise meta-analysis:
EM |
The estimated summary effect measure (according to the
argument |
EM_LOR |
The estimated summary odd ratio in the logarithmic scale when
|
tau |
The between-trial standard deviation. This element does not appear in the case of a fixed-effect pairwise meta-analysis. |
In a random-effects network meta-analysis, EM refer to all possible
pairwise comparisons of interventions in the network. Furthermore,
tau is typically assumed to be common for all observed comparisons
in the network.
Loukia M. Spineli
Gelman, A, Rubin, DB. Inference from iterative simulation using multiple sequences. Stat Sci 1992;7(4):457–72. doi: 10.1214/ss/1177011136
Mavridis D, White IR, Higgins JP, Cipriani A, Salanti G. Allowing for uncertainty due to missing continuous outcome data in pairwise and network meta-analysis. Stat Med 2015;34(5):721–41. doi: 10.1002/sim.6365
Spineli LM, Kalyvas C, Papadimitropoulou K. Quantifying the robustness of primary analysis results: A case study on missing outcome data in pairwise and network meta-analysis. Res Synth Methods 2021;12(4):475–90. doi: 10.1002/jrsm.1478
Spineli LM. An empirical comparison of Bayesian modelling strategies for missing binary outcome data in network meta-analysis. BMC Med Res Methodol 2019;19(1):86. doi: 10.1186/s12874-019-0731-y
Turner NL, Dias S, Ades AE, Welton NJ. A Bayesian framework to account for uncertainty due to missing binary outcome data in pairwise meta-analysis. Stat Med 2015;34(12):2062–80. doi: 10.1002/sim.6475
White IR, Higgins JP, Wood AM. Allowing for uncertainty due to missing data in meta-analysis–part 1: two-stage methods. Stat Med 2008;27(5):711–27. doi: 10.1002/sim.3008
data("pma.taylor2004") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_taylor.rds', package = 'rnmamod')) # Perform the sensitivity analysis (default arguments) # Note: Ideally, set 'n_iter' to 10000 and 'n_burnin' to 1000 run_sensitivity(full = res, assumption = "IDE-ARM", var_misspar = 1, n_chains = 3, n_iter = 1000, n_burnin = 100, n_thin = 5)data("pma.taylor2004") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_taylor.rds', package = 'rnmamod')) # Perform the sensitivity analysis (default arguments) # Note: Ideally, set 'n_iter' to 10000 and 'n_burnin' to 1000 run_sensitivity(full = res, assumption = "IDE-ARM", var_misspar = 1, n_chains = 3, n_iter = 1000, n_burnin = 100, n_thin = 5)
Performs a Bayesian pairwise meta-analysis for each pairwise comparison with at least two trials in the network.
run_series_meta(full, n_chains, n_iter, n_burnin, n_thin, inits = NULL)run_series_meta(full, n_chains, n_iter, n_burnin, n_thin, inits = NULL)
full |
|
n_chains |
Integer specifying the number of chains for the MCMC
sampling; an argument of the |
n_iter |
Positive integer specifying the number of Markov chains for the
MCMC sampling; an argument of the |
n_burnin |
Positive integer specifying the number of iterations to
discard at the beginning of the MCMC sampling; an argument of the
|
n_thin |
Positive integer specifying the thinning rate for the MCMC
sampling; an argument of the |
inits |
A list with the initial values for the parameters; an argument
of the |
run_series_meta inherits the arguments data,
measure, model, assumption, heter_prior,
mean_misspar, and var_misspar from run_model
(now contained in the argument full). This prevents specifying
a different Bayesian model from that considered in run_model.
Therefore, the user needs first to apply run_model, and then
use run_series_meta (see 'Examples').
For a binary outcome, when measure is "RR" (relative risk) or "RD"
(risk difference) in run_model, run_series_meta
currently performs a series of pairwise meta-analysis using the odds ratio
as effect measure for being the base-case effect measure in
run_model for a binary outcome (see also 'Details' in
run_model).
run_series_meta runs a series of Bayesian pairwise meta-analyses
in JAGS. The progress of the simulation appears on the R console.
The number of times the function is used is also printed on the console
(in red) and is equal to the number of observed pairwise comparisons
in the network (see 'Examples').
The model is updated until convergence using the
autojags function of the R-package
R2jags with 2 updates and
number of iterations and thinning equal to n_iter and n_thin,
respectively.
