  We describe a regularized regression model for the selection of
gene-environment (GxE) interactions. The model focuses on a single
environmental exposure and induces a main-effect-before-interaction
hierarchical structure. We propose an efficient fitting algorithm and screening
rules that can discard large numbers of irrelevant predictors with high
accuracy. We present simulation results showing that the model outperforms
existing joint selection methods for (GxE) interactions in terms of selection
performance, scalability and speed, and provide a real data application. Our
implementation is available in the gesso R package.
