ABSTRACT
Multiplicity issues are generally encountered in preclinical and clinical trials with multiple comparisons, tests for multiple endpoints, and multiple objectives. In preclinical applications, the objectives may correspond to testing across multiple genetic markers. This chapter presents some useful definitions of error rates, the power evaluations in multiple testing problems, and simple Bonferroni procedures that counteract the problem of multiplicity. In order to choose an appropriate multiple testing method, it is critical to select the set of relevant hypotheses that reflect the objectives of a clinical study or preclinical experiment. However, preserving the comparison-wise error rate for a single test is not the same concept as preserving the error rate for multiple tests under consideration. The family-wise error rate (FWER) control across multiple tests is a form of simultaneous inference, where all inferences in a family are jointly corrected up to a pre-specified error rate.
