Structured detection of interactions with the directed lasso

When considering low-dimensional gene-treatment or gene-environment interactions we might suspect groups of genes to interact with treatment or environment in a similar way. For example, genes associated with related biological processes might interact with an environmental factor or a clinical treatment in its effect on a phenotype correspondingly. We use the idea of a structured interaction model together with penalized regression to limit the model complexity in a model in which we believe the interactions might behave in a similar way. We propose the directed lasso, a regression modeling strategy using a pairwise fused lasso penalty to encourage interaction model simplicity through fusion of effect size. We compare the performance of the directed lasso to the lasso and other methods in a simulation study and on data sampled from a breast cancer clinical trial.