Package 'MendelianRandomization'

Description

Two sets of example data are included in the package: one illustrating uncorrelated variants, and the other correlated variants. These are the data on correlated variants.

Usage

calcium

calciumse

fastgluc

fastglucse

calc.rho

Format

An object of class numeric of length 6.

An object of class numeric of length 6.

An object of class numeric of length 6.

An object of class numeric of length 6.

An object of class matrix (inherits from array) with 6 rows and 6 columns.

Details

The variables calcium, and fastgluc are the genetic associations with calcium and fasting glucose for 6 genetic variants reported by Burgess et al (2015). The respective standard errors of the associations are given as calciumse and fastglucse. The matrix of correlations between the genetic variants is given as calc.rho.

These data can be used to test out the various functions in the package.

References

Stephen Burgess, Robert A Scott, Nic J Timpson, George Davey Smith, Simon G Thompson. Using published data in Mendelian randomization: a blueprint for efficient identification of causal risk factors. Eur J Epidemiol 2015; 30(7):543-552. doi: 10.1007/s10654-015-0011-z.

Description

An object containing the confidence intervals produced using the conditional likelihood ratio method (CLR) and other identification-robust methods.

Slots

Exposure

The name of the exposure variable.

Outcome

The name of the outcome variable.

Correlation

The matrix of correlations between genetic variants.

ARlower

The lower bounds of the causal estimate based on inverting Anderson and Rubin's test.

ARupper

The upper bounds of the causal estimate based on inverting Anderson and Rubin's test.

Klower

The lower bounds of the causal estimate based on inverting Kleibergen's test.

Kupper

The upper bounds of the causal estimate based on inverting Kleibergen's test.

CLRlower

The lower bounds of the causal estimate based on inverting Moreira's conditional likelihood ratio test.

CLRupper

The upper bounds of the causal estimate based on inverting Moreira's conditional likelihood ratio test.

CIMin

The smallest value used in the search to find the confidence interval.

CIMax

The largest value used in the search to find the confidence interval.

CIStep

The step size used in the search to find the confidence interval.

Alpha

The significance level used in constructing the confidence interval (default is 0.05).

Description

Internal function of mr_cML. Estimate theta, b vector, r vector with constrained maximum likelihood.

Usage

cML_estimate(
  b_exp,
  b_out,
  se_exp,
  se_out,
  K,
  initial_theta = 0,
  initial_mu = rep(0, length(b_exp)),
  maxit = 100
)

Arguments

Value

A list contains: theta is the estimate causal effect, b_vec is the estimated vector of b, r_vec is the estimated vector of r.

Examples

cML_estimate(b_exp = ldlc,b_out = chdlodds,se_exp = ldlcse,
se_out = chdloddsse, K = 5)

Description

Internal function of mr_cML. Get estimated theta, se of estimated theta and negative log-likelihood, using multiple random starting points.

Usage

cML_estimate_random(
  b_exp,
  b_out,
  se_exp,
  se_out,
  K,
  random_start = 0,
  maxit = 100
)

Arguments

Value

A list contains: theta is the estimate causal effect, se is standard error of estimated theta, l is negative log-likelihood, r_est is estimated r vector.

Examples

cML_estimate_random(b_exp = ldlc,b_out = chdlodds,se_exp = ldlcse,
se_out = chdloddsse, K = 5)

Description

Internal function of mr_cML. Get the standard error of estimated theta from constrained maximum likelihood.

Usage

cML_SdTheta(b_exp, b_out, se_exp, se_out, theta, b_vec, r_vec)

Arguments

Value

Standard error of theta.

Examples

# First get estimates:
MLE_result = cML_estimate(b_exp = ldlc,b_out = chdlodds,se_exp = ldlcse,
se_out = chdloddsse, K = 5)

# Calculate standard error:
cML_SdTheta(b_exp = ldlc,b_out = chdlodds,se_exp = ldlcse,
se_out = chdloddsse, theta = MLE_result$theta, b_vec = MLE_result$b_vec, r_vec = MLE_result$r_vec)

Description

An object containing the estimate produced using the debiased inverse-variance weighted (dIVW) method as well as various statistics.

Slots

Over.dispersion

Should the method consider overdispersion (balanced horizontal pleiotropy)? Default is TRUE.

Exposure

The name of the exposure variable.

Outcome

The name of the outcome variable.

Estimate

The causal point estimate from the median-based method.

StdError

The standard error associated with Estimate (obtained from bootstrapping).

CILower

The lower bound of the confidence interval for Estimate based on StdError.

CIUpper

The upper bound of the confidence interval for Estimate based on StdError.

Alpha

The significance level used in constructing the confidence interval (default is 0.05).

Pvalue

P-value associated with the causal estimate from the Wald method.

SNPs

The number of SNPs that used in the calculation.

Condition

A measure defined as (average F-statistic -1)*sqrt(# snps) that needs to be large for reliable asymptotic approximation based on the dIVW estimator. It is recommended to be greater than 20.

Description

An object containing the estimate produced using the MR-Egger method as well as various statistics.

The MR-Egger model uses a random-effects model; a fixed-effect model does not make sense as pleiotropy leads to heterogeneity between the causal estimates targeted by the genetic variants. The (multiplicative) random-effects model allows over-dispersion in the regression model. Under-dispersion is not permitted (in case of under-dispersion, the residual standard error is set to 1).

Slots

Model

Model always takes the value random, as only random-effects analyses are permitted.

Exposure

The name of the exposure variable.

Outcome

The name of the outcome variable.

Correlation

The matrix of correlations between genetic variants.

Robust

Whether robust regression was used in the regression model relating the genetic associations with the outcome and those with the exposure.

Penalized

Whether weights in the regression model were penalized for variants with heterogeneous causal estimates.

Estimate

The causal point estimate from the MR-Egger method.

StdError.Est

The standard error associated with Estimate.

Pvalue.Est

P-value associated with the causal estimate from the Wald method.

CILower.Est

The lower bound of the confidence interval for Estimate based on StdError.Est.

CIUpper.Est

The upper bound of the confidence interval for Estimate based on StdError.Est.

Intercept

The intercept estimate from the MR-Egger method. Under the InSIDE assumption, the intercept represents the average pleiotropic effect (average direct effect on the outcome) of a genetic variant. If the intercept differs from zero, this is evidence that the genetic variants are not all valid instruments; specifically, there is directional pleiotropy.

StdError.Int

The standard error associated with Intercept.

Pvalue.Int

P-value associated with the intercept from the Wald method.

CILower.Int

The lower bound of the confidence interval for Intercept based on StdError.Int.

CIUpper.Int

The upper bound of the confidence interval for Estimate based on StdError.Int.

Alpha

The significance level used in constructing the confidence interval (default is 0.05).

SNPs

The number of SNPs that were used in the calculation.

Causal.pval

P-value associated with the causal estimate.

Pleio.pval

P-value associated with the intercept (p-value for the MR-Egger intercept test of directional pleiotropy).

RSE

The estimated residual standard error from the regression model.

Heter.Stat

Heterogeneity statistic (Cochran's Q statistic) and associated p-value: the null hypothesis is that the MR-Egger regression model describes the associations with the outcome with no excess heterogeneity.

I.sq

A measure of heterogeneity between the genetic associations with the exposure (see Bowden IJE 2016: "Assessing the suitability of summary data for Mendelian randomization analyses using MR-Egger regression: The role of the I2 statistic."). Low values of I.sq relate both to large differences in precision between MR-Egger and IVW estimates, and to more weak instrument bias (in a two-sample setting, this is attenuation of MR-Egger estimate towards the null).

Description

Generate the list of inverse of covariance matrices used in MVMR-cML-DP

Usage

invcov_mvmr(se_bx, se_by, rho_mat)

Arguments

Value

A list of inverse of covariance matrices with respect to each genetic variant, retaining the ordering in se_bx

Description

An object containing the estimate produced using the inverse-variance weighted (IVW) method as well as various statistics.

Slots

Model

The model used for estimation: random-effects ("random") or fixed-effect ("fixed"). The default option ("default") is to use a fixed-effect model when there are three or fewer genetic variants, and a random-effects model when there are four or more. The (multiplicative) random-effects model allows for heterogeneity between the causal estimates targeted by the genetic variants by allowing over-dispersion in the regression model. Under-dispersion is not permitted (in case of under-dispersion, the residual standard error is set to 1, as in a fixed-effect analysis).

Exposure

The name of the exposure variable.

Outcome

The name of the outcome variable.

Correlation

The matrix of correlations between genetic variants.

Robust

Whether robust regression was used in the regression model relating the genetic associations with the outcome and those with the exposure.

Penalized

Whether weights in the regression model were penalized for variants with heterogeneous causal estimates.

Estimate

The causal point estimate from the inverse-variance weighted method.

StdError

The standard error associated with Estimate.

CILower

The lower bound of the confidence interval for Estimate based on StdError.

CIUpper

The upper bound of the confidence interval for Estimate based on StdError.

Alpha

The significance level used in constructing the confidence interval (default is 0.05).

Pvalue

P-value associated with the causal estimate.

SNPs

The number of SNPs that were used in the calculation.

RSE

The estimated residual standard error from the regression model.

Heter.Stat

Heterogeneity statistic (Cochran's Q statistic) and associated p-value: the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more variants may be pleiotropic.

Fstat

An approximation of the first-stage F statistic for all variants based on the summarized data.

Description

Two sets of example data are included in the package: one illustrating uncorrelated variants, and the other correlated variants. These are the data on uncorrelated variants.

The variables ldlc, hdlc, trig, and chdlodds are the genetic associations with (respectively) LDL-cholesterol, HDL-cholesterol, triglycerides, and coronary heart disease (CHD) risk for 28 genetic variants reported by Waterworth et al (2010). The respective standard errors of the associations are given as ldlcse, hdlcse, trigse, and chdloddsse.

These data can be used to test out the various functions in the package.

Usage

ldlc

hdlc

hdlcse

ldlcse

trig

trigse

chdlodds

chdloddsse

lipid_effect

lipid_other

lipid_eaf

Format

An object of class numeric of length 28.

An object of class numeric of length 28.

An object of class numeric of length 28.

An object of class numeric of length 28.

