A0313
Title: Inference for dose response functions on dose intervals via semiparametric minimum variance weighting
Authors: Zheng Zhang - Renmin University of China (China) [presenting]
Abstract: Continuous treatments arise commonly in practice and have gained increasing attention in recent years, but the existing literature focuses mainly on the population dose-response function (DRF). The aim is to estimate the dose-response function on treatment intervals (DRFTI) under the unconfoundedness assumption. To address the challenges incurred by the high dimensional confounders, a flexible single-index model is considered for the generalized propensity score (GPS), and the semiparametric efficiency bound is derived for the DRFTI under the parametric marginal structural model. It is shown that the DRFTI can be identified through a weighted least square regression of the response on the treatment variable, where the weights are a function of the GPS and the density function of the treatment variable. A robust estimator is proposed for the weights by minimizing their variance subject to an increasing number of single-index moment restrictions. The root n consistency and asymptotic normality of the proposed estimators for the DRFTI model are established. The estimator is shown to attain the semiparametric efficiency bound if the outcome regression function is also single-indexed. A consistent variance estimator is also proposed without the need to estimate the influence function. Monte Carlo simulations and a real data application demonstrate the practical value of the proposed method.
