A primary challenge of characterizing joint effects and GxE to provide biological insights into mechanisms is the lack of explicit links between statistical and biological interactions. This issue has been vigorously debated in the epidemiologic literature for decades [Cordell 2002; Siemiatycki and Thomas 1981; Thompson 1991; VanderWeele 2011; Weinberg 2012b]. While it is generally recognized that the simple existence of multiplicative interactions between two risk factors does not readily identify a unique model for biologic mechanisms for interactions, there is considerable debate whether tests for interaction in alternative scales could be more insightful for this purpose. We present some of these alternatives in the statistical methods section of this paper.