An object of class numeric of length 28.

An object of class numeric of length 28.

An object of class numeric of length 28.

An object of class numeric of length 28.

An object of class character of length 28.

An object of class character of length 28.

An object of class numeric of length 28.

References

Dawn Waterworth, Sally Ricketts, ..., Manj Sandhu: Genetic variants influencing circulating lipid levels and risk of coronary artery disease. Arterioscler Thromb Vasc Biol 2010; 30:2264-227. doi: 10.1161/atvbaha.109.201020.

Description

An object containing the estimate produced using the maximum-likelihood method as well as various statistics.

Slots

Model

The model used for estimation: fixed-effect ("fixed") or random-effects ("random").

Exposure

The name of the exposure variable.

Outcome

The name of the outcome variable.

Correlation

The matrix of correlations between genetic variants.

Psi

The correlations between genetic associations with the exposure and with the outcome.

Estimate

The causal point estimate from the inverse-variance weighted method.

StdError

The standard error associated with Estimate.

CILower

The lower bound of the confidence interval for Estimate based on StdError.

CIUpper

The upper bound of the confidence interval for Estimate based on StdError.

Alpha

The significance level used in constructing the confidence interval (default is 0.05).

Pvalue

P-value associated with the causal estimate.

SNPs

The number of SNPs that were used in the calculation.

RSE

The estimated residual standard error from the regression model.

Heter.Stat

Heterogeneity statistic (likelihood ratio statistic) and associated p-value: the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more variants may be pleiotropic.

Description

The function mr_allmethods implements Mendelian randomization analyses using summarized data to calculate estimates (as well as standard errors and confidence interval limits) for all the methods included in the package (or alternatively for the group of methods chosen).

Usage

mr_allmethods(object, method = "all", ...)

## S4 method for signature 'MRInput'
mr_allmethods(object, method = "all", ...)

Arguments

Details

See mr_median, mr_egger, and mr_ivw for details of how each of the methods is implemented.

Value

An object of type MRAll with the following slots :

References

See mr_median, mr_egger, and mr_ivw.

Examples

mr_allmethods(mr_input(bx = ldlc, bxse = ldlcse,
  by = chdlodds, byse = chdloddsse), method="main", iterations = 100)
  # iterations is set to 100 to reduce runtime for the mr_median method,
  # at least 10000 iterations are recommended in practice

Description

The mr_clr function calculates confidence intervals based on inverting the conditional likelihood ratio and other identification-robust tests.

Usage

mr_clr(object, nx, ny, alpha = 0.05, CIMin = -10, CIMax = 10, CIStep = 0.01)

## S4 method for signature 'MRInput'
mr_clr(object, nx, ny, alpha = 0.05, CIMin = -10, CIMax = 10, CIStep = 0.01)

Arguments

Details

In weak instrument settings, usual inference based on point estimates and standard errors may not be accurate. This method calculates confidence intervals based on inverting identification-robust tests proposed in Wang and Kang (2021, Biometrics) that provide valid inferences regardless of instrument strength.

This includes conditional likelihood ratio (CLR), Kleibergen (K), and Anderson and Rubin (AR) tests.

Evidence from the econometrics literature suggests that CLR inference is the best option in terms of power under a wide range of settings.

Please note that these methods do not provide point estimates, only confidence intervals. While most examples provide a confidence interval that is a single range of values, in some cases the confidence interval may comprise multiple ranges of values. In other cases, a valid confidence interval may not exist.

Value

The output from the function is an CLR object containing:

References

Description of the CLR method: "Weak-instrument robust tests in two-sample summary-data Mendelian randomization", S. Wang and H. Kang, Biometrics, 2021.

Examples

mr_clr(mr_input(bx = calcium, bxse = calciumse,
   by = fastgluc, byse = fastglucse, correl = calc.rho), nx=6351, ny=133010)

Description

Constrained maximum likelihood (cML) based Mendelian Randomization method robust to both correlated and uncorrelated pleiotropy.

Usage

mr_cML(
  object,
  MA = TRUE,
  DP = TRUE,
  K_vec = 0:(length(object@betaX) - 2),
  random_start = 0,
  num_pert = 200,
  random_start_pert = 0,
  maxit = 100,
  random_seed = 314,
  n,
  Alpha = 0.05
)

## S4 method for signature 'MRInput'
mr_cML(
  object,
  MA = TRUE,
  DP = TRUE,
  K_vec = 0:(length(object@betaX) - 2),
  random_start = 0,
  num_pert = 200,
  random_start_pert = 0,
  maxit = 100,
  random_seed = 314,
  n,
  Alpha = 0.05
)

Arguments

Details

The MRcML method selects invalid IVs with correlated and/or uncorrelated peliotropic effects using constrained maximum likelihood. cML-BIC gives results of the selected model with original data, while cML-MA-BIC averages over all candidate models. cML-BIC-DP and cML-MA-BIC-DP are the versions with data-perturbation to account for selection uncertainty when many invalid IVs have weak pleiotropic effects.

When DP is performed, two goodness-of-fit (GOF) tests are developed to check whether the model-based and DP- based variance estimates converge to the same estimate. Small p-values of GOF tests indicate selection uncertainty is not ignorable, and results from DP is more reliable. See reference for more details.

As the constrained maximum likelihood function is non-convex, multiple random starting points could be used to find a global minimum. For some starting points the algorithm may not converge and a warning message will be prompted, typically this will not affect the results.

Value

The output from the function is an MRcML object containing:

References

Xue, H., Shen, X., & Pan, W. (2021). Constrained maximum likelihood-based Mendelian randomization robust to both correlated and uncorrelated pleiotropic effects. The American Journal of Human Genetics, 108(7), 1251-1269.

Examples

# Perform cML-MA-BIC-DP:
mr_cML(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds,
byse = chdloddsse), num_pert=5, MA = TRUE, DP = TRUE, n = 17723)
# num_pert is set to 5 to reduce computational time
# the default value of 200 is recommended in practice

# Perform cML-BIC-DP:
mr_cML(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds,
byse = chdloddsse), MA = TRUE, DP = FALSE,, n = 17723)

Description

Contamination mixture method for robust and efficient estimation under the 'plurality valid' assumption.

Usage

mr_conmix(object, psi = 0, CIMin = NA, CIMax = NA, CIStep = 0.01, alpha = 0.05)

## S4 method for signature 'MRInput'
mr_conmix(object, psi = 0, CIMin = NA, CIMax = NA, CIStep = 0.01, alpha = 0.05)

Arguments

Details

The contamination mixture method is implemented by constructing a likelihood function based on the variant-specific causal estimates. If a genetic variant is a valid instrument, then its causal estimate will be normally distributed about the true value of the causal effect. If a genetic variant is not a valid instrument, then its causal estimate will be normally distributed about some other value. We assume that the values estimated by invalid instruments are normally distributed about zero with a large standard deviation. This enables a likelihood function to be specified that is a product of two-component mixture distributions, with one mixture distribution for each variant. The computational time for maximizing this likelihood directly is exponential in the number of genetic variants. We use a profile likelihood approach to reduce the computational complexity to be linear in the number of variants.

We consider different values of the causal effect in turn. For each value, we calculate the contribution to the likelihood for each genetic variant as a valid instrument and as an invalid instrument. If the contribution to the likelihood as a valid instrument is greater, then we take the variant's contribution as a valid instrument; if less, then its contribution is taken as an invalid instrument. This gives us the configuration of valid and invalid instruments that maximizes the likelihood for the given value of the causal effect. This is a profile likelihood, a one-dimensional function of the causal effect. The point estimate is then taken as the value of the causal effect that maximizes the profile likelihood.

Confidence intervals are evaluated by calculating the log-likelihood function, and finding all points within a given vertical distance of the maximum of the log-likelihood function (which is the causal estimate). As such, if the log-likelihood function is multimodal, then the confidence interval may include multiple disjoint ranges. This may indicate the presence of multiple causal mechanisms by which the exposure may influence the outcome with different magnitudes of causal effect. As the confidence interval is determined by a grid search, care must be taken when chosing the minimum (CIMin) and maximum (CIMax) values in the search, as well as the step size (CIStep). The default values will not be suitable for all applications.

Value

The output from the function is an MRConMix object containing:

References

Stephen Burgess, Christopher N Foley, Elias Allara, Joanna Howson. A robust and efficient method for Mendelian randomization with hundreds of genetic variants: unravelling mechanisms linking HDL-cholesterol and coronary heart disease. Nat Comms 2020. doi: 10.1038/s41467-019-14156-4.

Examples

mr_conmix(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds,
   byse = chdloddsse), psi = 3, CIMin = -1, CIMax = 5, CIStep = 0.01)

Description

The mr_divw function implements the debiased inverse-variance weighted method.

Usage

mr_divw(object, over.dispersion = TRUE, alpha = 0.05, diagnostics = FALSE)

## S4 method for signature 'MRInput'
mr_divw(object, over.dispersion = TRUE, alpha = 0.05, diagnostics = FALSE)

Arguments

Details

The debiased inverse-variance weighted method (dIVW) removes the weak instrument bias of the IVW method and is more robust under many weak instruments.

Value

The output from the function is a DIVW object containing:

References

Ting Ye, Jun Shao, Hyunseung Kang (2021). Debiased Inverse-Variance Weighted Estimator in Two-Sample Summary-Data Mendelian Randomization. The Annals of Statistics, 49(4), 2079-2100. Also available at https://arxiv.org/abs/1911.09802.

Examples

mr_divw(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse))

Description

The mr_egger function implements the MR-Egger method introduced by Bowden et al (2015).

This method provides: 1) a test of the for directional pleiotropy (the MR-Egger intercept test), 2) a test for a causal effect, and 3) an estimate of the causal effect. If the intercept term differs from zero, then the genetic variants are not all valid instrumental variables and the standard (inverse-variance weighted) estimate is biased. If the InSIDE (Instrument Strength Independent of Direct Effect) assumption holds, then the MR-Egger slope parameter provides a test for a causal effect, and a consistent estimate of the causal effect even if the intercept differs from zero.

