simultaneously in a 2-degree of freedom test [Kraft, et al. 2007]. Alternative versions of this test have been proposed [Dai, et al. 2012b] and the GxE independence assumption can be incorporated into joint tests to improve power using MLE [Chatterjee and Carroll 2005] or empirical-Bayes methods [Mukherjee and Chatterjee 2008]. These tests are scale independent under the restricted situation of dichotomous G and dichotomous E, although they are sensitive to choice of scale for continuous or categorical G or E. Additionally, joint tests can have increased power over traditional marginal and interaction tests, particularly if the genetic effects are modest [Lindstrom, et al. 2009] After a variant is identified with the joint test method, standard practice is to characterize the full joint effects, including a separate examination of the marginal and GxE interaction effects. This produces stratum-specific relative risks that are jointly cross classified with their 95% confidence intervals. Some recent examples have identified novel genetic loci using the joint test that do not show strong evidence for multiplicative interaction when a standard GxE interaction test is performed [Hancock, et al. 2012; Manning, et al. 2012]. In one case the joint test allowed for identification of novel genetic loci not
