Conditional separable effects

TL;DR

This paper introduces the concept of conditional separable effects for causal inference in settings with post-treatment variables, providing identifiable estimands and estimators, and demonstrates their application in a prostate cancer trial.

Contribution

It proposes a new causal effect estimand, the conditional separable effect, with falsifiable assumptions and practical estimators, addressing limitations of principal stratum effects.

Findings

Derived identification results for conditional separable effects

Developed a doubly robust estimator based on influence functions

Applied method to estimate effects of chemotherapy on quality of life

Abstract

Researchers are often interested in treatment effects on outcomes that are only defined conditional on a post-treatment event status. 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, a naive contrast of outcomes conditional on the post-treatment variable is not an average causal effect, even in a randomized experiment. Therefore the effect in the principal stratum of those who would have the same value of the post-treatment variable regardless of treatment, such as the always survivors in a truncation by death setting, is often advocated for causal inference. While this principal stratum effect is a well defined causal contrast, it is often hard to justify that it is relevant to scientists, patients or policy makers, and it cannot be identified without relying on unfalsifiable assumptions. Here we formulate alternative estimands, the conditional separable effects, that have a natural causal interpretation under assumptions that can be falsified in a randomized experiment. We provide identification results and introduce different estimators, including a doubly robust estimator derived from the nonparametric influence function. As an illustration, we estimate a conditional separable effect of chemotherapies on quality of life in patients with prostate cancer, using data from a randomized clinical trial.