Abstract: We propose a new modeling and estimation approach that selects an optimal treatment regime by constructing a robust estimating equation. The method is protected against a misspecification of the propensity score model, the outcome regression model for the nontreated group, and the potential nonmonotonic treatment difference model. Our method also allows residual errors to depend on the covariates. We include a single index structure to facilitate the nonparametric estimation of the treatment difference. We then identify the optimal treatment by maximizing the value function. We also establish the theoretical properties of the treatment assignment strategy. Lastly, we demonstrate the performance and effectiveness of our proposed estimators using extensive simulation studies and an analysis of a real data set from a study on the effect of maternal smoking on baby birth weight.

Key words and phrases: Double- and multi-robust, optimal treatment regimes, propensity score, value function.