Clinical trials often involve multiple objectives related to multiple settings such as treatment arms, endpoints (primary, secondary, or tertiary), and subgroups. In such clinical trials, multiplicity issues caused by multiple statistical tests need to be adequately handled throughout studies. Novel statistical methods to account for several sources of multiplicity have been developed and applied in recent clinical trials. This article briefly reviews and summarizes the multiplicity issues in clinical trials that have multiple objectives and discusses the considerations in trial design, analysis, data interpretation, and the reporting of results. Relevant textbooks, articles, an international conference, guidances, and a web site are provided as references.
For many clinical trials, including the confirmatory ones, it is usually required that the FWER should be strongly controlled. The closed testing procedure, which is proposed by Marcus et al. (1976), is a procedure for strongly controlling the FWER. It is widely used for many methods of multiplicity control, for example, Holm method, step-down Dunnett method, fixed sequence method, and gatekeeping methods, etc. This article addresses the fundamental theory of the closed testing procedure, including the proof of strongly controlling the FWER, and several examples. For introduction, Fisher’s protected LSD method is examined and improved.
Multiplicity issues are encountered in confirmatory clinical trials with multiple clinical objectives. In order to control the familywise error rate in a clinical trial at a desirable level, a variety of multiplicity adjustment methods are commonly used. In this paper, we focus on the multiplicity testing procedures for non-pre-specified hypothesis ordering consisting of the single-step and data-driven hypothesis ordering, and illustrate them according to the distributional information.
Gatekeeping procedures and mixture procedures are multiple testing procedures controlling the familywise error rate in the strong sense, and deal with hierarchically ordered multiple objectives in clinical trials. As applications of gatekeeping procedures and mixture procedures have been increasing, methodological issues and examples with respect to these procedures have drawn attention. In this article, we show the relationship of the closed testing procedure and gatekeeping procedures, the relationship of gatekeeping procedures and mixture procedures.
In confirmatory clinical trials, family wise error rate (FWER) must be controlled in the strong sense. Gatekeeping procedure are widely used in clinical trials to adjust for hypothesis testing problems with a hierarchical structure. This approach ensures FWER control in the strong sense, because of the algorithm for constructing the gatekeeping procedure based on the closed testing principle. In this article, we present an overview of the gatekeeping procedure and current practice in the use of the approach.
Multiple test procedures are often used in the analysis of clinical trials including multiple objectives. To control the familywise error rate in the strong sense, various powerful procedures for structured hypotheses have been developed. In this paper, we introduce the graphical approach based on Bonferroni-based closed test procedures. Using the graphical approach, one can discuss different test strategies with the clinical team and build the appropriate multiple test procedure for the given study objectives. We illustrate not only the property of the graphical approach but also how to perform it by using SAS or R. Moreover, fixed sequence procedure and fallback procedure are presented within the framework of the graphical approach.
Recently, complex testing strategies based on the closed testing principle have been used especially in global clinical trials to assess efficacy of an investigational drug. This may be due to multiple/co-primary endpoints, multiple doses and/or multiplicity consideration of key secondary endpoints. In this review, focusing on different situations in Japan for multiple/co-primary endpoints and multiplicity consideration of key secondary endpoints from Europe and America, I will outline multiplicity issues discussed in PMDA review examples.