A false-discovery-rate-based loss framework for selection of interactions

Interaction effects have been consistently found important in explaining the variation in outcomes in many scientific research fields. Yet, in practice, variable selection including interactions is complicated due to the limited sample size, conflicting philosophies regarding model interpretability, and accompanying amplified multiple-testing problems. The lack of statistically sound algorithms for automatic variable selection with interactions has discouraged activities in exploring important interaction effects. In this article, we investigated issues of selecting interactions from three aspects: (1) What is the model space to be searched? (2) How is the hypothesis-testing performed? (3) How to address the multiple-testing issue? We propose loss functions and corresponding decision rules that control FDR in a Bayesian context. Properties of the decision rules are discussed and their performance in terms of power and FDR is compared through simulations. Methods are illustrated on data from a colorectal cancer study assessing the chemotherapy treatments and data from a diffuse large-B-cell lymphoma study assessing the prognostic effect of gene expressions.