The output of run_series_meta is not end-user-ready. The
series_meta_plot function inherits the output of
run_series_meta as an S3 object and processes it further to provide
an end-user-ready output.
run_series_meta can be used only for a network of interventions.
In the case of two interventions, the execution of the function will
be stopped and an error message will be printed on the R console.
An R2jags output on the summaries of the posterior distribution, and the Gelman-Rubin convergence diagnostic (Gelman et al., 1992) of the following monitored parameters:
EM |
The summary effect estimate (according to the argument
|
tau |
The between-trial standard deviation for pairwise comparisons with at least two trials, when the random-effects model has been specified. |
single |
A binary vector that indicates the comparisons in |
Loukia M. Spineli
Gelman A, Rubin DB. Inference from iterative simulation using multiple sequences. Stat Sci 1992;7(4):457–72. doi: 10.1214/ss/1177011136
jags,
run_model, series_meta_plot
data("nma.dogliotti2014") # Show the first six trials of the dataset (one-trial-per-row format) head(nma.dogliotti2014) # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_dogliotti.rds', package = 'rnmamod')) # Run separate random-effects pairwise meta-analyses # Note: Ideally, set 'n_iter' to 10000 and 'n_burnin' to 1000 run_series_meta(full = res, n_chains = 3, n_iter = 1000, n_burnin = 100, n_thin = 1)data("nma.dogliotti2014") # Show the first six trials of the dataset (one-trial-per-row format) head(nma.dogliotti2014) # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_dogliotti.rds', package = 'rnmamod')) # Run separate random-effects pairwise meta-analyses # Note: Ideally, set 'n_iter' to 10000 and 'n_burnin' to 1000 run_series_meta(full = res, n_chains = 3, n_iter = 1000, n_burnin = 100, n_thin = 1)
Performs the unrelated mean effects model of Dias et al. (2013) that has been refined (Spineli, 2021) and extended to address aggregate binary and continuous missing participant outcome data via the pattern-mixture model (Spineli et al. 2021; Spineli, 2019). This model offers a global evaluation of the plausibility of the consistency assumption in the network.
run_ume(full, n_iter, n_burnin, n_chains, n_thin, inits = NULL)run_ume(full, n_iter, n_burnin, n_chains, n_thin, inits = NULL)
full |
|
n_iter |
Positive integer specifying the number of Markov chains for the
MCMC sampling; an argument of the |
n_burnin |
Positive integer specifying the number of iterations to
discard at the beginning of the MCMC sampling; an argument of the
|
n_chains |
Positive integer specifying the number of chains for the MCMC
sampling; an argument of the |
n_thin |
Positive integer specifying the thinning rate for the MCMC
sampling; an argument of the |
inits |
A list with the initial values for the parameters; an argument
of the |
run_ume inherits the arguments data,
measure, model, assumption, heter_prior,
mean_misspar, var_misspar, and ref from
run_model.
This prevents specifying a different Bayesian model from that considered in
run_model.Therefore, the user needs first to apply
run_model, and then use run_ume (see 'Examples').
The run_ume function also returns the arguments data,
model, measure, assumption, n_chains,
n_iter, n_burnin, and n_thin as specified by the user
to be inherited by other relevant functions of the package.
Initially, run_ume calls the improved_ume function to
identify the frail comparisons, that is, comparisons between
non-baseline interventions in multi-arm trials not investigated in any
two-arm or multi-arm trial of the network (Spineli, 2021). The 'original'
model of Dias et al. (2013) omits the frail comparisons from the estimation
process. Consequently, the number of estimated summary effects is less
than those obtained by performing separate pairwise meta-analyses
(see run_series_meta).
For a binary outcome, when measure is "RR" (relative risk) or "RD"
(risk difference) in run_model, run_ume currently
considers the odds ratio as effect measure for being the base-case
effect measure in run_model for a binary outcome
(see also 'Details' in run_model).
run_ume calls the prepare_ume function which contains
the WinBUGS code as written by Dias et al. (2013) for binomial and normal
likelihood to analyse binary and continuous outcome data, respectively.
prepare_ume has been extended to incorporate the
pattern-mixture model with informative missingness parameters for binary
and continuous outcome data (see 'Details' in run_model).
prepare_ume has also been refined to account for the
multi-arm trials by assigning conditional univariate normal distributions
on the underlying trial-specific effect size of comparisons with the
baseline arm of the multi-arm trial (Spineli, 2021).
run_ume runs Bayesian unrelated mean effects model in JAGS.