Usage

mr_egger(
  object,
  robust = FALSE,
  penalized = FALSE,
  correl = FALSE,
  distribution = "normal",
  alpha = 0.05,
  ...
)

## S4 method for signature 'MRInput'
mr_egger(
  object,
  robust = FALSE,
  penalized = FALSE,
  correl = FALSE,
  distribution = "normal",
  alpha = 0.05,
  ...
)

Arguments

Details

The causal estimate is obtained by regression of the associations with the outcome on the associations with the risk factor, with weights being the inverse-variances of the associations with the outcome. The intercept is estimated (in contrast with the inverse-variance weighted method, where the intercept is set to zero).

As part of the analysis, the genetic variants are orientated so that all of the associations with the risk factor are positive (and signs of associations with the outcome are changed to keep the orientation consistent if required). Re-orientation of the genetic variants is performed automatically as part of the function.

The MR-Egger model uses a random-effects model ("random"); a fixed-effect model does not make sense as pleiotropy leads to heterogeneity between the causal estimates targeted by the genetic variants. The (multiplicative) random-effects model allows over-dispersion in the regression model. Under-dispersion is not permitted (in case of under-dispersion, the residual standard error is set to 1).

Value

The output of the function is an Egger object containing:

References

Jack Bowden, George Davey Smith, Stephen Burgess. Mendelian randomization with invalid instruments: effect estimation and bias detection through Egger regression. International Journal of Epidemiology 2015; 44:512–525. doi: 10.1093/ije/dyv080.

Confidence intervals, and robust and penalized weights: Stephen Burgess, Jack Bowden, Frank Dudbridge, Simon G Thompson. Robust instrumental variable methods using multiple candidate instruments with application to Mendelian randomization. arXiv 2016; 1606.03729.

I-squared statistic: Jack Bowden and others. Assessing the suitability of summary data for Mendelian randomization analyses using MR-Egger regression: The role of the I2 statistic. Int J Epidemiol 2016 (to appear).

Examples

mr_egger(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse))
mr_egger(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse),
  robust = TRUE)
mr_egger(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse),
  penalized = TRUE)
mr_egger(mr_input(calcium, calciumse, fastgluc, fastglucse, corr=calc.rho))
  ## correlated variants

Description

The mr_forest function draws a forest plot of causal estimates. The default option plots the variant-specific causal estimates (by/bx) and the estimate from the mr_ivw function using default settings (assuming variants are uncorrelated, random-effects for 4+ variants). Options allow users to plot estimates from a variety of different methods.

Usage

mr_forest(
  object,
  alpha = 0.05,
  snp_estimates = TRUE,
  methods = "ivw",
  ordered = FALSE
)

## S4 method for signature 'MRInput'
mr_forest(
  object,
  alpha = 0.05,
  snp_estimates = TRUE,
  methods = "ivw",
  ordered = FALSE
)

Arguments

Details

As the function produces a ggplot object, graphical parameters can be changed by adding commands from the ggplot2 package.

Examples

mr_forest(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse),
  alpha = 0.01, ordered = TRUE)
mr_forest(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse),
  methods = c("ivw", "wmedian", "egger"), snp_estimates = FALSE)
forest = mr_forest(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse))
# how to change x-axis limits
# library(ggplot2)
# forest2 = forest + coord_cartesian(xlim=c(-5,5))
# forest2

Description

The mr_funnel function draws a funnel plot of variant-specific causal estimates. Estimates (by/bx) are plotted against the precision of the estimates (abs(bx)/byse). Precision is the reciprocal of standard error. A vertical dashed line is plotted at the estimate from the mr_ivw function.

Usage

mr_funnel(object, CI = TRUE)

## S4 method for signature 'MRInput'
mr_funnel(object, CI = TRUE)

Arguments

Details

As the function produces a ggplot object, graphical parameters can be changed by adding commands from the ggplot2 package.

Examples

mr_funnel(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse))

Description

Heterogeneity-penalized model-averaging method for efficient modal-based estimation.

Usage

mr_hetpen(
  object,
  prior = 0.5,
  CIMin = -1,
  CIMax = 1,
  CIStep = 0.001,
  alpha = 0.05
)

## S4 method for signature 'MRInput'
mr_hetpen(
  object,
  prior = 0.5,
  CIMin = -1,
  CIMax = 1,
  CIStep = 0.001,
  alpha = 0.05
)

Arguments

Details

This method was developed as a more efficient version of the mode-based estimation method of Hartwig et al. It proceeds by evaluating weights for all subsets of genetic variants (excluding the null set and singletons). Subsets receive greater weight if they include more variants, but are severely downweighted if the variants in the subset have heterogeneous causal estimates. As such, the method will identify the subset with the largest number (by weight) of variants having similar causal estimates.

Confidence intervals are evaluated by calculating a log-likelihood function, and finding all points within a given vertical distance of the maximum of the log-likelihood function (which is the causal estimate). As such, if the log-likelihood function is multimodal, then the confidence interval may include multiple disjoint ranges. This may indicate the presence of multiple causal mechanisms by which the exposure may influence the outcome with different magnitudes of causal effect. As the confidence interval is determined by a grid search, care must be taken when chosing the minimum (CIMin) and maximum (CIMax) values in the search, as well as the step size (CIStep). The default values will not be suitable for all applications.

The method should give consistent estimates as the sample size increases if a weighted plurality of the genetic variants are valid instruments. This means that the largest group of variants with the same causal estimate in the asymptotic limit are the valid instruments.

The current implementation of the method evaluates a weight and an estimate for each of the subsets of genetic variants. This means that the method complexity doubles for each additional genetic variant included in the analysis. Currently, the method provides a warning message when used with 25+ variants, and fails to run with 30+.

Value

The output from the function is an MRHetPen object containing:

References

Stephen Burgess, Verena Zuber, Apostolos Gkatzionis, Christopher N Foley. Improving on a modal-based estimation method: model averaging for consistent and efficient estimation in Mendelian randomization when a plurality of candidate instruments are valid. bioRxiv 2017. doi: 10.1101/175372.

Examples

mr_hetpen(mr_input(bx = ldlc[1:10], bxse = ldlcse[1:10], by = chdlodds[1:10],
   byse = chdloddsse[1:10]), CIMin = -1, CIMax = 5, CIStep = 0.01)

Description

The mr_input function is required for inputting and formatting data for use in any of the estimation functions provided in this package. The MRInput class outputted by the function can also be viewed graphically using the mr_plot function.

Usage

mr_input(
  bx = 0,
  bxse = 0,
  by = 0,
  byse = 0,
  correlation = matrix(),
  exposure = "exposure",
  outcome = "outcome",
  snps = "snp",
  effect_allele = NA,
  other_allele = NA,
  eaf = NA
)

Arguments

Details

The beta-coefficients are assumed to be estimated for uncorrelated (independent) genetic variants, although a correlation matrix can be specified if the variants are correlated in their distributions. We also assume that the beta-coefficients for associations with the exposure and with the outcome are uncorrelated (corresponding to a two-sample Mendelian randomization analysis), although correlation between associations with the exposure and with the outcome generally have little impact on causal estimates or standard errors.

If the four variables are not all the same length, then an error message will be reported. The analyses will still try to run, but the output may be misleading. However, in some analyses (for example, the standard IVW and MR-Egger methods), the values of bxse are not used in the analysis, and can therefore safely be omitted (provided that the other variables are correctly labelled).

Value

An MRInput object containing:

Description

The mr_ivw function implements the inverse-variance method, informally known as the "Toby Johnson" method. With a single genetic variant, this is simply the ratio method.

Usage

mr_ivw(
  object,
  model = "default",
  robust = FALSE,
  penalized = FALSE,
  weights = "simple",
  psi = 0,
  correl = FALSE,
  distribution = "normal",
  alpha = 0.05,
  ...
)

## S4 method for signature 'MRInput'
mr_ivw(
  object,
  model = "default",
  robust = FALSE,
  penalized = FALSE,
  weights = "simple",
  psi = 0,
  correl = FALSE,
  distribution = "normal",
  alpha = 0.05,
  ...
)

Arguments

Details

With multiple uncorrelated genetic variants, this estimate can be thought of as: 1) the inverse-variance weighted combination of the ratio estimates from a meta-analysis; 2) the ratio estimate from combining the genetic variants into a weighted score and then using this score as an instrumental variable (the same estimate is obtained from the two-stage least squares method using individual-level data); 3) the coefficient from weighted linear regression of the associations with the outcome on the associations with the risk factor fixing the intercept to zero and using the inverse-variance weights.

Here, we implement the method using weighted linear regression. If the variants are correlated, the method is implemented using generalized weighted linear regression; this is hard coded using matrix algebra.

The causal estimate is obtained by regression of the associations with the outcome on the associations with the risk factor, with the intercept set to zero and weights being the inverse-variances of the associations with the outcome.

With a single genetic variant, the estimate is the ratio of coefficients betaY/betaX and the standard error is the first term of the delta method approximation betaYse/betaX.

Value

The output from the function is an IVW object containing:

References

Original implementation: The International Consortium for Blood Pressure Genome-Wide Association Studies. Genetic variants in novel pathways influence blood pressure and cardiovascular disease risk. Nature 2011; 478:103-109. doi: 10.1038/nature10405.

Detailed description of method: Stephen Burgess, Adam S Butterworth, Simon G Thompson. Mendelian randomization analysis with multiple genetic variants using summarized data. Genetic Epidemiology 2013; 37:658-665. doi: 10.1002/gepi.21758.

Robust and penalized weights: Stephen Burgess, Jack Bowden, Frank Dudbridge, Simon G Thompson. Robust instrumental variable methods using multiple candidate instruments with application to Mendelian randomization. arXiv 2016; 1606.03729.

Heterogeneity test: Fabiola del Greco, Cosetta Minelli, Nuala A Sheehan, John R Thompson. Detecting pleiotropy in Mendelian randomisation studies with summary data and a continuous outcome. Stat Med 2015; 34(21):2926-2940. doi: 10.1002/sim.6522.

Simple versus delta weights (first-order versus second-order): Stephen Burgess, Jack Bowden. Integrating summarized data from multiple genetic variants in Mendelian randomization: bias and coverage properties of inverse-variance weighted methods. arXiv:1512.04486.

