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Group sequential methods for the Mann-Whitney parameter.

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.

SUBMITTER: Nowak CP

PROVIDER: S-EPMC9523827 | biostudies-literature | 2022 Oct

REPOSITORIES: biostudies-literature

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Group sequential methods for the Mann-Whitney parameter.

Nowak Claus P CP Mütze Tobias T Konietschke Frank F

Statistical methods in medical research 20220613 10

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 non ...[more]

PMID: 35698787

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Project description:BackgroundThe malaria risk analysis of multiple populations is crucial and of great importance whilst compressing limitations. However, the exponential growth in diversity and accumulation of genetic variation data obtained from malaria-infected patients through Genome-Wide Association Studies opens up unprecedented opportunities to explore the significant differences between genetic markers (risk factors), particularly in the resistance or susceptibility of populations to malaria risk. Thus, this study proposes using statistical tests to analyse large-scale genetic variation data, comprising 20,854 samples from 11 populations within three continents: Africa, Oceania, and Asia.MethodsEven though statistical tests have been utilized to conduct case-control studies since the 1950s to link risk factors to a particular disease, several challenges faced, including the choice of data (ordinal vs. non-ordinal) and test (parametric vs. non-parametric). This study overcomes these challenges by adopting the Mann-Whitney U test to analyse large-scale genetic variation data; to explore the statistical significance of markers between populations; and to further identify the highly differentiated markers.ResultsThe findings of this study revealed a significant difference in the genetic markers between populations (p < 0.01) in all the case groups and most control groups. However, for the highly differentiated genetic markers, a significant difference (p < 0.01) was present for most genetic markers with varying p-values between the populations in the case and control groups. Moreover, several genetic markers were observed to have very significant differences (p < 0.001) across all populations, while others exist between certain specific populations. Also, several genetic markers have no significant differences between populations.ConclusionsThese findings further support that the genetic markers contribute differently between populations towards malaria resistance or susceptibility, thus showing differences in the likelihood of malaria infection. In addition, this study demonstrated the robustness of the Mann-Whitney U test in analysing genetic markers in large-scale genetic variation data, thereby indicating an alternative method to explore genetic markers in other complex diseases. The findings hold great promise for genetic markers analysis, and the pipeline emphasized in this study can fully be reproduced to analyse new data.

Project description:When the distributional assumptions for a t-test are not met, the default position of many analysts is to resort to a rank-based test, such as the Wilcoxon-Mann-Whitney Test to compare the difference in means between two samples. The Wilcoxon-Mann-Whitney Test presents no danger of tied observations when the observations in the data are continuous. However, in practice, observations are discretized due various logical reasons, or the data are ordinal in nature. When ranks are tied, most textbooks recommend using mid-ranks to replace the tied ranks, a practice that affects the distribution of the Wilcoxon-Mann-Whitney Test under the null hypothesis. Other methods for breaking ties have also been proposed. In this study, we examine four tie-breaking methods-average-scores, mid-ranks, jittering, and omission-for their effects on Type I and Type II error of the Wilcoxon-Mann-Whitney Test and the two-sample t-test for various combinations of sample sizes, underlying population distributions, and percentages of tied observations. We use the results to determine the maximum percentage of ties for which the power and size are seriously affected, and for which method of tie-breaking results in the best Type I and Type II error properties. Not surprisingly, the underlying population distribution of the data has less of an effect on the Wilcoxon-Mann-Whitney Test than on the t-test. Surprisingly, we find that the jittering and omission methods tend to hold Type I error at the nominal level, even for small sample sizes, with no substantial sacrifice in terms of Type II error. Furthermore, the t-test and the Wilcoxon-Mann-Whitney Test are equally effected by ties in terms of Type I and Type II error; therefore, we recommend omitting tied observations when they occur for both the two-sample t-test and the Wilcoxon-Mann-Whitney due to the bias in Type I error that is created when tied observations are left in the data, in the case of the t-test, or adjusted using mid-ranks or average-scores, in the case of the Wilcoxon-Mann-Whitney.

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Group sequential methods for the Mann-Whitney parameter.

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Group sequential methods for the Mann-Whitney parameter.

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