The progress of the simulation appears on the R console. The model is
updated until convergence using the autojags
function of the R-package
R2jags with 2 updates and
number of iterations and thinning equal to n_iter and n_thin,
respectively.
The output of run_ume is not end-user-ready. The
ume_plot function uses the output of run_ume as an S3
object and processes it further to provide an end-user-ready output.
run_ume can be used only for a network of interventions. In the case
of two interventions, the execution of the function will be stopped and an
error message will be printed on the R console.
An R2jags output on the summaries of the posterior distribution, and the Gelman-Rubin convergence diagnostic (Gelman et al., 1992) of the following monitored parameters:
EM |
The summary effect estimate (according to the argument
|
dev_o |
The deviance contribution of each trial-arm based on the observed outcome. |
hat_par |
The fitted outcome at each trial-arm. |
tau |
The between-trial standard deviation (assumed common across the observed pairwise comparisons) for the whole network, when a random-effects model has been specified. |
m_tau |
The between-trial standard deviation (assumed common across the observed pairwise comparisons) for the subset of multi-arm trials, when a random-effects model has been specified. |
The output also includes the following elements:
leverage_o |
The leverage for the observed outcome at each trial-arm. |
sign_dev_o |
The sign of the difference between observed and fitted outcome at each trial-arm. |
model_assessment |
A data-frame on the measures of model assessment: deviance information criterion, number of effective parameters, and total residual deviance. |
jagsfit |
An object of S3 class |
Furthermore, run_ume returns a character vector with the pairwise
comparisons observed in the network, obs_comp, and a character
vector with comparisons between the non-baseline interventions observed in
multi-arm trials only, frail_comp. Both vectors are used in
ume_plot function.
Loukia M. Spineli
Dias S, Welton NJ, Sutton AJ, Caldwell DM, Lu G, Ades AE. Evidence synthesis for decision making 4: inconsistency in networks of evidence based on randomized controlled trials. Med Decis Making 2013;33(5):641–56. doi: 10.1177/0272989X12455847
Gelman A, Rubin DB. Inference from iterative simulation using multiple sequences. Stat Sci 1992;7(4):457–72. doi: 10.1214/ss/1177011136
Spineli LM. A Revised Framework to Evaluate the Consistency Assumption Globally in a Network of Interventions. Med Decis Making 2021. doi: 10.1177/0272989X211068005
Spineli LM, Kalyvas C, Papadimitropoulou K. Continuous(ly) missing outcome data in network meta-analysis: a one-stage pattern-mixture model approach. Stat Methods Med Res 2021;30(4):958–75. doi: 10.1177/0962280220983544
Spineli LM. An empirical comparison of Bayesian modelling strategies for missing binary outcome data in network meta-analysis. BMC Med Res Methodol 2019;19(1):86. doi: 10.1186/s12874-019-0731-y
autojags,
jags,
prepare_ume, run_model,
run_series_meta, ume_plot
data("nma.liu2013") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_liu.rds', package = 'rnmamod')) # Run random-effects unrelated mean effects model # Note: Ideally, set 'n_iter' to 10000 and 'n_burnin' to 1000 run_ume(full = res, n_chains = 3, n_iter = 1000, n_burnin = 100, n_thin = 1)data("nma.liu2013") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_liu.rds', package = 'rnmamod')) # Run random-effects unrelated mean effects model # Note: Ideally, set 'n_iter' to 10000 and 'n_burnin' to 1000 run_ume(full = res, n_chains = 3, n_iter = 1000, n_burnin = 100, n_thin = 1)
Creates a scatterplot of the SUCRA values from the network meta-analysis and the network meta-regression for a specified level or value of the investigated covariate.
scatterplot_sucra(full, reg, cov_value, drug_names)scatterplot_sucra(full, reg, cov_value, drug_names)
full |
|
reg |
An object of S3 class |
cov_value |
A list of two elements in the following order: 1) a number
for the covariate value of interest (see 'Arguments' in
|
drug_names |
A vector of labels with the name of the interventions in
the order they appear in the argument |
The names of the interventions appear above each point in the plot. Three coloured rectangles are drawn in the scatterplot: a red rectangle for SUCRA values up to 50%, a yellow rectangular for SUCRA values between 50% and 80%, and a green rectangle for SUCRA values over 80%. Interventions falling at the green area are considered as the highest ranked interventions, whilst interventions falling at the red area are considered as the lowest ranked interventions.
