On Two-Stage Hypothesis Testing Procedures Via Asymptotically Independent Statistics

Kooperberg and LeBlanc (2008) proposed a two-stage testing procedure to screen for significant interactions in genome-wide association (GWA) studies by a soft threshold on marginal associations (MA), though its theoretical properties and generalization have not been elaborated. In this article, we discuss conditions that are required to achieve strong control of the Family-Wise Error Rate (FWER) by such procedures for low or high-dimensional hypothesis testing. We provide proof of asymptotic independence of marginal association statistics and interaction statistics in linear regression, logistic regression, and Cox proportional hazard models in a randomized clinical trial (RCT) with a rare event. In case-control studies nested within a RCT, a complementary criterion, namely deviation from baseline independence (DBI) in the case-control sample, is advocated as a screening tool for discovering significant interactions or main effects. Simulations and an application to a GWA study in Women’s Health Initiative (WHI) are presented to show utilities of the proposed two-stage testing procedures in pharmacogenetic studies