| Title: | Stratified Analysis with Nonparametric Covariable Adjustment |
|---|---|
| Description: | There are several functions to implement the method for analysis in a randomized clinical trial with strata with following key features. A stratified Mann-Whitney estimator addresses the comparison between two randomized groups for a strictly ordinal response variable. The multivariate vector of such stratified Mann-Whitney estimators for multivariate response variables can be considered for one or more response variables such as in repeated measurements and these can have missing completely at random (MCAR) data. Non-parametric covariance adjustment is also considered with the minimal assumption of randomization. The p-value for hypothesis test and confidence interval are provided. |
| Authors: | Atsushi Kawaguchi |
| Maintainer: | Atsushi Kawaguchi <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.6 |
| Built: | 2024-12-10 06:40:19 UTC |
| Source: | CRAN |
A Package for Implementation of the method in Kawaguchi, Koch, and Wang (2011)
Atsushi Kawaguchi. [email protected]
Kawaguchi A., Koch, G. G. (2015). sanon: An R Package for Stratified Analysis with Nonparametric Covariable Adjustment. Journal of Statistical Software, 67(9), 1-37. doi:10.18637/jss.v067.i09
Kawaguchi A., Koch, G. G., Wang, X. (2011). Stratified Multivariate Mann-Whitney Estimators for the Comparison of Two Treatments with Randomization Based Covariance Adjustment. Statistics in Biopharmaceutical Research, Vol. 3, No. 2, 217-231.
This is a special function used in the context of sanon. It identifies categorical covariables when they appear on the right hand side of a formula.
catecovar(x, ref = NULL)catecovar(x, ref = NULL)
x |
variable name |
ref |
character for the reference group for the categorical covariable. |
In the sanon, the categorical covariable is converted into a dummy variable. The reference group is specified in the ref argument.
coef is a generic function which extracts model coefficients from objects returned by modeling functions. coefficients is an alias for it.
## S3 method for class 'sanon' coef(object, ...)## S3 method for class 'sanon' coef(object, ...)
object |
an object of class " |
... |
further arguments passed to or from other methods. |
All object classes which are returned by model fitting functions should provide a coef method or use the default one.
Coefficients extracted from the model object object.
##### Example 3.1 Randomized Clinical Trial of Chronic Pain ##### data(cpain) out1 = sanon(response ~ grp(treat, ref="placebo") + strt(center) + strt(diagnosis), data=cpain) coef(out1) coefficients(out1) ##### Example 3.2 Randomized Clinical Trial of Respiratory Disorder ##### data(resp) P = rbind(rep(0, 4), diag(4), rep(0, 4)) out23 = sanon(cbind(baseline, visit1, visit2, visit3, visit4) ~ grp(treatment, ref="P") + strt(center) + strt(sex) + covar(age), data=resp, P=P) # each four visits coef(out23) coefficients(out23)##### Example 3.1 Randomized Clinical Trial of Chronic Pain ##### data(cpain) out1 = sanon(response ~ grp(treat, ref="placebo") + strt(center) + strt(diagnosis), data=cpain) coef(out1) coefficients(out1) ##### Example 3.2 Randomized Clinical Trial of Respiratory Disorder ##### data(resp) P = rbind(rep(0, 4), diag(4), rep(0, 4)) out23 = sanon(cbind(baseline, visit1, visit2, visit3, visit4) ~ grp(treatment, ref="P") + strt(center) + strt(sex) + covar(age), data=resp, P=P) # each four visits coef(out23) coefficients(out23)
Computes confidence intervals for one or more parameters in a fitted model.
