As discussed above, characterization studies focus on the joint effects, looking at relative and absolute risks rather than narrowly focusing on specific forms of interactions. Nevertheless, several methods described in this section can be extended in ways that make them quite useful for characterization as well as discovery. The assumption of independence of G and E, exploited in the case-only method for testing multiplicative interaction [Piegorsch, et al. 1994], can also be exploited in a case-control study to make efficient inference regarding all parameters of a general logistic regression model. Having all of the parameters, allows for characterization of the full joint effects using a maximum likelihood estimation (MLE) method [Chatterjee and Carroll 2005]. Similarly, the robust empirical-Bayes method can be applied to make inference about all of the parameters of a logistic regression models [Mukherjee and Chatterjee 2008]. Methods have been developed for testing for additive interactions in case-control data [Knol, et al. 2011; Rothman 1986], and the assumption of GxE independence can be exploited to improve power to test for additive interaction based on case-control study data [Han, et al. 2012].
