Multiplicity adjustment in clinical trials with multiple correlated testing

Abstract

Statistical analyses of commonly occurring clinical trials that have correlated primary endpoints are often complex because multiple comparison adjustments are necessary. In practice, most statisticians resort to numerical simulation, even though such approaches can be computationally demanding and are often restricted to specific scenarios. The paper provides an analytical approach to one-sided multiple comparisons adjustment for mean values of multivariate normal data that have known positive definite covariance matrices. We use the maximum of test statistics to control the familywise error rate (FWER). This approach is equivalent to adjusting the minimum p-value but is simple to use and enables analytical evaluation. We derive a formula for the cumulative probability functions (CDFs) of the maximal test statistics when the correlations are known to be sufficiently small. When the correlations are considered to be more pronounced, we provide majorizing inequalities for the CDFs of the maximal test statistics. In addition, we address calculation of power and testing of conditional hypotheses for correlated primary endpoints. Theoretical results are illustrated by examples and are supported by extensive numerical studies.