Group sequential methods for the Mann-Whitney parameter

Claus P Nowak, Tobias Mütze, Frank Konietschke, Claus P Nowak, Tobias Mütze, Frank Konietschke

Abstract

Late phase clinical trials are occasionally planned with one or more interim analyses to allow for early termination or adaptation of the study. While extensive theory has been developed for the analysis of ordered categorical data in terms of the Wilcoxon-Mann-Whitney test, there has been comparatively little discussion in the group sequential literature on how to provide repeated confidence intervals and simple power formulas to ease sample size determination. Dealing more broadly with the nonparametric Behrens-Fisher problem, we focus on the comparison of two parallel treatment arms and show that the Wilcoxon-Mann-Whitney test, the Brunner-Munzel test, as well as a test procedure based on the log win odds, a modification of the win ratio, asymptotically follow the canonical joint distribution. In addition to developing power formulas based on these results, simulations confirm the adequacy of the proposed methods for a range of scenarios. Lastly, we apply our methodology to the FREEDOMS clinical trial (ClinicalTrials.gov Identifier: NCT00289978) in patients with relapse-remitting multiple sclerosis.

Keywords: Brunner-Munzel test; Wilcoxon-Mann-Whitney test; error spending; group sequential methods; nonparametric relative effect; win odds.

Conflict of interest statement

Declaration of conflicting interests: The author(s) declared the following potential conflicts of interest with respect to the research, authorship, and/or publication of this article: Claus P. Nowak and Tobias Mütze are employees of Novartis Pharma AG.

Figures

Figure 1.
Figure 1.
Normal distribution—Setting 1 Notes: The lines show the relative frequency of the 100000 simulation runs, where the null hypothesis could be rejected at some stage based on the Brunner-Munzel test (with t-approximation) as in (5), the Wilcoxon-Mann-Whitney test as in (1) and the log win odds test as in (9) for five different total maximum sample sizes, two error spending functions, up to four stages in total as well as two different allocation ratios.
Figure 2.
Figure 2.
Normal distribution—Setting 2 Notes: The lines show the relative frequency of the 100000 simulation runs, where the null hypothesis could be rejected at some stage based on the Brunner-Munzel test (with t-approximation) as in (5), the Wilcoxon-Mann-Whitney test as in (1) and the log win odds test as in (9) for five different total maximum sample sizes, two error spending functions, up to four stages in total as well as two different allocation ratios.
Figure 3.
Figure 3.
Normal distribution—Setting 3 Notes: The lines show the relative frequency of the 100000 simulation runs, where the null hypothesis could be rejected at some stage based on the Brunner-Munzel test (with t-approximation) as in (5), the Wilcoxon-Mann-Whitney test as in (1) and the log win odds test as in (9) for five different total maximum sample sizes, two error spending functions, up to four stages in total as well as two different allocation ratios.

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