Conditional Separable Effects

Abstract

Researchers are often interested in treatment effects on outcomes that are only defined conditional on posttreatment events. For example, in a study of the effect of different cancer treatments on quality of life at end of follow-up, the quality of life of individuals who die during the study is undefined. In these settings, naive contrasts of outcomes conditional on posttreatment events are not average causal effects, even in randomized experiments. Therefore, the effect in the principal stratum of those who would have the same value of the posttreatment variable regardless of treatment (such as the survivor average causal effect) is often advocated for causal inference. While principal stratum effects are average causal effects, they refer to a subset of the population that cannot be observed and may not exist. Therefore, it is not clear how these effects inform decisions or policies. Here we propose the conditional separable effects, quantifying causal effects of modified versions of the study treatment in an observable subset of the population. These effects, which may quantify direct effects of the study treatment, require transparent reasoning about candidate modified treatments and their mechanisms. We provide identifying conditions and various estimators of these effects along with an applied example. Supplementary materials for this article are available online.