Event

Multiple endpoints are increasingly used in clinical trials. The significance of some of these clinical trials is established if at least r null hypotheses are rejected among m that are simultaneously tested. The usual approach in multiple hypothesis testing is to control the family-wise error rate, which is defined as the probability that at least one type-I error is made. More recently, the q-generalized family-wise error rate has been introduced to control the probability of making at least q false rejections.

For procedures controlling this global type-I error rate, we define a type-II r-generalized family-wise error rate which is directly related to the r-power defined as the probability of rejecting at least r false null hypotheses.

We obtain very general power formulas which can be used to compute the sample size for single-step and step-wise procedures. These are implemented in our R package rPowerSampleSize available on the CRAN, making them directly available to end-users. Complexities of the formulas are presented to gain insight into computation time issues.  Comparison with Monte-Carlo strategy is also presented. We compute sample sizes for two clinical trials involving multiple endpoints; one designed to investigate the effectiveness of a drug against acute heart failure, the other for the immunogenicity of a vaccine strategy against pneumococcus.