Statistica Sinica 28 (2018), 137-156
Abstract: In a clinical trial, statistical reports have been typically concerned about the mean difference between two groups. Now there is increasing interest in the heterogeneity of the treatment effects, which means that the same treatment can have different effects on different people. In this article, we focus on the treatment benefit rate (TBR) and the treatment harm rate (THR), defined as the proportion of people who have a better outcome on the treatment than the control and the proportion of people who have a worse outcome on the treatment than the control, respectively. We propose a relatively weak assumption to obtain bounds for the TBR and the THR, which are shown to be always better than the covariates adjusted simple bounds. We prove that the TBR and THR are identifiable under a different conditional independence assumption. We also derive the corresponding estimators, the asymptotic distributions, and the over-identified test. We perform simulation studies to assess the performance of the proposed estimators and compare them with the proposed bounds. The simulation results show that the proposed estimators work quite well when the conditional independence assumption hold, they are not sensitive to small violation of the assumption, and the bounds we proposed can perform better than the estimators when the sample size is small. We illustrate application of the proposed methods in a double-blinded, randomized clinical trial.
Key words and phrases: Causal effect, heterogeneity, potential outcome, treatment benefit rate, treatment harm rate.