Estimation of conditional average 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 and direct marketing. Within a given set of regression models or machine learning algorithms, those that best estimate the regression function may not be best for estimating the effect of a treatment; therefore, there is a need for methods of model selection targeted to treatment effect estimation. In this thesis, we demonstrate an application of the focused information criterion (FIC) for model selection in this setting and develop a treatment effect cross-validation (TECV) aimed at minimizing treatment effect estimation errors. Theoretically, TECV possesses a model selection consistency property when the data splitting ratio is properly chosen. Practically, TECV has the flexibility to compare different types of models and estimation procedures.In the usual regression settings, it is well established that model averaging (or more generally, model combining) frequently produces substantial performance gains over selecting a single model, and the same is true for the goal of treatment effect estimation. We develop a model combination method (TEEM) that properly weights each model based on its (estimated) accuracy for estimating treatment effects. When the baseline covariate is one-dimensional, the TEEM algorithm automatically produces a treatment effect estimate that converges at almost the same rate as the best model in a candidate set.We illustrate the methods of FIC, TECV, and TEEM with simulation studies, data from a clinical trial comparing treatments of patients with HIV, and a benchmark public policy dataset from a work skills training program. The examples show that the methods developed in this thesis often exhibit good performance for the important goal of estimating treatment effects conditional on covariates.