Clinical trials with nested subgroups: Analysis, sample size determination and internal pilot studies

Abstract

The importance of subgroup analyses has been increasing due to a growing interest in personalized medicine and targeted therapies. Considering designs with multiple nested subgroups and a continuous endpoint, we develop methods for the analysis and sample size determination. First, we consider the joint distribution of standardized test statistics that correspond to each (sub)population. We derive multivariate exact distributions where possible, providing approximations otherwise. Based on these results, we present sample size calculation procedures. Uncertainties about nuisance parameters which are needed for sample size calculations make the study prone to misspecifications. We discuss how a sample size review can be performed in order to make the study more robust. To this end, we implement an internal pilot study design where the variances and prevalences of the subgroups are reestimated in a blinded fashion and the sample size is recalculated accordingly. Simulations show that the procedures presented here do not inflate the type I error significantly and maintain the prespecified power as long as the sample size of the smallest subgroup is not too small. We pay special attention to the case of small sample sizes and attain a lower boundary for the size of the internal pilot study.

Reporting of health equity considerations in cluster and individually randomized trials

“…It is important to note that subgroup analyses should be carefully planned and informed by wellformulated hypotheses: the higher the number of subgroup analyses, the higher the risk of spurious findings due to multiple statistical tests [47]. When planning a trial, investigators need to consider potential population differences in baseline risk of the condition or problem being studied and the possibility of differential effectiveness of the intervention and decide whether subgroup analyses are appropriate and can be accommodated in the sample-size calculation [48][49][50]. If additional subgroup hypotheses of interest are identified during the analyses, they should be clearly presented as exploratory and interpreted with caution [51][52][53].…”

A new conditional performance score for the evaluation of adaptive group sequential designs with sample size recalculation

“…For reasonably large sample sizes, the t ‐test statistic will approach the z ‐test statistic. Therefore, in the following, we will assume that the sample sizes per group are sufficiently high and thus that the test statistics are normally distributed . The trial is stopped at interim with rejection of H 0 if where α 1 denotes the corresponding local one‐sided significance level for the interim analysis and is the corresponding normal quantile.…”

“…The null hypothesis H 0 is rejected at the final analysis if where α 1+2 denotes the corresponding local one‐sided significance level for the final analysis. It can easily be seen that for large sample sizes, approximately it holds that so the joint distribution of Z 1 and Z 1+2 approximates a fully specified multivariate normal distribution, compare for example Reference . Using this joint distribution, local significance levels for the interim analysis and the final analysis can be specified.…”

Design and estimation in clinical trials with subpopulation selection

“…An overview of different multiple testing approaches for this purpose is given in the work of Alosh et al and the references therein. A single‐stage design with one biomarker tests, for example, the null hypotheses, ie, the treatment effect of the full population is zero, ie, H 0 F and the treatment effect in the subgroup of interest is zero, ie, H 0 S . These designs are usually employed for exploratory subgroup analysis in phase II (ie, to identify an interesting subgroup) or for confirmatory subgroup analysis in phase III, examining the treatment benefit of prespecified subgroups.…”

“…A single-stage design with one biomarker tests, for example, the null hypotheses, ie, the treatment effect of the full population is zero, ie, H 0F and the treatment effect in the subgroup of interest is zero, ie, H 0S . 5,[8][9][10][11][12] These designs are usually employed for exploratory subgroup analysis in phase II (ie, to identify an interesting subgroup) or for confirmatory subgroup analysis in phase III, examining the treatment benefit of prespecified subgroups. Corresponding multistage designs are constructed either as extensions of group sequential approaches 13 or using combination tests.…”