On the exact size of tests of treatment effects in multi-arm clinical trials

Abstract

Summary: When testing treatment effects in multi-arm clinical trials, the Bonferroni method or the method of Simes 1986) is used to adjust for the multiple comparisons. When control of the family-wise error rate is required, these methods are combined with the close testing principle of Marcus et al. (1976). Under weak assumptions, the resulting p-values all give rise to valid tests provided that the basic test used for each treatment is valid. However, standard tests can be far from valid, especially when the endpoint is binary and when sample sizes are unbalanced, as is common in multi-arm clinical trials.This paper looks at the relationship between size deviations of the component test an..