A linear mixed model framework for gene‐based gene–environment interaction tests in twin studies

Interaction between genes and environments (G×E) can be well investigated in families due to the shared genes and environment among family members. However, the majority of the current tests of G×E interaction between a set of variants and an environment are only suitable for studies with unrelated subjects. In this paper, we extend several G×E interaction tests to a linear mixed model framework to study interaction between a set of correlated environments and a candidate gene in families. The correlated environments can either be modeled separately or jointly in one model. We demonstrate theoretically that the tests developed by modeling correlated environments separately are valid and present a computationally fast alternative to detect G×E interaction in families. For either strategy, we propose treating the genetic main effects as a random effect to reduce the number of main‐effect parameters and thus improve the power to detect interactions. Additionally, we propose a generalization of a test of interaction that adaptively sums the interactions using a sequential algorithm. This generalized set of tests, referred to as the sequential algorithm for the sum of powered score (Seq‐SPU) family of tests, can be expressed as a weighted version of the SPU. We find that the adaptive version of our test, Seq‐aSPU, can outperform aSPU in cases where the interactions effects are in opposite directions. We applied these methods to the Minnesota Center for Twin and Family Research data set and found one significant gene in interaction with four psychosocial environmental factors affecting the alcohol consumption among the twins.