  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.