When the covariate is binary, specify in the second element of
cov_value the name of the level for which the scatterplot will be
created.
scatterplot_sucra is integrated in metareg_plot.
scatterplot_sucra can be used only for a network of interventions.
Otherwise, the execution of the function will be stopped and an error
message will be printed on the R console.
A scatterplot of the SUCRA values under the network meta-analysis (y-axis) against the SUCRA values under the network meta-regression (x-axis) for a specified level or value of the investigated covariate.
Loukia M. Spineli
Salanti G, Ades AE, Ioannidis JP. Graphical methods and numerical summaries for presenting results from multiple-treatment meta-analysis: an overview and tutorial. J Clin Epidemiol 2011;64(2):163–71. doi: 10.1016/j.jclinepi.2010.03.016
metareg_plot, run_metareg,
run_model
Illustrates the posterior mean of deviance contribution of the
individual data points under the unrelated mean effects model (via
run_ume) against the posterior mean of deviance contribution
under the consistency model (via run_model).
scatterplots_dev(full, ume, colour)scatterplots_dev(full, ume, colour)
full |
A numeric vector with the posterior mean of deviance obtained
using the consistency model (see 'Value' in |
ume |
A numeric vector with the posterior mean of deviance obtained
using the unrelated mean effects model (see 'Value' in
|
colour |
A string to define the colour of the points in the plot. |
scatterplots_dev is integrated in the ume_plot
function to compare the models regarding the posterior mean of deviance.
This scatterplot has also been considered by Dias et al. (2013).
When the majority of data points are scattered across the diagonal line,
we may conclude that the compared models have a good agreement. Data points
systematically scattered above or below the diagonal line may
contribute more to the poor fit of the unrelated mean effects model and the
consistency model, respectively.
A scatterplot of the posterior mean deviance contribution of the
individual data points from the unrelated mean effects model against those
from the consistency model. Each data point corresponds to a trial-arm
indicated by a pair of numbers. The first number refers to the position
of the trial in the dataset, and the second number refers to the
corresponding trial-arm (see 'Arguments' and 'Value' in
data_preparation).
Loukia M. Spineli
Dias S, Welton NJ, Sutton AJ, Caldwell DM, Lu G, Ades AE. Evidence synthesis for decision making 4: inconsistency in networks of evidence based on randomized controlled trials. Med Decis Making 2013a;33(5):641–56. doi: 10.1177/0272989X12455847
data_preparation, run_model,
run_ume, ume_plot
Facilitates the comparison of the consistency model
(via run_model) with a series of pairwise meta-analyses
(via run_series_meta) regarding the estimated summary effect
sizes and between-trial standard deviation for comparisons with at
least two trials.
series_meta_plot(full, meta, drug_names, save_xls)series_meta_plot(full, meta, drug_names, save_xls)
full |
|
meta |
An object of S3 class |
drug_names |
A vector of labels with the name of the interventions in
the order they appear in the argument |
save_xls |
Logical to indicate whether to export the tabulated results
to an 'xlsx' file (via the |
series_meta_plot can be used only for a network of
interventions. Otherwise, the execution of the function will be stopped and
an error message will be printed on the R console.
For a binary outcome, when measure is "RR" (relative risk) or "RD"
(risk difference) in run_model, series_meta_plot
currently presents the results in the odds ratio for being the
base-case effect measure in run_model for a binary
outcome (see also 'Details' in run_model).
The user can detect any inconsistencies in the estimated effects from the compared models and explore the gains in precision stemming from applying network meta-analysis. Furthermore, the user can investigate the plausibility of the common between-trial heterogeneity assumption which is typically considered in network meta-analysis.
The R console prints the data-frame with the estimated summary effect sizes and between-trial standard deviation of comparisons under both models. The comparisons have at least two trials. In the case of a fixed-effect model, the data-frame is printed without the results on the between-trial standard deviation.
