A note on false positives and power in G × E modelling of twin data

The variance components models for gene-environment interaction proposed by Purcell in 2002 are widely used. In both the bivariate and the univariate parameterization of these models, the variance decomposition of trait T is a function of moderator M. We show that if M and T are correlated, and moderator M is correlated between twins as well, the univariate parameterization produces a considerable increase in false positive moderation effects. A simple extension of this univariate moderation model prevents this elevation of the false positive rate provided the covariance between M and T is itself not also subject to moderation. If the covariance between M and T varies as a function of M, then moderation effects observed in the univariate setting should be interpreted with care as these can have their origin in either moderation of the covariance between M and T or in moderation of the unique paths of T. We conclude that researchers should use the full bivariate moderation model to study the presence of moderation on the covariance between M and T. If such moderation can be ruled out, subsequent use of the extended univariate moderation model, as proposed in this paper, is recommended as this model is more powerful than the full bivariate moderation model.