Examples

mr_ivw(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse))
mr_ivw(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse),
  robust = TRUE)
mr_ivw(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse),
  penalized = TRUE)
mr_ivw(mr_input(calcium, calciumse, fastgluc, fastglucse, corr=calc.rho))
  ## correlated variants

Description

The mr_lasso function performs the MR-Lasso method, which applies lasso-type penalization to the direct effects of genetic variants on the outcome. The causal estimate is described as a post-lasso estimate, and is obtained by performing the IVW method using only those genetic variants that are identified as valid by the lasso procedure.

Usage

mr_lasso(object, distribution = "normal", alpha = 0.05, lambda = numeric(0))

## S4 method for signature 'MRInput'
mr_lasso(object, distribution = "normal", alpha = 0.05, lambda = numeric(0))

Arguments

Details

MR-Lasso extends the IVW model to include an intercept term for each genetic variant. These intercept terms represent associations between the genetic variants and the outcome which bypass the risk factor. The causal effect estimates are estimated by weighted linear regression where the intercept terms are subject to lasso-type penalization. The lasso penalization will tend to shrink the intercept terms corresponding to the valid instruments to zero.

The lasso penalty relies on a tuning parameter which controls the level of sparsity. The default is to use a heterogeneity stopping rule, but a fixed value may be specified.

As part of the analysis, the genetic variants are orientated so that all of the associations with the risk factor are positive (and signs of associations with the outcome are changed to keep the orientation consistent if required). Re-orientation of the genetic variants is performed automatically as part of the function.

The MR-Lasso method is performed in two steps. First, a regularized regression model is fitted, and some genetic variants are identified as valid instruments. Second, the causal effect is estimated using standard IVW with only the valid genetic variants. The post-lasso method will be performed as long as at least two genetic variants are identified as valid instruments. The default heterogeneity stopping rule will always return at least two genetic variants as valid instruments. The main estimate given by the method is the post-lasso estimate. However, parameter estimates from the regularized regression model used to identify invalid variants are also provided for completeness.

If a substantial proportion of genetic variants are removed from the analysis, the MR-Lasso method may give a false impression of confidence in the causal estimate due to homogeneity of the variant-specific causal estimates amongst the remaining variants. However, it is not reasonable to claim that there is strong evidence for a causal effect after a large number of variants with heterogeneous estimates have been removed from the analysis.

Value

The output from the function is an MRLasso object containing:

References

Jessica MB Rees, Angela M Wood, Frank Dudbridge, Stephen Burgess. Robust methods in Mendelian randomization via penalization of heterogeneous causal estimates. PLoS ONE 2019; 14(9):e0222362

Examples

mr_lasso(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse))

Description

The mr_loo function draws a forest plot of causal estimates from the mr_ivw function using default settings (assuming variants are uncorrelated, random-effects for 4+ variants) omitting each variant in turn. So the estimate labelled snp_1 includes all variants except the labelled variant, and so on. The mr_ivw estimate including all variants ("IVW estimate") is also provided for reference.

Usage

mr_loo(object, alpha = 0.05)

## S4 method for signature 'MRInput'
mr_loo(object, alpha = 0.05)

Arguments

Details

As the function produces a ggplot object, graphical parameters can be changed by adding commands from the ggplot2 package.

Examples

mr_loo(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse),
  alpha = 0.01)

Description

The mr_maxlik function implements the maximum-likelihood method introduced by Burgess et al (2013).

Usage

mr_maxlik(
  object,
  model = "default",
  correl = FALSE,
  psi = 0,
  distribution = "normal",
  alpha = 0.05,
  ...
)

## S4 method for signature 'MRInput'
mr_maxlik(
  object,
  model = "default",
  correl = FALSE,
  psi = 0,
  distribution = "normal",
  alpha = 0.05,
  ...
)

Arguments

Details

A likelihood function is defined by assuming that the summarized data for each genetic variant are normally distributed. A bivariate normal distribution is assumed for the associations of each genetic variant with the exposure and with the outcome. The mean of the association with the outcome is taken as the mean association with the exposure multiplied by the causal effect parameter.

Thus, if there are K genetic variants, then K+1 parameters are estimated by the method: one for each gene–exposure association, plus the causal parameter. If the number of genetic variants is large, then maximization of this function may be an issue. If the maximum likelihood estimate substantially differs from the inverse-variance weighted estimate, this may indicate that convergence has not occurred in the optimization algorithm.

The variance-covariance matrices for the bivariate normal distributions are obtained from the standard error estimates provided. The correlation psi between genetic associations with the exposure and with the outcome due to sample overlap can be specified; its default value is zero.

Two features why this method may be preferred over the inverse-variance weighted method are the incorporation in the model of uncertainty in the genetic associations with the exposure, and of correlation between the genetic association estimates with exposure and outcome for each variant. The method is implemented both for uncorrelated and correlated genetic variants. It can also be used for a single genetic variant.

The original version of the maximum-likelihood method assumed that all genetic variants identify the same causal estimate; a fixed-effect model. The causal estimate may be overly precise if the fixed-effect model is incorrect and there is substantial heterogeneity in the causal estimates from the different variants. The random-effects analysis implemented here is an ad hoc solution to the problem of heterogeneity, but one that should result in reasonable confidence intervals that incorporate this heterogeneity.

Value

The output from the function is an MaxLik object containing:

References

Stephen Burgess, Adam S Butterworth, Simon G Thompson. Mendelian randomization analysis with multiple genetic variants using summarized data. Genetic Epidemiology 2013; 37:658-665. doi: 10.1002/gepi.21758.

Examples

mr_maxlik(mr_input(bx = ldlc[1:10], bxse = ldlcse[1:10],
  by = chdlodds[1:10], byse = chdloddsse[1:10]))
mr_maxlik(mr_input(bx = ldlc[1:10], bxse = ldlcse[1:10],
  by = chdlodds[1:10], byse = chdloddsse[1:10]), psi=0.2)
mr_maxlik(mr_input(calcium, calciumse, fastgluc, fastglucse, corr=calc.rho))
  ## correlated variants

Description

The mr_mbe function implements the mode-based method introduced by Hartwig, Bowden and Davey Smith (2017).

Usage

mr_mbe(
  object,
  weighting = "weighted",
  stderror = "simple",
  phi = 1,
  seed = 314159265,
  iterations = 10000,
  distribution = "normal",
  alpha = 0.05
)

## S4 method for signature 'MRInput'
mr_mbe(
  object,
  weighting = "weighted",
  stderror = "delta",
  phi = 1,
  seed = 314159265,
  iterations = 10000,
  distribution = "normal",
  alpha = 0.05
)

Arguments

Details

The mode-based estimation (MBE) method takes the variant-specific ratio estimates from each genetic variant in turn, and calculates the modal estimate. This is implemented by constructing a kernel-smoothed density out of the ratio estimates, and taking the maximum value as the modal estimate. The standard error is calculated by a bootstrap procedure, and confidence intervals based on the estimate having a normal distribution.

The method should give consistent estimates as the sample size increases if a plurality (or weighted plurality) of the genetic variants are valid instruments. This means that the largest group of variants with the same causal estimate in the asymptotic limit are the valid instruments.

Value

The output from the function is an MRMBE object containing:

References

Fernando Pires Hartwig, George Davey Smith, Jack Bowden. Robust inference in summary data Mendelian randomization via the zero modal pleiotropy assumption. International Journal of Epidemiology 2017; 46(6): 1985-1998. doi: 10.1093/ije/dyx102.

Examples

mr_mbe(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse), iterations=100)
mr_mbe(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse),
   phi=0.5, iterations=100)
mr_mbe(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse),
   weighting="weighted", stderror="delta", iterations=100)
# iterations set to 100 to reduce computational time,
#  more iterations are recommended in practice

Description

The mr_median function implements the weighted median (default) or simple median method introduced by Bowden et al (2016) to calculate the median of the ratio instrumental variable estimates evaluated using each genetic variant individually.

Usage

mr_median(
  object,
  weighting = "weighted",
  distribution = "normal",
  alpha = 0.05,
  iterations = 10000,
  seed = 314159265
)

## S4 method for signature 'MRInput'
mr_median(
  object,
  weighting = "weighted",
  distribution = "normal",
  alpha = 0.05,
  iterations = 10000,
  seed = 314159265
)

Arguments

Details

The median-based methods have greater robustness to individual genetic variants with strongly outlying causal estimates compared with the inverse-variance weighted and MR-Egger methods. Formally, the simple median method gives a consistent estimate of the causal effect when at least 50% of the genetic variants are valid instrumental variables (for the weighted median method, when 50% of the weight comes from valid instrumental variables).

When the weighting is "simple", the estimate is obtained by calculating the ratio causal estimates from each genetic variants theta = betaY/betaX, and finding the median estimate.

When the weighting is "weighted", the estimate is obtained by:

1. Calculating the ratio causal estimates and ordering the genetic variants according to the magnitude of their estimates, i.e.

   $\theta_1 < \theta_2 < ... < \theta_J$

2. Calculate normalized inverse-variance weights for each genetic variant $w_1, w_2, ..., w_J$, as:

   $w_j = \frac{\beta_{Xj}^2}{se(\beta_{Yj})^2} / \sum_{i=1}^{J} \frac{\beta_{Xi}^2}{se(\beta_{Yi})^2}$

3. Find k such that

   $s_k = \sum_{i = 1}^k w_i < 0.5$

   and

   $s_{k+1} = \sum_{i = 1}^{k+1} w_i > 0.5$

4. Calculate the weighted median estimate by extrapolation as:

   $\theta_{WM} = \theta_k + (\theta_{k+1} - \theta_k) \times \frac{0.5 - s_k}{s_{k+1} - s_k}$

The simple median estimate is the same as the weighted median estimate when all the weights are equal. Standard errors for both the simple and weighted median methods are calculated through bootstrapping.

When the weighting is "penalized", the weighted method is used, but the contribution of genetic variants with outlying (heterogeneous) ratio estimates to the analysis is downweighted.

Value

The output from the function is a WeightedMedian object containing:

References

Jack Bowden, George Davey Smith, Philip C Haycock, Stephen Burgess. Consistent estimation in Mendelian randomization with some invalid instruments using a weighted median estimator. Genetic Epidemiology 2016; 40(4):304-314. doi: 10.1002/gepi.21965.