## S3 method for class 'sanon' confint(object, parm = NULL, level = 0.95, ...) ## S3 method for class 'confint.sanon' print(x, ...)## S3 method for class 'sanon' confint(object, parm = NULL, level = 0.95, ...) ## S3 method for class 'confint.sanon' print(x, ...)
object, x
|
an object of class " |
parm |
a specification of which parameters are to be given confidence intervals, either a vector of numbers or a vector of names. If missing, all parameters are considered. |
level |
the confidence level required. |
... |
further arguments passed to or from other methods. |
Confidence intervals for adjusted parameters in the weighted least squares are computed based on an asymptotic normal.
ci |
A matrix (or vector) with columns giving Mann-Whiteney estimates and their lower and upper confidence limits for each parameter with estimates. The interval will be labelled as Lower for (1 - level)/2 limit and Upper for 1 - (1 - level)/2 limit (by default 0.025 and 0.975). |
level |
Confidence level |
advarnames |
Adjust variable names in the weighted least squares method |
##### Example 3.1 Randomized Clinical Trial of Chronic Pain ##### data(cpain) out1 = sanon(response ~ grp(treat, ref="placebo") + strt(center) + strt(diagnosis), data=cpain) confint(out1) ##### Example 3.2 Randomized Clinical Trial of Respiratory Disorder ##### data(resp) P = rbind(rep(0, 4), diag(4), rep(0, 4)) out23 = sanon(cbind(baseline, visit1, visit2, visit3, visit4) ~ grp(treatment, ref="P") + strt(center) + strt(sex) + covar(age), data=resp, P=P) # each four visits confint(out23)##### Example 3.1 Randomized Clinical Trial of Chronic Pain ##### data(cpain) out1 = sanon(response ~ grp(treat, ref="placebo") + strt(center) + strt(diagnosis), data=cpain) confint(out1) ##### Example 3.2 Randomized Clinical Trial of Respiratory Disorder ##### data(resp) P = rbind(rep(0, 4), diag(4), rep(0, 4)) out23 = sanon(cbind(baseline, visit1, visit2, visit3, visit4) ~ grp(treatment, ref="P") + strt(center) + strt(sex) + covar(age), data=resp, P=P) # each four visits confint(out23)
Inference by contrast of parameters in a fitted model.
contrast( object, C = diag(length(object$b)), confint = FALSE, level = 0.95, ... ) ## S3 method for class 'contrast' print(x, ...)contrast( object, C = diag(length(object$b)), confint = FALSE, level = 0.95, ... ) ## S3 method for class 'contrast' print(x, ...)
object, x
|
an object of class " |
C |
contrast matrix. The number of column should be same as the length of |
confint |
logical value for whether the confidence interval is computed (only if C has one row). |
level |
the confidence level required (only if C has one row). |
... |
further arguments passed to or from other methods. |
This function provide the inference based on contrast after applying the function sanon.
The contrast matrix C should be defined by the user. If the the number of row of C = 1, the confidence interval for the estimator is produced.
C |
contrast matrix |
Cb |
contrast estimates |
VCb |
variance and covariance matrix of |
se |
standard error of |
level |
confidence level |
UL |
upper confidence limit (only if the number of row of C = 1, otherwise |
LL |
lower confidence limit (only if the number of row of C = 1, otherwise |
Q |
test statistic |
df |
degree of freedom |
p |
p-value |
##### Example 3.2 Randomized Clinical Trial of Respiratory Disorder ##### data(resp) P = rbind(rep(0, 4), diag(4), rep(0, 4)) out23 = sanon(cbind(baseline, visit1, visit2, visit3, visit4) ~ grp(treatment, ref="P") + strt(center) + strt(sex) + covar(age), data=resp, P=P) # Homogeneity of the xi_k across the four visits contrast(out23, C=cbind(diag(3), rep(-1, 3))) # Comparison between treatments for the average of the xi_k across the 4 visits contrast(out23, C=matrix(rep(1, 4)/4, ncol=4))##### Example 3.2 Randomized Clinical Trial of Respiratory Disorder ##### data(resp) P = rbind(rep(0, 4), diag(4), rep(0, 4)) out23 = sanon(cbind(baseline, visit1, visit2, visit3, visit4) ~ grp(treatment, ref="P") + strt(center) + strt(sex) + covar(age), data=resp, P=P) # Homogeneity of the xi_k across the four visits contrast(out23, C=cbind(diag(3), rep(-1, 3))) # Comparison between treatments for the average of the xi_k across the 4 visits contrast(out23, C=matrix(rep(1, 4)/4, ncol=4))
This is a special function used in the context of sanon. It identifies covariables when they appear on the right hand side of a formula.