Furthermore, series_meta_plot exports the data-frame to an 'xlsx'
file at the working directory of the user.
series_meta_plot returns a panel of two forest plots: (1) a
forest plot on the posterior median and 95% credible interval of the summary
effect size for the observed comparisons from network meta-analysis and the
corresponding pairwise meta-analyses, and (2) a forest plot on the
posterior median and 95% credible interval of the between-trial standard
deviation for these observed comparisons. The estimated median and 95%
credible intervals of the between-trial standard deviation from network
meta-analysis appear in the forest plot as a solid and two dotted parallel
blue lines, respectively. The different levels of heterogeneity appear as
green, yellow, orange, and red rectangles to indicate a low, reasonable,
fairly high, and fairly extreme heterogeneity, respectively, following the
classification of Spiegelhalter et al. (2004).
When a fixed-effect model has been fitted, only the forest plot on the
estimated summary effect sizes is shown.
Loukia M. Spineli
Spiegelhalter DJ, Abrams KR, Myles JP. Bayesian approaches to clinical trials and health-care evaluation. John Wiley and Sons, Chichester, 2004.
run_model, run_series_meta,
write_xlsx
data("nma.dogliotti2014") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_dogliotti.rds', package = 'rnmamod')) # Read results from 'run_series_meta' (using the default arguments) meta <- readRDS(system.file('extdata/meta_dogliotti.rds', package = 'rnmamod')) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "aspirin", "aspirin plus clopidogrel", "dabigatran 110 mg", "dabigatran 150 mg", "rivaroxaban", "vitamin K antagonist", "apixaban") # Plot the results from both models series_meta_plot(full = res, meta = meta, drug_names = interv_names)data("nma.dogliotti2014") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_dogliotti.rds', package = 'rnmamod')) # Read results from 'run_series_meta' (using the default arguments) meta <- readRDS(system.file('extdata/meta_dogliotti.rds', package = 'rnmamod')) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "aspirin", "aspirin plus clopidogrel", "dabigatran 110 mg", "dabigatran 150 mg", "rivaroxaban", "vitamin K antagonist", "apixaban") # Plot the results from both models series_meta_plot(full = res, meta = meta, drug_names = interv_names)
Applies the pattern-mixture model under a specific assumption about the informative missingness parameter in trial-arms with continuous missing participant outcome data and uses the Taylor series to obtain the effect size and standard error for each trial (Mavridis et al., 2015).
taylor_continuous(data, measure, mean_value, var_value, rho)taylor_continuous(data, measure, mean_value, var_value, rho)
data |
A data-frame in the long arm-based format. Two-arm trials occupy one row in the data-frame. Multi-arm trials occupy as many rows as the number of possible comparisons among the interventions. See 'Format' for the specification of the columns. |
measure |
Character string indicating the effect measure with values
|
mean_value |
A numeric value for the mean of the normal distribution of the informative missingness parameter. The same value is considered for all trial-arms of the dataset. The default argument is 0 and corresponds to the missing-at-random assumption. For the informative missingness ratio of means, the mean value is defined in the logarithmic scale. |
var_value |
A positive non-zero number for the variance of the normal
distribution of the informative missingness parameter. When the
|
rho |
A numeric value in the interval [-1, 1] that indicates the correlation coefficient between two informative missingness parameters in a trial. The same value is considered across all trials of the dataset. The default argument is 0 and corresponds to uncorrelated missingness parameters. |
The columns of the data-frame in the argument data refer to
the following ordered elements for a continuous outcome:
| id | A unique identifier for each trial. |
| y1 | The observed mean outcome in the first arm of the comparison. |
| y2 | The observed mean outcome in the second arm of the comparison. |
| sd1 | The observed standard deviation of the outcome in the first arm of the comparison. |
| sd2 | The observed standard deviation of the outcome in the second arm of the comparison. |
| m1 | The number of missing participants in the first arm of the comparison. |
| m2 | The number of missing participants in the second arm of the comparison. |
| n1 | The number randomised in the first arm of the comparison. |
| n2 | The number randomised in the second arm of the comparison. |
| t1 | An identifier for the intervention in the first arm of the comparison. |
| t2 | An identifier for the intervention in the second arm of the comparison. |
The taylor_continuous function is integrated in the
unrelated_effects_plot function.