Examples

mr_median(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse),
  weighting = "weighted", iterations = 100)
  # iterations is set to 100 to reduce runtime for the mr_median method,
  # 10000 iterations are recommended in practice
mr_median(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse),
  weighting = "simple", iterations = 100)
mr_median(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse),
  weighting = "penalized", iterations = 100)

Description

The mr_mvcML function performs multivariable Mendelian randomization via the constrained maximum likelihood method, which is robust to both correlated and uncorrelated pleiotropy.

Usage

mr_mvcML(
  object,
  n,
  DP = TRUE,
  rho_mat = diag(ncol(object@betaX) + 1),
  K_vec = 0:(ceiling(nrow(object@betaX)/2)),
  random_start = 0,
  num_pert = 100,
  min_theta_range = -0.5,
  max_theta_range = 0.5,
  maxit = 100,
  alpha = 0.05,
  seed = 314159265
)

## S4 method for signature 'MRMVInput'
mr_mvcML(
  object,
  n,
  DP = TRUE,
  rho_mat = diag(ncol(object@betaX) + 1),
  K_vec = 0:(ceiling(nrow(object@betaX)/2)),
  random_start = 0,
  num_pert = 200,
  min_theta_range = -0.5,
  max_theta_range = 0.5,
  maxit = 100,
  alpha = 0.05,
  seed = 314159265
)

Arguments

Details

Multivariable MRcML (MVMRcML) is an extension of MRcML to deal with multiple exposures of interest. It is robust to both correlated and uncorrelated pleiotropy as its univariable version.

In practice, the data perturbation (DP) version is preferred in practice for a more robust inference as it can account for the uncertainty in model selection. However, it may take a longer time especially when the number of IVs is large (so the range of K_vec can be large too). One strategy is to try a small range of K (the number of invalid IVs) first (with a small num_pert), then adjust it if the number of selected invalid IVs fall close to the boundary. You can also use other methods, e.g. mr_mvlasso, to get a rough sense of the number of invalid IVs.

Similar to mr_cML, multiple random starting points could be used to find a global minimum.

Value

The output from the function is an MVMRcML object containing:

References

Lin, Z., Xue, H., & Pan, W. (2023). Robust multivariable Mendelian randomization based on constrained maximum likelihood. The American Journal of Human Genetics, 110(4), 592-605.

Examples

# Perform MVMRcML-DP:
mr_mvcML(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse),
   by = chdlodds, byse = chdloddsse), n = 17723, num_pert = 5, random_start = 5)
  # num_pert is set to 5 to reduce runtime for the mr_mvcML method,
  # At least 100 perturbations should be used and more is preferred for a stable result.

rho_mat = matrix(c(1,-0.1,0.2,0,-0.1,1,-0.3,0,
 				  0.2,-0.3,1,0,0,0,0,1),ncol=4) ## Toy example of rho_mat
mr_mvcML(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse),
   by = chdlodds, byse = chdloddsse), n = 17723, num_pert = 5, rho_mat = rho_mat)

# Perform MVMRcML-BIC:
mr_mvcML(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse),
   by = chdlodds, byse = chdloddsse), n = 17723, DP = FALSE)

Description

The mr_mvegger function performs multivariable Mendelian randomization via the MR-Egger method. This is implemented by multivariable weighted linear regression.

Usage

mr_mvegger(
  object,
  orientate = 1,
  correl = FALSE,
  distribution = "normal",
  alpha = 0.05
)

## S4 method for signature 'MRMVInput'
mr_mvegger(
  object,
  orientate = 1,
  correl = FALSE,
  distribution = "normal",
  alpha = 0.05
)

Arguments

Details

Multivariable MR-Egger is an extension of the MR-Egger method to deal with genetic variants that are associated with multiple risk factors.

We implement the method using multivariable weighted linear regression. If the variants are correlated, the method is implemented using generalized weighted linear regression; this is hard coded using matrix algebra.

The causal estimate is obtained by regression of the associations with the outcome on the associations with the risk factors, with the intercept estimated and weights being the inverse-variances of the associations with the outcome.

Value

The output from the function is an MVEgger object containing:

References

Jessica Rees, Angela Wood, Stephen Burgess. Extending the MR-Egger method for multivariable Mendelian randomization to correct for both measured and unmeasured pleiotropy. Statistics in Medicine 2017; 36(29): 4705-4718. doi: 10.1002/sim.7492.

Examples

mr_mvegger(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse),
   by = chdlodds, byse = chdloddsse), orientate = 1)

Description

The mr_mvgmm function performs multivariable Mendelian randomization via the generalized method of moments method.

Usage

mr_mvgmm(object, nx, ny, cor.x = NULL, robust = TRUE, alpha = 0.05, ...)

## S4 method for signature 'MRMVInput'
mr_mvgmm(object, nx, ny, cor.x = NULL, robust = TRUE, alpha = 0.05, ...)

Arguments

Details

Robust inference in two-sample multivariable Mendelian randomization using the generalized method of moments. The method accounts for overdispersion heterogeneity in genetic variant-outcome associations.

Value

The output from the function is an MVGMM object containing:

References

Description of the generalized method of moments: Hansen, L. P. (1982). Large sample properties of generalized method of moments estimators. Econometrica, pp.1029-1054.

Examples

mr_mvgmm(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse),
   by = chdlodds, byse = chdloddsse), nx=rep(17723,3), ny=17723)

Description

The mr_mvinput function is required for inputting and formatting data for use in the multivariable Mendelian randomization functions provided in this package.

Usage

mr_mvinput(
  bx = matrix(),
  bxse = matrix(),
  by = 0,
  byse = 0,
  correlation = matrix(),
  exposure = "exposure",
  outcome = "outcome",
  snps = "snp",
  effect_allele = NA,
  other_allele = NA,
  eaf = NA
)

Arguments

Details

The beta-coefficients are assumed to be estimated for uncorrelated (independent) genetic variants, although a correlation matrix can be specified if the variants are correlated in their distributions. We also assume that the beta-coefficients for associations with the exposure and with the outcome are uncorrelated (corresponding to a two-sample Mendelian randomization analysis), although correlation between associations with the exposure and with the outcome generally have little impact on causal estimates or standard errors.

If the variables are not all the same length, then an error message will be reported. The analyses will still try to run, but the output may be misleading. However, in some analyses (for example, the standard IVW and MR-Egger methods), the values of bxse are not used in the analysis, and can therefore safely be omitted (provided that the other variables are correctly labelled).

Value

An MRMVInput object containing:

Description

The mr_mvivw function performs multivariable Mendelian randomization via the inverse-variance method. This is implemented by multivariable weighted linear regression.

Usage

mr_mvivw(
  object,
  model = "default",
  robust = FALSE,
  correl = FALSE,
  correl.x = NULL,
  nx = NA,
  distribution = "normal",
  alpha = 0.05,
  ...
)

## S4 method for signature 'MRMVInput'
mr_mvivw(
  object,
  model = "default",
  robust = FALSE,
  correl = FALSE,
  correl.x = NULL,
  nx = NA,
  distribution = "normal",
  alpha = 0.05,
  ...
)

Arguments

Details

Multivariable Mendelian randomization is an extension of Mendelian randomization to deal with genetic variants that are associated with multiple risk factors. Two scenarios are envisioned for its use: 1) risk factors that are biologically related, such as lipid fractions; and 2) risk factors where there is potentially a network of causal effects (mediation) from one risk factor to another. In both cases, under the extended assumptions of multivariable Mendelian randomization, coefficients represent the direct causal effects of each risk factor in turn with the other risk factors being fixed.

We implement the method using multivariable weighted linear regression. If the variants are correlated, the method is implemented using generalized weighted linear regression; this is hard coded using matrix algebra.

The causal estimate is obtained by regression of the associations with the outcome on the associations with the risk factors, with the intercept set to zero and weights being the inverse-variances of the associations with the outcome.

Value

The output from the function is an MVIVW object containing:

References

Description of approach: Stephen Burgess, Simon G Thompson. Multivariable Mendelian Randomization: the use of pleiotropic genetic variants to estimate causal effects. American Journal of Epidemiology 2015; 181(4):251-260. doi: 10.1093/aje/kwu283.

Description of inverse-variance weighted method: Stephen Burgess, Frank Dudbridge, Simon G Thompson. Re: "Multivariable Mendelian randomization: the use of pleiotropic genetic variants to estimate causal effects." American Journal of Epidemiology 2015; 181(4):290-291. doi: 10.1093/aje/kwv017.

Use for mediation analysis: Stephen Burgess, Deborah J Thompson, Jessica MB Rees, Felix R Day, John R Perry, Ken K Ong. Dissecting causal pathways using Mendelian randomization with summarized genetic data: Application to age at menarche and risk of breast cancer. Genetics 2017; 207(2):481-487. doi: 10.1534/genetics.117.300191.

Calculation of conditional F statistics: Ashish Patel, Dipender Gill, Dmitry Shungin, Christos Mantzoros, Lotte Bjerre Knudsen, Jack Bowden, Stephen Burgess. Robust use of phenotypic heterogeneity at drug target genes for mechanistic insights: application of multivariable Mendelian randomization to GLP1R gene region. Pre-print.

Examples

mr_mvivw(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse),
   by = chdlodds, byse = chdloddsse))

Description

The mr_mvivwme function performs multivariable Mendelian randomization via the inverse-variance method with measurement error.

Usage

mr_mvivwme(
  object,
  model = "default",
  correl = FALSE,
  correl.x = NULL,
  distribution = "normal",
  alpha = 0.05,
  max_iter = 100,
  no_ini = 1,
  seed = 20201201,
  ...
)

## S4 method for signature 'MRMVInput'
mr_mvivwme(
  object,
  model = "default",
  correl = FALSE,
  correl.x = NULL,
  distribution = "normal",
  alpha = 0.05,
  max_iter = 100,
  no_ini = 1,
  seed = 20201201,
  ...
)

Arguments

Details

The extension of multivariable Mendelian randomization to account for measurement error in the genetic associations with the exposure traits.

Value

The output from the function is an MVIVWME object containing:

References

Zhu, Jiazheng, Stephen Burgess, and Andrew J. Grant. Bias in Multivariable Mendelian Randomization Studies Due to Measurement Error on Exposures, 2022. https://doi.org/10.48550/arXiv.2203.08668.