covar(x)covar(x)
x |
variable name |
The data are from a multicenter randomized clinical trial to compare test and control treatments for the management of chronic pain, and they have had previous consideration in Stokes et al. (2000, chap. 13).
data(cpain)data(cpain)
A data frame with 193 observations and 4 variables
treata factor with levels active and placebo for treatment
responsea factor with five levels poor, fair, moderate, good and excel for pain status after treatment for 4 weeks
centera factor with two levels I and II for two centers
diagnosisa factor with four levels A, B, C, and D for diagnoses
Stokes, M. E., Davis, C. S., and Koch, G. G. (2000), Categorical Data Analysis using the SAS System, Cary: SAS Publishing.
This is a special function used in the context of sanon. It identifies group variables when they appear on the right hand side of a formula.
grp(x, ref = NULL)grp(x, ref = NULL)
x |
variable name |
ref |
character for the reference group for treatment group. |
The data are from two period cross-over design clinical trial for relief of heartburn, and listings of the data appear in Koch, Gitomer, Skalland, and Stokes (1983). The variables are as follows:
data(heartburn)data(heartburn)
A data frame with 60 observations and 9 variables.
centera factor vector for two centers
sequencea factor with levels AP and PA for sequence groups
agea numeric vector for age
sexa factor for sex with levels female and male
freqa numeric vector for weekly frequency of condition from previous medical history
MD1a numeric vector for time to relief from first dose during period 1
MD2a numeric vector for time to relief from first dose during period 2
res1a factor vector for relief status for period 1 (R = relief from first dose within 15 min, NF = no relief from first dose within 15 min)
ref2a factor vector for relief status for period 2 with same categories as res1
Koch G, Gitomer S, Skalland L, Stokes M (1983). "Some non-parametric and categorical data analyses for a change-over design study and discussion of apparent carry-over effects." Statistics in Medicine, 2(3), 397–412.
The data are from a randomized clinical trial to compare a test treatment to placebo for a respiratory disorder, and listings of the data appear in Stokes et al. (2000, chap. 15, pp. 495-496) and Koch et al. (1990). The variables are as follows:
data(resp)data(resp)
A data frame with 111 observations and 9 variables.
centera factor vector for two centers
treatmenta factor with levels A and P for active and placebo treatments, respectively
sexa factor with levels F and M for female and male, respectively
agea numeric vector for age
baselinea numeric vector for patient global ratings of symptom control according to 5 categories (4 = excellent, 3 = good, 2 = fair, 1 = poor, 0 = terrible) at baseline measurement
visit1a numeric vector for patient global ratings of symptom control at visit 1 with same categories as baseline
visit2a numeric vector for patient global ratings of symptom control at visit 2 with same categories as baseline
visit3a numeric vector for patient global ratings of symptom control at visit 3 with same categories as baseline
visit4a numeric vector for patient global ratings of symptom control at visit 4 with same categories as baseline
Stokes, M. E., Davis, C. S., and Koch, G. G. (2000), Categorical Data Analysis using the SAS System, Cary: SAS Publishing.
Koch, G. G., Carr, G. J., Amara, I. A., Stokes, M. E., and Uryniak, T. J. (1990), "Categorical Data Analysis," in Statistical Methodology in Pharmaceutical Sciences, ed. D. A. Berry, New York: Marcel Dekker, pp. 291-475.
