A synthetic estimator for the efficacy of clinical trials with all-or-nothing compliance.

A critical issue in the analysis of clinical trials is patients' noncompliance to assigned treatments. In the context of a binary treatment with all or nothing compliance, the intent-to-treat analysis is a straightforward approach to estimating the effectiveness of the trial. In contrast, there exist 3 commonly used estimators with varying statistical properties for the efficacy of the trial, formally known as the complier-average causal effect. The instrumental variable estimator may be unbiased but can be extremely variable in many settings. The as treated and per protocol estimators are usually more efficient than the instrumental variable estimator, but they may suffer from selection bias. We propose a synthetic approach that incorporates all 3 estimators in a data-driven manner. The synthetic estimator is a linear convex combination of the instrumental variable, per protocol, and as treated estimators, resembling the popular model-averaging approach in the statistical literature. However, our synthetic approach is nonparametric; thus, it is applicable to a variety of outcome types without specific distributional assumptions. We also discuss the construction of the synthetic estimator using an analytic form derived from a simple normal mixture distribution. We apply the synthetic approach to a clinical trial for post-traumatic stress disorder.