Hierarchical testing of multiple endpoints in group‐sequential trials

Abstract

We consider the situation of testing hierarchically a (key) secondary endpoint in a group-sequential clinical trial that is mainly driven by a primary endpoint. By 'mainly driven', we mean that the interim analyses are planned at points in time where a certain number of patients or events have accrued on the primary endpoint, and the trial will run either until statistical significance of the primary endpoint is achieved at one of the interim analyses or to the final analysis. We consider both the situation where the trial is stopped as soon as the primary endpoint is significant as well as the situation where it is continued after primary endpoint significance to further investigate the secondary endpoint. In addition, we investigate how to achieve strong control of the familywise error rate (FWER) at a pre-specified significance level alpha for both the primary and the secondary hypotheses. We systematically explore various multiplicity adjustment methods. Starting point is a naive strategy of testing the secondary endpoint at level alpha whenever the primary endpoint is significant. Hung et al. (J. Biopharm. Stat. 2007; 17:1201-1210) have already shown that this naive strategy does not maintain the FWER at level alpha. We derive a sharp upper bound for the rejection probability of the secondary endpoint in the naive strategy. This suggests a number of multiple test strategies and also provides a benchmark for deciding whether a method is conservative or might be improved while maintaining the FWER at alpha. We use a numerical example based on a real case study to illustrate the results of different hierarchical test strategies.

Perspectives on the Use of Adaptive Designs in Clinical Trials. Part II. Panel Discussion

“…Since we aim at controlling the FWER in the strong sense, simulations under the assumption that all treatment effects are the same (including the one from the control group) will not be sufficient and simulation over a fine enough and large enough grid of all possible configurations may not be feasible. The configuration where Type I error rate is largest may well be "hidden" (for simple examples see Glimm et al, 2010;Posch et al, 2010) and may be missed easily. Simulation of the operation characteristics of various design options, e.g.…”

Group-Sequential Strategies in Clinical Trials with Multiple Co-Primary Outcomes

“…In practice, use of DF-B should be carefully considered. In a similar but not identical setting, i.e., at least one endpoint with one interim analysis, and one primary and one secondary endpoints, the behavior of the Type I error for hierarchical hypothesis testing has been well-studied (Glimm et al, 2010; Hung et al, 2007; Tamhane et al, 2010). By the analogy between these studies and the investigation given in Appendix 2, one simple solution is to test the hypothesis for the second-tested endpoint only once although further investigation will be required to evaluate more general situations with more than two analyses.…”

“…The first question is the choice of the stopping boundary based on an alpha-spending function for each endpoint. If the trial was designed to detect effects on at least one endpoint with a prespecified ordering of endpoints, then the selection of different boundaries for each endpoint (i.e., the O’Brien-Fleming-type for the primary endpoint and the Pocock-type boundary for the secondary endpoint) can provide a higher power than using the same boundary for both endpoints (Glimm et al, 2010; Tamhane et al, 2010). However, as shown in Section 4, the selection of a different boundary has a minimal effect on the overall power and average sample number.…”

Sequential tests controlling generalized familywise error rates

“…Moreover, an answer is needed for each question, and thus, each individual hypothesis has to be tested instead of one composite hypothesis. Such problems arise in clinical trials for testing multiple efficacy and safety endpoints [11,14,26,27], DNA and protein sequence analysis [24,30], epidemiology [10], cybersecurity [20], and so on.…”

“…We assume that each sampled unit i contributes to the total cost of an experiment regardless of how many components X ij (such as vital signs of patients or electronic measurements of manufactured parts) are recorded on unit i. This is quite common in many experiments (e.g., [4,11,15,26]). For example, in clinical trials, certain amount is budgeted for each participating patient, covering the cost of a treatment, service, insurance, incentive, and possibly, accommodation and transportation.…”