This is a function for computing a stratified multivariate Mann-Whitney estimator that addresses the comparison between two randomized groups for a strictly ordinal response variable. Response variables may have some missing completely at random (MCAR) values for some patients. Non-parametric covariable adjustment is considered through the difference estimates between mean covariable and the weighted least squares method. Although such estimators can be computed directly as weighted linear combinations of within-stratum Mann-Whitney estimators, consistent estimation of their covariance matrix is done using methods for multivariate U-statistics.
sanon(outcome, ...) ## S3 method for class 'formula' sanon(formula, data = list(), ...) ## Default S3 method: sanon( outcome, group, strt = NULL, covar = NULL, catecovar = NULL, ref = NULL, covref = NULL, P = NULL, res.na.action = "default", ... ) ## S3 method for class 'sanon' print(x, ...)sanon(outcome, ...) ## S3 method for class 'formula' sanon(formula, data = list(), ...) ## Default S3 method: sanon( outcome, group, strt = NULL, covar = NULL, catecovar = NULL, ref = NULL, covref = NULL, P = NULL, res.na.action = "default", ... ) ## S3 method for class 'sanon' print(x, ...)
outcome |
vector of observations of length n, or a matrix with n rows for the response (or outcome) variables |
... |
further arguments passed to or from other methods. |
formula |
a formula object, with the response on the left of a ~ operator, and the terms on the right. |
data |
a data.frame in which to interpret the variables named in the formula. |
group |
numeric vector of observations of length n for treatment group. The reference group can be specified in |
strt |
numeric or factor vector of observations of length n, or a matrix with n rows for strata. |
covar |
numeric or factor vector of observations of length n, or a matrix with n rows for covariable. |
catecovar |
numeric or factor vector of observations of length n, or a matrix with n rows for categorical covariable. |
ref |
character for the reference group for treatment group in |
covref |
character vector for the reference group for categorical covariables in |
P |
a matrix for weighted least squares estimation. |
res.na.action |
character for setting NA actions. "default", "LOCF1", "LOCF2", "replace", and "remove" are available. default is "default". see the details. |
x |
an object of class " |
sanon has two specifications for the input, variable and formula based.
In the variable based input, one can specify R objects to outcome, group, and strata variables, and covariable.
In the formula based input, the formula consists of variable names in a data.frame.
The strata and group variables, and covariable are recognized by functions strt, grp, covar, and catecovar.
outcome can be contained missing values, which should be coded by NA.
Five options for the management of missing values can be specifed in the argument res.na.action;
"default" = the method in Kawaguchi et al. (2011), "LOCF1" and "LOCF2" = last observation carried forward with respect to kernels of U-statistics and observed velues, repsectively, "replace" = missing values are managed as tied with all other values in the same stratum, and "remove" = the complete cases analaysis.
For res.na.action = "LOCF1" or "LOCF2", the order in the outcome is considered as the time order in imputing.
if the baseline measurement is missing, then the corresponding subject is removed.
outcome can be also multiple (repeatly measured).
If more than two strata are specified, these are taking a cross-classification.
The group variable can be specifies its reference group in the argument ref in the sanon or in the function grp.
N |
Sample size |
Nna |
tne number of subjects with missing values |
nhik |
Sample size in each strata, group, and response |
nik |
Sample size in each group and response |
xi |
(multivariate) Mann-Whitney estimate(s) that addresses the comparison between two randomized groups |
g |
the difference estimates between mean covariable |
f |
a vector consisting of |
Vf |
estimated covariance matrix of |
b |
fully adjustmented estimators for all covariables and the strata |
Vb |
covariance matrix of |
se |
standard error of |
Q |
test statistics for |
p |
p-value for |
outnames |
outcome or response names |
covarnames |
covariable names |
advarnames |
variable names adjusting in the weighted least squares |
bnames |
variable names of adjusted in the weighted least squares |
reslevels |
levels for response variables |
grouplevels |
levels for the group variable |
strtout |
resulting (cross-classification) strata |
strtlevels |
resulting (cross-classification) strata levels |
strtnames |
resulting (cross-classification) strata names |
matP |
design matrix used in the weighted least squares |
Kawaguchi A., Koch, G. G. (2015). sanon: An R Package for Stratified Analysis with Nonparametric Covariable Adjustment. Journal of Statistical Software, 67(9), 1-37. doi:10.18637/jss.v067.i09
Kawaguchi, A., Koch, G. G., Wang, X. (2011): Stratified Multivariate Mann-Whitney Estimators for the Comparison of Two Treatments with Randomization Based Covariance Adjustment. Statistics in Biopharmaceutical Research, Vol. 3, No. 2, 217-231.