A data-frame that additionally includes the following elements:
EM |
The effect size adjusted for the missing participants and obtained using the Taylor series. |
se.EM |
The standard error of the effect size adjusted for the missing participants and obtained using the Taylor series. |
Loukia M. Spineli
Mavridis D, White IR, Higgins JP, Cipriani A, Salanti G. Allowing for uncertainty due to missing continuous outcome data in pairwise and network meta-analysis. Stat Med 2015;34(5):721–41. doi: 10.1002/sim.6365
run_model, unrelated_effects_plot
Applies the pattern-mixture model under a specific assumption about the informative missingness odds ratio in trial-arms with binary missing participant outcome data and uses the Taylor series to obtain the odds ratio (in the logarithmic scale) and standard error for each trial (White et al., 2008).
taylor_imor(data, mean_value, var_value, rho)taylor_imor(data, mean_value, var_value, rho)
data |
A data-frame in the long arm-based format. Two-arm trials occupy one row in the data-frame. Multi-arm trials occupy as many rows as the number of possible comparisons among the interventions. See 'Format' for the specification of the columns. |
mean_value |
A numeric value for the mean of the normal distribution of the informative missingness odds ratio in the logarithmic scale. The same value is considered for all trial-arms of the dataset. The default argument is 0 and corresponds to the missing-at-random assumption. |
var_value |
A positive non-zero number for the variance of the normal distribution of the informative missingness odds ratio in the logarithmic scale. The default argument is 1. |
rho |
A numeric value in the interval [-1, 1] that indicates the correlation coefficient between two missingness parameters in a trial. The same value is considered across all trials of the dataset. The default argument is 0 and corresponds to uncorrelated missingness parameters. |
The columns of the data-frame in the argument data refer to
the following ordered elements for a binary outcome:
| id | A unique identifier for each trial. |
| r1 | The observed number of events in the first arm of the comparison. |
| r2 | The observed number of events in the second arm of the comparison. |
| m1 | The number of missing participants in the first arm of the comparison. |
| m2 | The number of missing participants in the second arm of the comparison. |
| n1 | The number of participants randomised in the first arm of the comparison. |
| n2 | The number of participants randomised in the second arm of the comparison. |
| t1 | An identifier for the intervention in the first arm of the comparison. |
| t2 | An identifier for the intervention in the second arm of the comparison. |
The taylor_imor function is integrated in the
unrelated_effects_plot function.
A data-frame that additionally includes the following elements:
EM |
The odds ratio in the logarithmic scale (log OR) adjusted for missing participants and obtained using the Taylor series. |
se.EM |
The standard error of the log OR adjusted for missing participants and obtained using the Taylor series. |
Loukia M. Spineli
White IR, Higgins JP, Wood AM. Allowing for uncertainty due to missing data in meta-analysis–part 1: two-stage methods. Stat Med 2008;27(5):711–27. doi: 10.1002/sim.3008
run_model, unrelated_effects_plot
Classifies a systematic review with multiple interventions as having low, unclear or high quality regarding the transitivity evaluation.
trans_quality( plan_protocol, plan_methods, report_results, discuss_trans, proper_table )trans_quality( plan_protocol, plan_methods, report_results, discuss_trans, proper_table )
plan_protocol |
Character string that indicates how the systematic
review planned in the protocol to assess the transitivity assumption. The
following values can be considered: |
plan_methods |
Character string that indicates whether the systematic
review described in the methods section a strategy to assess the
transitivity assumption. The following values can be considered:
|
report_results |
Character string that indicates whether the systematic
review reported in the results section the transitivity evaluation and
which strategy was employed. The following values can be considered:
|
discuss_trans |
Character string that indicates whether the systematic
review discussed the transitivity assumption and which model parameters
where considered. The following values can be considered: |
proper_table |
Character string that indicates whether the systematic
review reported a proper table of characteristics. The following values can
be considered: |
A systematic review with "Low" quality of transitivity
evaluation does not provide a protocol, nor describe the evaluation
strategy in the methods section, does not report the evaluation results,
nor discusses the transitivity evaluation and does not provide a table of
characteristics. On the contrary, a systematic review with "High"
quality of transitivity evaluation provides an evaluation plan in the
protocol (including at least one direct method), describes the evaluation
strategy in the methods section (including at least one direct method),
reports the evaluation results in the results section, discusses the
transitivity evaluation while considering at least one model parameter
(if NMA has been conducted), and provides a proper table of
characteristics. Otherwise, the systematic review is judged to have an
"Unclear" quality of transitivity evaluation.
A character with value "Low", "Unclear", or
"High" to indicate low, unclear, or high-quality of transitivity
evaluation.
