Multiplicity Adjustment in Clinical Trials with Multiple Correlated Testing

• Activity Number: 325
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Boris Zaslavsky* and Fang Chen
• Companies: FDA/CBER and SAS Institute
• Keywords: significance level ; multivariate normal distribution ; maximal statistics ; multiple testing ; conditional distribution

Abstract

Statistical analysis of commonly occurring clinical trials that have correlated primary endpoints are often complex because multiple comparisons 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 analytical solutions 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 probability density functions (PDFs) of the maximal test statistics when the correlations are known to be sufficiently small. When this assumption cannot be justified, we provide majorizing inequalities for the PDFs 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.