##### Example 3.1 Randomized Clinical Trial of Chronic Pain ##### data(cpain) out11 = sanon(response ~ grp(treat, ref="placebo") + strt(center) + strt(diagnosis), data=cpain) out11 summary(out11) # R objects are also available attach(cpain) out12 = sanon(outcome=response, group=treat, strt=cbind(center, diagnosis), ref="placebo") out12 summary(out12) ##### Example 3.2 Randomized Clinical Trial of Respiratory Disorder ##### data(resp) out21 = sanon(cbind(baseline, visit1, visit2, visit3, visit4) ~ grp(treatment, ref="P") + strt(center) + strt(sex) + covar(age), data=resp) out21 summary(out21) # the matrix P can be specified P = rbind(rep(0, 4), diag(4), rep(0, 4)) out22 = sanon(cbind(baseline, visit1, visit2, visit3, visit4) ~ grp(treatment, ref="P") + strt(center) + strt(sex) + covar(age), data=resp, P=P) out22 summary(out22)##### Example 3.1 Randomized Clinical Trial of Chronic Pain ##### data(cpain) out11 = sanon(response ~ grp(treat, ref="placebo") + strt(center) + strt(diagnosis), data=cpain) out11 summary(out11) # R objects are also available attach(cpain) out12 = sanon(outcome=response, group=treat, strt=cbind(center, diagnosis), ref="placebo") out12 summary(out12) ##### Example 3.2 Randomized Clinical Trial of Respiratory Disorder ##### data(resp) out21 = sanon(cbind(baseline, visit1, visit2, visit3, visit4) ~ grp(treatment, ref="P") + strt(center) + strt(sex) + covar(age), data=resp) out21 summary(out21) # the matrix P can be specified P = rbind(rep(0, 4), diag(4), rep(0, 4)) out22 = sanon(cbind(baseline, visit1, visit2, visit3, visit4) ~ grp(treatment, ref="P") + strt(center) + strt(sex) + covar(age), data=resp, P=P) out22 summary(out22)
The data are from a randomized clinical trial to compare a test treatment to placebo for a seborrheic dermatitis, and listings of the data appear in Ramaswamy, Koch, and Amara (1997). The variables are as follows:
data(sebor)data(sebor)
A data frame with 167 observations and 8 variables.
centera factor vector for eight centers
treata factor with levels placebo and test for placebo and test treatments, resectively
score1a numeric vector for patient global scores for the face according to 6 categories (0 = cleared, 1 = excellent improvement, 2 = moderate improvement, 3 = slight improvement, 4 = no change, 5 = exacerbation)
score2a numeric vector for patient global scores for the scalp with same categories as score1
score3a numeric vector for patient global scores for the chest with same categories as score1
severity1a numeric vector for the baseline desease severity for the face according to 3 categories (1 = mild, 2 = moderate, 3 = severe)
severity2a numeric vector for the baseline desease severity for the scalp with same categories as severity1
severity3a numeric vector for the baseline desease severity for the chest with same categories as severity1
Ramaswamy R, Koch G, Amara I (1997). "Application of rank analysis of covariance methods to analysis of multiple anatomical regions with treatment for seborrheic dermatitis." Journal of Biopharmaceutical Statistics, 7(3), 403–416.
The data are from a randomized clinical trial to compare a test treatment to placebo for skin conditions, and listings of the data appear in Stanish, Gillings, Koch (1978a, b). The variables are as follows:
data(skin)data(skin)
A data frame with 172 observations and 6 variables.
centera factor vector for two centers
treata factor with levels A and P for active and placebo treatments, skinectively
stagea numeric vector for initial severity of the skin condition according to 3 categories (3 = fair, 4 = poor, 5 = exacerbation) at baseline measurement
res1a numeric vector for extent of improvement at visit 1 according to 5 categories (1 = rapidly improving, 2 = slowly improving, 3 = stable, 4 = slowly worsening, 5 = rapidly worsening)
res2a numeric vector for extent of improvement at visit 2 with same categories as res1
res3a numeric vector for extent of improvement at visit 3 with same categories as res1
Stanish W, Gillings D, Koch G (1978a). "An application of multivariate ratio methods for the analysis of a longitudinal clinical trial with missing data." Biometrics, 34(2), pp. 305–317.
