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In many scenarios such as genome-wide association studies where dependencesbetween variables commonly exist, it is often of interest to infer theinteraction effects in the model. However, testing pairwise interactions amongmillions of variables in complex and high-dimensional data suffers from lowstatistical power and huge computational cost. To address these challenges, wepropose a two-stage testing procedure with false discovery rate (FDR) control,which is known as a less conservative multiple-testing correction.Theoretically, the difficulty in the FDR control dues to the data dependenceamong test statistics in two stages, and the fact that the number of hypothesistests conducted in the second stage depends on the screening result in thefirst stage. By using the Cram\'er type moderate deviation technique, we showthat our procedure controls FDR at the desired level asymptotically in thegeneralized linear model (GLM), where the model is allowed to be misspecified.In addition, the asymptotic power of the FDR control procedure is rigorouslyestablished. We demonstrate via comprehensive simulation studies that ourtwo-stage procedure is computationally more efficient than the classical BHprocedure, with a comparable or improved statistical power. Finally, we applythe proposed method to a bladder cancer data from dbGaP where the scientificgoal is to identify genetic susceptibility loci for bladder cancer.

Two-stage Hypothesis Tests for Variable Interactions with FDR Control