  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.
