Simultaneous estimation of gene-gene and gene-environment interactions for numerous loci using double penalized log-likelihood.

Many common human diseases are considered to be caused by complex multifactorial processes. For these diseases, it is expected that numerous genetic and environmental factors and, possibly, their interactions play a role. Therefore, simultaneously analyzing the effects of numerous genes and environmental factors is a more realistic approach compared to single gene analyses, but the large number of genes and environmental factors pose a challenge, not in the least due to the limitations created by the tools available for analyzing such high-dimensional models. In the present manuscript we propose a method that is capable of identifying "true" interactions in a setting where the number of effects to be estimated is very large and can even surpass the number of observations. Basically, all possible (interaction) effects are entered in a double penalized model, where main effects are ridge penalized, whereas the interactions are subjected to a least absolute shrinkage and selection operator (lasso) penalty. Results from the simulations and real data show that the proposed method is capable of detecting interactions even with relative small effect sizes.