Examples

mr_mvivwme(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse),
   by = chdlodds, byse = chdloddsse))

Description

The mr_mvlasso function performs the multivariable MR-Lasso method, which applies lasso-type penalization to the direct effects of genetic variants on the outcome. The causal estimates are described as post-lasso estimates, and are obtained by performing the multivariable IVW method using only those genetic variants that are identified as valid by the lasso procedure.

Usage

mr_mvlasso(
  object,
  orientate = 1,
  distribution = "normal",
  alpha = 0.05,
  lambda = numeric(0)
)

## S4 method for signature 'MRMVInput'
mr_mvlasso(
  object,
  orientate = 1,
  distribution = "normal",
  alpha = 0.05,
  lambda = numeric(0)
)

Arguments

Details

Multivariable MR-Lasso extends the multivariable IVW model to include an intercept term for each genetic variant. These intercept terms represent associations between the genetic variants and the outcome which bypass the risk factors. The regularized regression model is estimated by multivariable weighted linear regression where the intercept terms are subject to lasso-type penalization. The lasso penalization will tend to shrink the intercept terms corresponding to the valid instruments to zero.

The lasso penalty relies on a tuning parameter which controls the level of sparsity. The default is to use a heterogeneity stopping rule, but a fixed value may be specified.

As part of the analysis, the genetic variants are orientated so that all of the associations with one of the risk factors are positive (the first risk factor is used by default). Re-orientation of the genetic variants is performed automatically as part of the function.

The MR-Lasso method is performed in two steps. First, a regularized regression model is fitted, and some genetic variants are identified as valid instruments. Second, causal effects are estimated using standard multivariable IVW with only the valid genetic variants. The post-lasso method will be performed as long as the number of genetic variants identified as valid instruments is greater than the number of risk factors. The default heterogeneity stopping rule will always return more genetic variants as valid instruments than risk factors for identification. The main estimates given by the method are the post-lasso estimates. However, parameter estimates from the regularized regression model used to identify invalid variants are also provided for completeness.

If a substantial proportion of genetic variants are removed from the analysis, the multivariable MR-Lasso method may give a false impression of confidence in the causal estimate due to homogeneity of the variant-specific causal estimates amongst the remaining variants. However, it is not reasonable to claim that there is strong evidence for a causal effect after a large number of variants with heterogeneous estimates have been removed from the analysis.

Value

The output from the function is an MVLasso object containing:

References

Andrew J Grant, Stephen Burgess. Pleiotropy robust methods for multivariable Mendelian randomization. arXiv 2020; 2008.11997

Examples

mr_mvlasso(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse),
   by = chdlodds, byse = chdloddsse))

Description

The mr_mvmedian function performs multivariable Mendelian randomization via the median method. This is implemented by multivariable weighted quantile regression, with the quantile set to 0.5 (the median).

Usage

mr_mvmedian(
  object,
  distribution = "normal",
  alpha = 0.05,
  iterations = 10000,
  seed = 314159265
)

## S4 method for signature 'MRMVInput'
mr_mvmedian(
  object,
  distribution = "normal",
  alpha = 0.05,
  iterations = 10000,
  seed = 314159265
)

Arguments

Details

The multivariable median method is similar to the univariable weighted median method, except that it is implemented using quantile regression. The regression model is multivariable and weighted by the inverse of the variances of the variant-specific estimates. Confidence intervals are calculated by parametric bootstrap to estimate the standard error of the estimates, and then using quantiles of a normal or t-distribution (depending on the value of distribution).

Value

The output from the function is an MVMedian object containing:

Examples

mr_mvmedian(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse),
   by = chdlodds, byse = chdloddsse), iterations = 100)
  # iterations is set to 100 to reduce runtime for the mr_mvmedian method,
  # 10000 iterations are recommended in practice

Description

The mr_mvpcgmm function performs multivariable Mendelian randomization via the principal components generalized method of moments method.

Usage

mr_mvpcgmm(
  object,
  nx,
  ny,
  cor.x = NULL,
  r = NULL,
  thres = 0.99,
  robust = TRUE,
  alpha = 0.05,
  ...
)

## S4 method for signature 'MRMVInput'
mr_mvpcgmm(
  object,
  nx,
  ny,
  cor.x = NULL,
  r = NULL,
  thres = 0.99,
  robust = TRUE,
  alpha = 0.05,
  ...
)

Arguments

Details

When a Mendelian randomization analysis is performed using correlated genetic variants from a single gene region, there is a tradeoff between using too few variants (and compromising on power) and using too many variants (in which case, estimates can be highly sensitive to small variation in the correlation matrix). This method performs dimension reduction on a weighted version of the genetic correlation matrix to form principal components based on the genetic variants, which are then used as instruments. It is recommended not to include very highly correlated variants in this method (say, r^2 > 0.95), but the method should cope well with variants correlated below this level.

This function runs a multivariable version of the PC-GMM method, which can be used when there are distinct exposures associated with variants at a single gene region. Phenotypic heterogeneity (that is, the genetic associations with the exposures are not collinear) at genomic loci encoding drug targets can be exploited by multivariable Mendelian randomization to provide insight on the pathways by which pharmacological interventions may affect disease risk.

This method provides two-sample multivariable Mendelian randomization estimates and associated confidence intervals that account for overdispersion heterogeneity in dimension-reduced genetic associations (when robust = TRUE).

Value

The output from the function is an MVPCGMM object containing:

References

Description of multivariable Mendelian randomization: Stephen Burgess, Simon G Thompson. Multivariable Mendelian Randomization: the use of pleiotropic genetic variants to estimate causal effects. American Journal of Epidemiology 2015; 181(4):251-260. doi: 10.1093/aje/kwu283.

Description of the PC-GMM method: "Robust use of phenotypic heterogeneity at drug target genes for mechanistic insights: application of cis-multivariable Mendelian randomization to GLP1R gene region" (Preprint).

Examples

mr_mvpcgmm(mr_mvinput(bx = cbind(ldlc, hdlc, trig), bxse = cbind(ldlcse, hdlcse, trigse),
   by = chdlodds, byse = chdloddsse, correlation = diag(length(ldlc))), nx=rep(17723,3), ny=17723)
# Note this example does not use variants from a single gene region, and is provided
#  to demonstrate that the code works, rather than to illustrate a recommended use case.

Description

The mr_pcgmm function performs multivariable Mendelian randomization via the principal components generalized method of moments method.

Usage

mr_pcgmm(
  object,
  nx,
  ny,
  r = NULL,
  thres = 0.99,
  robust = TRUE,
  alpha = 0.05,
  ...
)

## S4 method for signature 'MRInput'
mr_pcgmm(
  object,
  nx,
  ny,
  r = NULL,
  thres = 0.99,
  robust = TRUE,
  alpha = 0.05,
  ...
)

Arguments

Details

When a Mendelian randomization analysis is performed using correlated genetic variants from a single gene region, there is a tradeoff between using too few variants (and compromising on power) and using too many variants (in which case, estimates can be highly sensitive to small variation in the correlation matrix). This method performs dimension reduction on a weighted version of the genetic correlation matrix to form principal components based on the genetic variants, which are then used as instruments. It is recommended not to include very highly correlated variants in this method (say, r^2 > 0.95), but the method should cope well with variants correlated below this level.

This function runs a univariable version of the PC-GMM method, which can be used when there are a single exposure associated with variants at a given gene region.

This method provides two-sample univariable Mendelian randomization estimates and associated confidence intervals that account for overdispersion heterogeneity in dimension-reduced genetic associations (when robust = TRUE).

Value

The output from the function is an PCGMM object containing:

References

Description of the PC-GMM method: "Robust use of phenotypic heterogeneity at drug target genes for mechanistic insights: application of cis-multivariable Mendelian randomization to GLP1R gene region" (Preprint).

Examples

mr_pcgmm(mr_input(bx = calcium, bxse = calciumse,
   by = fastgluc, byse = fastglucse, correlation = calc.rho), nx=6351, ny=133010)

Description

The mr_pivw function implements the penalized inverse-variance weighted (pIVW) method.

Usage

mr_pivw(
  object,
  lambda = 1,
  over.dispersion = TRUE,
  delta = 0,
  sel.pval = NULL,
  Boot.Fieller = TRUE,
  alpha = 0.05
)

## S4 method for signature 'MRInput'
mr_pivw(
  object,
  lambda = 1,
  over.dispersion = TRUE,
  delta = 0,
  sel.pval = NULL,
  Boot.Fieller = TRUE,
  alpha = 0.05
)

Arguments

Details

The penalized inverse-variance weighted (pIVW) estimator accounts for weak instruments and balanced horizontal pleiotropy simultaneously in two-sample MR with summary statistics, i.e., an exposure sample (with IV-exposure effect Bx and standard error Bxse) and an outcome sample (with IV-outcome effect By and standard error Byse).

The pIVW estimator also allows for IV selection in three-sample MR, where weak IVs are screened out using an extra sample (with IV-exposure effect Bx* and standard error Bxse*) independent of the exposure sample and outcome sample. Generally, the P-value for Bx* can be computed by sel.pval=2*pnorm(abs(Bx*/Bxse*), lower.tail = FALSE), Given sel.pval and a z-score threshold delta, the variants kept in the analysis will be those with sel.pval<2*pnorm(delta,lower.tail = FALSE).

The mr_pivw function outputs a measure Condition that needs to be large for reliable asymptotic properties of the pIVW estimator. We also refer to Condition as effective sample size, which is a function of a measure of IV strength and the number of IVs. When delta is zero (i.e., no IV selection), Condition = (average F-statistic -1)*sqrt(# snps). When delta is not zero (i.e., IV selection is conducted), Condition = [(average F-statistic -1)*sqrt(# snps)]/c, where the numerator is computed using the selected variants, and the denominator c involves the selection probabilities of all variants (see more details in the paper). We suggest that Condition should be greater than 5 for the pIVW estimator to achieve reliable asymptotic properties.

