Model Selection for Estimating Treatment Effects

Abstract

Researchers often believe that a treatment’s effect on a response may be heterogeneous with respect to certain baseline covariates. This is an important premise of personalized medicine. Several methods for estimating heterogeneous treatment effects have been proposed. However, little attention has been given to the problem of choosing between estimators of treatment effects. Models that best estimate the regression function may not be best for estimating the effect of a treatment; therefore, there is a need for model selection methods targeted to treatment effect estimation. We demonstrate an application of the focused information criterion (FIC) in this setting and develop a treatment effect cross- validation (TE-CV) aimed at minimizing treatment effect estimation errors. Theoretically, TE- CV possesses a model selection consistency property when the data splitting ratio is properly chosen. Practically, TE-CV has the flexibility to compare different types of models. We illustrate the methods using simulation studies and data from a clinical trial comparing treatments of patients with HIV.