A note on p-value multiple-testing adjustment for two-step genome-wide gene-environment interactions scans

Two-step testing is the state-of-the art approach for performing genome-wide interaction scans (GWIS). It is computationally efficient and yields higher power than standard single-step-based GWIS for virtually all biologically plausible scenarios. However, while two-step tests control the genome-wide type I error rate at the desired level, the lack of associated valid p-values can make it difficult for users to compare with single step-results. We show how multiple-testing adjusted p-values can be defined for two-step test based on standard multiple-testing theory, and how they can be in turn scaled to make valid comparisons with single-step tests possible.