Value

The output from the function is a PIVW object containing:

References

Xu S., Wang P., Fung W.K. and Liu Z. (2022). A Novel Penalized Inverse-Variance Weighted Estimator for Mendelian Randomization with Applications to COVID-19 Outcomes. Biometrics. doi: 10.1111/biom.13732.

Examples

mr_pivw(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse))

Description

The function mr_plot has three functionalities. It can generate a visual representation of MRInput, MRMVInput and MRAll objects.

Usage

mr_plot(
  object,
  error = TRUE,
  line = "ivw",
  orientate = FALSE,
  interactive = TRUE,
  labels = FALSE
)

## S4 method for signature 'MRInput'
mr_plot(
  object,
  error = TRUE,
  line = "ivw",
  orientate = FALSE,
  interactive = TRUE,
  labels = FALSE
)

## S4 method for signature 'MRAll'
mr_plot(object)

## S4 method for signature 'MRMVInput'
mr_plot(
  object,
  error = TRUE,
  line = TRUE,
  orientate = FALSE,
  interactive = TRUE,
  labels = FALSE
)

Arguments

Details

The result is dependent on the type of object passed to mr_plot. When the object is an MRInput object, the function uses either the plot command (if interactive is set to FALSE) or plotly syntax (if interactive is set to TRUE) to plot the association estimates against each other. When the object is an MRMVInput object, functionality is similar except that we plot the estimated associations with the outcome on the y-axis, and fitted values of the associations with the outcome from the inverse-variance weighted method on the x-axis. If interactive is set to FALSE, then a static graph is produced. By setting labels to TRUE, the names of the genetic variants appear above the points. This produces a less visually appealing graph, but one where it is easier to identify the individual genetic variants. If interactive is set to TRUE, then the plot is interactive and the user can hover over the various points to see the name of the associated genetic variant and its association estimates. When the object is an MRAll object, the function generates a ggplot to compare the causal estimates proposed by different methods.

Examples

mr_plot(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse),
  line="egger", orientate = TRUE)
mr_plot(mr_input(bx = ldlc, bxse = ldlcse, by = chdlodds, byse = chdloddsse),
  line="ivw", interactive=FALSE) # produces a static graph
mr_plot(mr_allmethods(mr_input(bx = ldlc, bxse = ldlcse,
   by = chdlodds, byse = chdloddsse), method="all", iterations = 50))
  # iterations is set to 50 to reduce runtime for the mr_median method,
  # 10000 iterations are recommended in practice

Description

An object containing the estimates produced using the mr_allmethods function.

Slots

Data

The mr_input object that was used as an input to the mr_allmethods function. This includes the original data, so that a call to mr_plot can plot the original data and the various causal estimates.

Values

A data.frame object comprising estimates from the various methods called by the mr_allmethods function. The first column gives the names of the methods, then the causal estimates, standard errors, 95% confidence intervals, and p-values.

Method

A string indicating whether all methods are implemented ("all", the default option), or just main methods ("main"), or only a subset of methods ("ivw", "egger", or "median").

Description

An object containing the results of MRcML.

Slots

Exposure

The names of the exposure variables.

Outcome

The name of the outcome variable.

Estimate

Estimate of theta.

StdError

Standard error of estimate.

Pvalue

p-value of estimate.

BIC_invalid

Set of selected invalid IVs if cML-BIC is performed, i.e. without MA or DP.

GOF1_p

p-value of the first goodness-of-fit test.

GOF2_p

p-value of the second goodness-of-fit test.

SNPs

The number of SNPs that were used in the calculation.

Alpha

Significance level for the confidence interval for estimate, default is 0.05.

CILower

Lower bound of the confidence interval for estimate.

CIUpper

Upper bound of the confidence interval for estimate.

MA

Indicator of whether model average is applied.

DP

Indicator of whether data perturbation is applied.

Description

An object containing the estimate produced using the contamination mixture method as well as various statistics.

Slots

Exposure

The names of the exposure variables.

Outcome

The name of the outcome variable.

Psi

The value of the standard deviation of the distribution of invalid estimands (default is 1.5 times the standard deviation of the ratio estimates).

Estimate

The causal estimate from the contamination mixture method.

CIRange

The confidence interval for Estimate based on a grid search.

CILower

The lower limit of the confidence interval. If the confidence interval contains multiple ranges, then lower limits of all ranges will be reported.

CIUpper

The upper limit of the confidence interval. If the confidence interval contains multiple ranges, then upper limits of all ranges will be reported.

CIMin

The smallest value used in the search to find the confidence interval.

CIMax

The largest value used in the search to find the confidence interval.

CIStep

The step size used in the search to find the confidence interval.

Pvalue

The p-value associated with the estimate calculated using the likelihood function and a chi-squared distribution.

Valid

The numbers of genetic variants that were considered valid instruments at the causal estimate.

ValidSNPs

The names of genetic variants that were considered valid instruments at the causal estimate.

Alpha

The significance level used in constructing the confidence interval (default is 0.05).

SNPs

The number of SNPs that were used in the calculation.

Description

An object containing the estimate produced using the heterogeneity-penalized model-averaging mode-based estimation method as well as various statistics.

Slots

Exposure

The names of the exposure variables.

Outcome

The name of the outcome variable.

Prior

The value of the prior probability of a genetic variant being a valid instrument (default is 0.5).

Estimate

The causal estimate from the heterogeneity-penalized method.

CIRange

The confidence interval for Estimate based on a grid search.

CILower

The lower limit of the confidence interval. If the confidence interval contains multiple ranges, then lower limits of all ranges will be reported.

CIUpper

The upper limit of the confidence interval. If the confidence interval contains multiple ranges, then upper limits of all ranges will be reported.

CIMin

The smallest value used in the search to find the confidence interval.

CIMax

The largest value used in the search to find the confidence interval.

CIStep

The step size used in the search to find the confidence interval.

Alpha

The significance level used in constructing the confidence interval (default is 0.05).

SNPs

The number of SNPs that were used in the calculation.

Description

An object containing the four vectors of summary statistics required to calculate Mendelian randomization estimates.

Details

The beta-coefficients are assumed to be estimated for uncorrelated (independent) genetic variants, although a correlation matrix can be specified if the variants are correlated in their distributions. We also assume that the beta-coefficients for associations with the exposure and with the outcome are uncorrelated (corresponding to a two-sample Mendelian randomization analysis), although correlation between associations with the exposure and with the outcome generally have little impact on causal estimates or standard errors. Estimates can either be specified by the user, or extracted from the PhenoScanner tool.

Slots

betaX

A numeric vector of beta-coefficient values for genetic associations with the first variable (often referred to as the exposure, risk factor, or modifiable phenotype).

betaY

A numeric vector of beta-coefficient values for genetic associations with the second variable (often referred to as the outcome). For a disease outcome, the beta coefficients are log odds estimates from logistic regression analyses.

betaXse

The standard errors associated with the beta-coefficients in betaX.

betaYse

The standard errors associated with the beta-coefficients in betaY.

correlation

The matrix of correlations between genetic variants. If this variable is not provided, then we assume that genetic variants are uncorrelated.

exposure

The name of the exposure variable.

outcome

The name of the outcome variable.

snps

The names of the genetic variants (SNPs) included in the analysis. The slots exposure, outcome, and snps are not required, but may be useful for keeping track of various MRInput objects. They are also used by the mr_plot function.

effect_allele

The name of the effect allele for each SNP. The beta-coefficients are the associations with the exposure and outcome per additional copy of the effect allele.

other_allele

The name of the non-effect allele.

eaf

The expected allele frequencies (numeric). The slots effect_allele, other_allele, and eaf are neither required, nor currently used in the MendelianRandomization package. They are included for future compatibility with the MR-Base suite of functions.

Description

An object containing the estimates produced using the MR-Lasso method as well as various statistics.

Slots

Exposure

The names of the exposure variables.

Outcome

The name of the outcome variable.

Estimate

The causal estimate from the MR-Lasso method.

StdError

The standard error associated with Estimate.

CILower

The lower bounds of the confidence intervals for Estimate based on StdError.

CIUpper

The upper bounds of the confidence intervals for Estimate based on StdError.

Alpha

The significance level used in constructing the confidence interval (default is 0.05).

Pvalue

P-value associated with the causal estimate from the MR-Lasso method.

SNPs

The number of SNPs used in the calculation.

RegEstimate

The estimate from the regularized regression model used in the MR-Lasso method.

RegIntercept

The intercept estimates from the regularized regression model used in the MR-Lasso method. An intercept estimate of zero identifies the corresponding genetic variant as a valid instrument. Genetic variants with non-zero intercept estimates will be excluded from the post-lasso estimator.

Valid

The number of genetic variants that have been identified as valid instruments.

ValidSNPs

The names of genetic variants that have been identified as valid instruments.

Lambda

The value of the tuning parameter used to compute RegEstimate (default is to calulate Lambda using the heterogeneity stopping rule).

Description

An object containing the estimate produced using the mode-based estimation method of Hartwig et al as well as various statistics.

Slots

Exposure

The names of the exposure variables.

Outcome

The name of the outcome variable.

Weighting

Whether the analysis was weighted or unweighted.

StdErr

Whether the simple or delta version of the standard errors were used.

Phi

The value of the bandwidth factor.

Estimate

The causal estimate from the mode-based estimation method.

StdError

The standard errors associated with Estimate.

CILower

The lower bounds of the confidence interval for Estimate based on StdError.

CIUpper

The upper bounds of the confidence interval for Estimate based on StdError.

Alpha

The significance level used in constructing the confidence interval (default is 0.05).

Pvalue

P-value associated with the causal estimate.

SNPs

The number of SNPs that were used in the calculation.

Description

An object containing the summary statistics required to calculate multivariable Mendelian randomization estimates.

Details

The beta-coefficients are assumed to be estimated for uncorrelated (independent) genetic variants, although a correlation matrix can be specified if the variants are correlated in their distributions. We also assume that the beta-coefficients for associations with the exposure and with the outcome are uncorrelated (corresponding to a two-sample Mendelian randomization analysis), although correlation between associations with the exposure and with the outcome generally have little impact on causal estimates or standard errors.

