A rank-based sample size method for multiple outcomes in clinical trials

O'Brien (Biometrics 1984; 40:1079-1087) introduced a rank-sum-type global statistical test to summarize treatment's effect on multiple outcomes and to determine whether a treatment is better than others. This paper presents a sample size computation method for clinical trial design with multiple primary outcomes, and O'Brien's test or its modified test (Biometrics 2005; 61:532-539) is used for the primary analysis. A new measure, the global treatment effect (GTE), is introduced to summarize treatment's efficacy from multiple primary outcomes. Computation of the GTE under various settings is provided. Sample size methods are presented based on prespecified GTE both when pilot data are available and when no pilot data are available. The optimal randomization ratio is given for both cases. We compare our sample size method with the Bonferroni adjustment for multiple tests. Since ranks are used in our derivation, sample size formulas derived here are invariant to any monotone transformation of the data and are robust to outliers and skewed distributions. When all outcomes are binary, we show how sample size is affected by the success probabilities of outcomes. Simulation shows that these sample size formulas provide good control of type I error and statistical power. An application to a Parkinson's disease clinical trial design is demonstrated. Splus codes to compute sample size and the test statistic are provided.