A constrained sparse additive model for treatment effect-modifier selection

Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. This paper develops a sparse additive model focused on estimation of treatment effect-modification with simultaneous treatment effect-modifier selection. We propose a version of the sparse additive model uniquely constrained to estimate the interaction effects between treatment and pretreatment covariates, while leaving the main effects of the pretreatment covariates unspecified. The proposed regression model can effectively identify treatment effect-modifiers that exhibit possibly nonlinear interactions with the treatment variable, that are relevant for making optimal treatment decisions. A set of simulation experiments and an application to a dataset from a randomized clinical trial are presented to demonstrate the method.