Loukia M. Spineli
Spineli LM, Kalyvas C, Seide SE, Papadimitropoulou K. Low awareness of the transitivity assumption in complex networks of interventions: empirical evidence from 356 network meta-analyses. 2022 submitted
ume_plot hosts a toolkit of functions that facilitates
the comparison of the consistency model (via run_model) with
the unrelated mean effects model (via run_ume) regarding the
posterior summaries of the summary effect size for the pairwise comparisons
observed in the network, the between-trial standard deviation (tau)
and model assessment parameters.
ume_plot(full, ume, drug_names, save_xls)ume_plot(full, ume, drug_names, save_xls)
full |
|
ume |
|
drug_names |
A vector of labels with the name of the interventions in
the order they appear in the argument |
save_xls |
Logical to indicate whether to export the tabulated results
to an 'xlsx' file (via the |
The deviance information criterion (DIC) of the consistency model is compared with the DIC of the unrelated mean effects model (Dias et al., 2013). If the difference in DIC exceeds 5, the unrelated mean effects model is preferred. If the difference in DIC is less than -5, the consistency is preferred; otherwise, there is little to choose between the compared models.
For a binary outcome, when measure is "RR" (relative risk) or "RD"
(risk difference) in run_model, ume_plot currently
presents the results from network meta-analysis and unrelated mean effects
in the odds ratio for being the base-case effect measure in
run_model for a binary outcome (see also 'Details' in
run_model).
Furthermore, ume_plot exports table_effect_size and
table_model_assessment to separate 'xlsx' files (via the
write_xlsx function) to the working
directory of the user.
ume_plot can be used only for a network of interventions. In the
case of two interventions, the execution of the function will be stopped
and an error message will be printed on the R console.
ume_plot prints on the R console a message on the most
parsimonious model (if any) based on the DIC (red text). Then, the function
returns the following list of elements:
table_effect_size |
The posterior median, posterior standard deviation, and 95% credible interval of the summary effect size for each pairwise comparison observed in the network under the consistency model and the unrelated mean effects model. |
table_model_assessment |
The DIC, number of effective parameters, and total residual deviance under the consistency model and the unrelated mean effects model (Spiegelhalter et al., 2002). |
table_tau |
The posterior median and 95% credible interval of
tau under the consistency model and the unrelated mean effects
model. When a fixed-effect model has been performed, |
scatterplots |
The scatterplot and the Bland-Altman plot on the
posterior mean deviance contribution of the individual data points under
the consistency model and the unrelated mean effects model. See 'Details'
and 'Value' in |
levarage_plots |
The leverage plot under the consistency model
and the unrelated mean effects model, separately. See 'Details' and
'Value' in |
intervalplots |
A panel of interval plots on the summary effect
size under the consistency model and the unrelated mean effects model for
each pairwise comparison observed in the network. See 'Details' and
'Value' in |
Loukia M. Spineli
Dias S, Welton NJ, Sutton AJ, Caldwell DM, Lu G, Ades AE. Evidence synthesis for decision making 4: inconsistency in networks of evidence based on randomized controlled trials. Med Decis Making 2013;33(5):641–56. doi: 10.1177/0272989X12455847
Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A. Bayesian measures of model complexity and fit. J R Stat Soc B 2002;64(4):583–396. doi: 10.1111/1467-9868.00353
bland_altman_plot,
intervalplot_panel_ume, leverage_plot,
run_model, run_ume,
write_xlsx
data("nma.liu2013") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_liu.rds', package = 'rnmamod')) # Read results from 'run_ume' (using the default arguments) ume <- readRDS(system.file('extdata/ume_liu.rds', package = 'rnmamod')) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "pramipexole", "serotonin-norepinephrine reuptake inhibitor", "serotonin reuptake inhibitor", "tricyclic antidepressant", "pergolide") # Plot the results from both models ume_plot(full = res, ume = ume, drug_names = interv_names)data("nma.liu2013") # Read results from 'run_model' (using the default arguments) res <- readRDS(system.file('extdata/res_liu.rds', package = 'rnmamod')) # Read results from 'run_ume' (using the default arguments) ume <- readRDS(system.file('extdata/ume_liu.rds', package = 'rnmamod')) # The names of the interventions in the order they appear in the dataset interv_names <- c("placebo", "pramipexole", "serotonin-norepinephrine reuptake inhibitor", "serotonin reuptake inhibitor", "tricyclic antidepressant", "pergolide") # Plot the results from both models ume_plot(full = res, ume = ume, drug_names = interv_names)