Sample size determination with familywise control of both type I and type II errors in clinical trials

The concept of controlling familywise type I and type II errors at the same time is essentially an integrated process to deal with multiplicity issues in clinical trials. The process will select a multiple testing procedure (MTP) which controls the familywise type I error and calculate the per hypothesis sample size such that the "studywise power" is maintained at desired level. The power of a study can be defined in several ways and it depends on the objective. In this article, we provide general guidance on how to make the selection of MTPs and calculate sample size simultaneously. We introduce the concept of strong and weak control of the familywise type II error and generalized familywise type II error. We also proposed the novel Bonferroni+ and optimal Bonferroni+ procedures to allocate per hypothesis type II error. We demonstrated the value of the proposed work as it cannot be replaced by simple simulations. A real clinical trial is discussed throughout the article as an example.