Partial areas under the curve of the cumulative distribution function as a new composite estimand for randomized clinical trials

Abstract

Clinical trials often face the challenge of post-randomization events, such as the initiation of rescue therapy or the premature discontinuation of randomized treatment. Such events, called “intercurrent events” (ICEs) in ICH E9(R1), may influence the estimation and interpretation of treatment effects. According to ICH E9(R1), there are five strategies for handling ICEs. This study focuses on the composite strategy, which incorporates ICEs in the outcome of interest and defines the treatment effects using composite endpoints that combine the measured continuous variables and ICEs. An advantage of this strategy is that it avoids the occurrence of missing data because they are defined as part of the outcome of interest. In this study, we propose a new composite estimand: the difference in the partial areas under the curves (pAUCs) of the cumulative distribution function. While the pAUC is closely related to the trimmed mean approach proposed by Permutt and Li, it offers the advantage of allowing pre-specification of the cutoff value for a “good” response based on clinical considerations. This ensures that the pAUC can be calculated irrespective of the proportion of ICEs. We describe the causal interpretation of our method and its relationship with two other strategies (treatment policy and hypothetical strategies) using a potential outcome framework. We present simulation results in which our method performs reasonably well compared to several existing approaches in terms of type I error, power, and the proportion of undefined test statistics.