“…In marginal analysis, statistical testing of G×E interactions prevails, which spans from the classical linear model with interactions in a wide range of studies, such as case-control study, case only study and the two-stage screening study, to more sophisticated models, such as empirical Bayesian models and nonparametric and semiparametric models. 44 On the other hand, the joint methods, especially the penalized variable selection methods, for G×E interactions, have been motivated by the success of gene set-based association analysis over marginal analysis, as demonstrated by Wu and Cui, 45 Wu et al, 46 and Schaid et al 47 Recently, multiple penalization methods have been proposed to identify important G×E interactions under parametric, semiparametric, and nonparametric models recently. 7,8,11,12 Within the Bayesian framework, nonlinear interaction has not been sufficiently considered for G×E interactions.…”