Sparse estimation of gene–gene interactions in prediction models

Current assessment of gene–gene interactions is typically based on separate parallel analysis, where each interaction term is tested separately, while less attention has been paid on simultaneous estimation of interaction terms in a prediction model. As the number of interaction terms grows fast, sparse estimation is desirable from statistical and interpretability reasons. There is a large literature on sparse estimation, but there is a natural hierarchy between the interaction and its corresponding main effects that requires special considerations. We describe random-effect models that impose sparse estimation of interactions under both strong and weak-hierarchy constraints. We develop an estimation procedure based on the hierarchical-likelihood argument and show that the modelling approach is equivalent to a penalty-based method, with the advantage of the models being more transparent and flexible. We compare the procedure with some standard methods in a simulation study and illustrate its application in an analysis of gene–gene interaction model to predict body-mass index.