Stanish WM, Koch GG, Landis JR (1978b). "A computer program for multivariate ratio analysis (MISCAT)." Computer Programs in Biomedicine, 8(3-4), 197–207.
This is a special function used in the context of sanon. It identifies stratification variables when they appear on the right hand side of a formula.
strt(x)strt(x)
x |
variable name |
summary method for class "sanon".
## S3 method for class 'sanon' summary(object, ...) ## S3 method for class 'summary.sanon' print(x, ...)## S3 method for class 'sanon' summary(object, ...) ## S3 method for class 'summary.sanon' print(x, ...)
object, x
|
an object of class " |
... |
further arguments passed to or from other methods. |
This function provide the p value for the hypothesis test of coefficient in the model of weighted least squares method. Note that the estimates in the output are for the (xi_k - 0.5).
coefficients |
a p x 4 matrix with columns for the estimated coefficient, its standard error, chi-squared statistic and corresponding (two-sided) p-value. |
advarnames |
adjust variable names in weighted least squares method |
##### Example 3.1 Randomized Clinical Trial of Chronic Pain ##### data(cpain) sum1 = summary(sanon(response ~ grp(treat, ref="placebo") + strt(center) + strt(diagnosis) , data=cpain)) sum1 ##### Example 3.2 Randomized Clinical Trial of Respiratory Disorder ##### data(resp) sum22 = summary(sanon(cbind(baseline, visit1, visit2, visit3, visit4) ~ grp(treatment, ref="P") + strt(center) + strt(sex) + covar(age), data=resp)) sum22##### Example 3.1 Randomized Clinical Trial of Chronic Pain ##### data(cpain) sum1 = summary(sanon(response ~ grp(treat, ref="placebo") + strt(center) + strt(diagnosis) , data=cpain)) sum1 ##### Example 3.2 Randomized Clinical Trial of Respiratory Disorder ##### data(resp) sum22 = summary(sanon(cbind(baseline, visit1, visit2, visit3, visit4) ~ grp(treatment, ref="P") + strt(center) + strt(sex) + covar(age), data=resp)) sum22
Returns the variance-covariance matrix of the main parameters of a fitted model object.
## S3 method for class 'sanon' vcov(object, ...)## S3 method for class 'sanon' vcov(object, ...)
object |
an object of class " |
... |
further arguments passed to or from other methods. |
This is a generic function.
Coefficients extracted from the model object object.
##### Example 3.1 Randomized Clinical Trial of Chronic Pain ##### data(cpain) out1 = sanon(response ~ grp(treat, ref="placebo") + strt(center) + strt(diagnosis), data=cpain) vcov(out1) ##### Example 3.2 Randomized Clinical Trial of Respiratory Disorder ##### data(resp) P = rbind(rep(0, 4), diag(4), rep(0, 4)) out23 = sanon(cbind(baseline, visit1, visit2, visit3, visit4) ~ grp(treatment, ref="P") + strt(center) + strt(sex) + covar(age), data=resp, P=P) # each four visits vcov(out23)##### Example 3.1 Randomized Clinical Trial of Chronic Pain ##### data(cpain) out1 = sanon(response ~ grp(treat, ref="placebo") + strt(center) + strt(diagnosis), data=cpain) vcov(out1) ##### Example 3.2 Randomized Clinical Trial of Respiratory Disorder ##### data(resp) P = rbind(rep(0, 4), diag(4), rep(0, 4)) out23 = sanon(cbind(baseline, visit1, visit2, visit3, visit4) ~ grp(treatment, ref="P") + strt(center) + strt(sex) + covar(age), data=resp, P=P) # each four visits vcov(out23)