"Semiparametric Estimation and Inference for Distributional and General Treatment Effects"
There is a large literature on methods of analysis for randomized trials with noncompliance which focuses on the effect of treatment on the average outcome. This article considers evaluating the effect of treatment on the entire distribution and general functions of this effect. For distributional treatment effects, fully nonparametric and fully parametric approaches have been proposed. The fully nonparametric approach could be inefficient but the fully parametric approach is not robust to the violation of distribution assumptions. In this article, we develop a semi parametric instrumental variable method based on the empirical likelihood approach. Our method can be applied to general outcomes and general functions of outcome distributions, and allows us to predict a subject's latent compliance class based on an observed outcome value in observed assignment and treatment received groups. Asymptotic results for the estimators and likelihood ratio statistic re derived. A simulation study shows that our estimators of various treatment effects are substantially more efficient than the currently used fully nonparametric estimators. The method is illustrated by an analysis of data from a randomized trial of an encouragement intervention to improve adherence to prescribed depression treatments among depressed elderly patients in primary care practices.
This is a joint work with Jing Qin and Biao Zhang.