Slots

betaX

A matrix of beta-coefficient values for genetic associations with the risk factor variables. These should be arranged so that column 1 are the beta-coefficients for risk factor 1, and row 1 are the beta-coefficients for genetic variant 1.

betaY

A numeric vector of beta-coefficient values for genetic associations with the second variable (often referred to as the outcome). For a disease outcome, the beta coefficients are log odds estimates from logistic regression analyses.

betaXse

The matrix of standard errors associated with the beta-coefficients in betaX.

betaYse

The vector of standard errors associated with the beta-coefficients in betaY.

correlation

The matrix of correlations between genetic variants. If this variable is not provided, then we assume that genetic variants are uncorrelated.

exposure

The names of the exposure variables.

outcome

The name of the outcome variable.

snps

The names of the genetic variants (SNPs) included in the analysis. The slots exposure, outcome, and snps are not required, but may be useful for keeping track of various MRInput objects. They are also used by the mr_plot function.

effect_allele

The name of the effect allele for each SNP. The beta-coefficients are the associations with the exposure and outcome per additional copy of the effect allele.

other_allele

The name of the non-effect allele.

eaf

The expected allele frequencies (numeric). The slots effect_allele, other_allele, and eaf are neither required, nor currently used in the MendelianRandomization package. They are included for future compatibility with the MR-Base suite of functions.

Description

This is based on the profile likelihood of the set of valid IVs, which is not robust to uncertainty in model selection.

Usage

MVcML_SdTheta(b_exp, b_out, Sig_inv_l, theta, zero_ind, r_vec = NULL)

Arguments

Value

A vector

Description

An object containing the estimates produced using the multivariable MR-Egger method as well as various statistics.

Slots

Model

Model always takes the value random, as only random-effects analyses are permitted.

Orientate

The number of the risk factor that genetic associations are orientated to. The default value is 1, meaning that genetic associations with the first risk factor are set to be positive.

Exposure

The names of the exposure variables.

Outcome

The name of the outcome variable.

Correlation

The matrix of correlations between genetic variants.

Estimate

The causal estimates from the inverse-variance weighted method.

StdError.Est

The standard errors associated with Estimate.

CILower.Est

The lower bounds of the confidence interval for Estimate based on StdError.

CIUpper.Est

The upper bounds of the confidence interval for Estimate based on StdError.

Pvalue.Est

P-value associated with the causal estimate.

Intercept

The intercept estimate from the MR-Egger method. Under the InSIDE assumption, the intercept represents the average pleiotropic effect (average direct effect on the outcome) of a genetic variant. If the intercept differs from zero, this is evidence that the genetic variants are not all valid instruments; specifically, there is directional pleiotropy.

StdError.Int

The standard error associated with Intercept.

CILower.Int

The lower bound of the confidence interval for Intercept based on StdError.Int.

CIUpper.Int

The upper bound of the confidence interval for Estimate based on StdError.Int.

Pvalue.Int

P-value associated with the intercept.

Alpha

The significance level used in constructing the confidence interval (default is 0.05).

SNPs

The number of SNPs that were used in the calculation.

RSE

The estimated residual standard error from the regression model.

Heter.Stat

Heterogeneity statistic (Cochran's Q statistic) and associated p-value: the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more variants may be pleiotropic.

Description

An object containing the estimates produced using the multivariable generalized method of methods (GMM) method.

Slots

robust

Whether the robust model with overdispersion heterogeneity is estimated.

Exposure

The names of the exposure variables.

Outcome

The name of the outcome variable.

Correlation

The matrix of correlations between genetic variants if specified. If not specified, an identity matrix will be returned.

ExpCorrelation

Whether an exposure correlation matrix was specified.

CondFstat

The conditional F-statistic for each exposure.

Estimate

The causal estimates from the GMM method.

StdError

The standard errors associated with Estimate.

CILower

The lower bounds of the confidence interval for Estimate based on StdError.

CIUpper

The upper bounds of the confidence interval for Estimate based on StdError.

Overdispersion

The estimate of the overdispersion parameter for the robust model. If this is negative, then a value of zero is used in the method.

Pvalue

P-value associated with the causal estimates.

Alpha

The significance level used in constructing confidence intervals (default is 0.05).

Heter.Stat

Heterogeneity statistic (Cochran's Q statistic) and associated p-value (for non-robust model): the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more genetic variants may be pleiotropic.

Description

An object containing the estimates produced using the multivariable inverse-variance weighted (IVW) method as well as various statistics.

Slots

Model

The model used for estimation: random-effects ("random") or fixed-effect ("fixed"). The default option ("default") is to use a fixed-effect model when there are three or fewer genetic variants, and a random-effects model when there are four or more. The (multiplicative) random-effects model allows for heterogeneity between the causal estimates targeted by the genetic variants by allowing over-dispersion in the regression model. Under-dispersion is not permitted (in case of under-dispersion, the residual standard error is set to 1, as in a fixed-effect analysis).

Exposure

The names of the exposure variables.

Outcome

The name of the outcome variable.

Robust

Whether robust regression was used in the regression model relating the genetic associations with the outcome and those with the exposure.

Correlation

The matrix of correlations between genetic variants.

Estimate

The causal estimates from the inverse-variance weighted method.

StdError

The standard errors associated with Estimate.

CILower

The lower bounds of the confidence interval for Estimate based on StdError.

CIUpper

The upper bounds of the confidence interval for Estimate based on StdError.

Alpha

The significance level used in constructing the confidence interval (default is 0.05).

Pvalue

P-value associated with the causal estimate.

SNPs

The number of SNPs that were used in the calculation.

RSE

The estimated residual standard error from the regression model.

Heter.Stat

Heterogeneity statistic (Cochran's Q statistic) and associated p-value: the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more variants may be pleiotropic.

CondFstat

Conditional F statistics: An approximation of the first-stage conditional F statistics for all variants based on the summarized data. This represents the instrument strength for each exposure conditional on other exposures in the model. This is only reported if the sample sizes for the genetic associations with the exposures are provided.

Description

An object containing the estimates produced using the multivariable inverse-variance weighted (IVW) method with measurement error, as well as various statistics.

Slots

Model

The model used for estimation: random-effects ("random") or fixed-effect ("fixed"). The default option ("default") is to use a fixed-effect model when there are three or fewer genetic variants, and a random-effects model when there are four or more. The (multiplicative) random-effects model allows for heterogeneity between the causal estimates targeted by the genetic variants by allowing over-dispersion in the regression model. Under-dispersion is not permitted (in case of under-dispersion, the residual standard error is set to 1, as in a fixed-effect analysis).

Exposure

The names of the exposure variables.

Outcome

The name of the outcome variable.

Correlation

The matrix of correlations between genetic variants.

Estimate

The causal estimates from the inverse-variance weighted method.

StdError

The standard errors associated with Estimate.

CILower

The lower bounds of the confidence interval for Estimate based on StdError.

CIUpper

The upper bounds of the confidence interval for Estimate based on StdError.

Alpha

The significance level used in constructing the confidence interval (default is 0.05).

Pvalue

P-value associated with the causal estimate.

SNPs

The number of SNPs that were used in the calculation.

RSE

The estimated residual standard error from the regression model.

Heter.Stat

Heterogeneity statistic (Cochran's Q statistic) and associated p-value: the null hypothesis is that all genetic variants estimate the same causal parameter; rejection of the null is an indication that one or more variants may be pleiotropic.

Description

An object containing the estimates produced using the multivariable MR-Lasso method as well as various statistics.

Slots

Exposure

The names of the exposure variables.

Outcome

The name of the outcome variable.

Orientate

The number of the risk factor that genetic associations are orientated to. The default value is 1, meaning that genetic associations with the first risk factor are set to be positive.

Estimate

The causal estimates from the multivariable MR-Lasso method.

StdError

The standard errors associated with Estimate.

CILower

The lower bounds of the confidence intervals for Estimate based on StdError.

CIUpper

The upper bounds of the confidence intervals for Estimate based on StdError.

Alpha

The significance level used in constructing the confidence interval (default is 0.05).

Pvalue

P-values associated with the causal estimates from the multivariable MR-Lasso method.

SNPs

The number of SNPs used in the calculation.

RegEstimate

The estimates from the regularized regression model used in the multivariable MR-Lasso method.

RegIntercept

The intercept estimates from the regularized regression model used in the multivariable MR-Lasso method. An intercept estimate of zero identifies the corresponding genetic variant as a valid instrument. Genetic variants with non-zero intercept estimates will be excluded from the MR-Lasso method, which is obtained as a post-lasso estimator.

Valid

The number of genetic variants that have been identified as valid instruments.

ValidSNPs

The names of genetic variants that have been identified as valid instruments.

Lambda

The value of the tuning parameter used to compute RegEstimate (default is to calulate Lambda using the heterogeneity stopping rule).

Description

An object containing the estimates produced using the multivariable median method as well as various statistics.

Slots

Exposure

The names of the exposure variables.

Outcome

The name of the outcome variable.

Estimate

The causal estimates from the multivariable median method.

StdError

The standard errors associated with Estimate (obtained from bootstrapping).

CILower

The lower bounds of the confidence intervals for Estimate based on StdError.

CIUpper

The upper bounds of the confidence intervals for Estimate based on StdError.

Alpha

The significance level used in constructing the confidence interval (default is 0.05).

Pvalue

P-values associated with the causal estimates from the Wald method.

SNPs

The number of SNPs that used in the calculation.

Description

This is the internal MVMRcML-BIC function of mr_mvcML.

Usage

MVmr_cML(
  b_exp,
  b_out,
  se_bx,
  Sig_inv_l,
  n,
  K_vec = as.numeric(c()),
  random_start = 1L,
  min_theta_range = -0.5,
  max_theta_range = 0.5,
  maxit = 100L,
  thres = 1e-04
)

Arguments

Value

A list

BIC_theta

Estimated causal effect from MVMR-cML-BIC

BIC_invalid

Invalid IVs selected by MVMR-cML-BIC

l_vec

A vector of negative log-likelihood corresponding to each K.

K_vec

A vector of candidate K's

theta_vec

A matrix of causal parameter estimates, each column corresponds to a candidate K.

Conv_vec

A vector of successful convergence indicators corresponding to each K.

Converge

Indicator of successful convergence, 0 means success, 1 means failure.

BIC_vec

Data perturbation with successful convergence

Khat

The length of BIC_invalid.