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Abstract:
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Many studies aim to assess treatment effects on outcomes in individuals characterized by status on a particular post-treatment variable. For example, we may be interested in the effect of cancer therapies on quality of life, and quality of life is only well-defined in the those individuals who are alive. Similarly, we may be interested in the effect of vaccines on post-infections outcomes, which are only of interest in those individuals who become infected. In these settings, a naive contrast of outcomes conditional on the post-treatment variable does not have a causal interpretation, 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 survivor average causal effect, is often advocated for causal inference. Whereas this principal stratum effect is a well defined causal contrast, it cannot be identified without strong untestable assumptions, and its practical relevance is ambiguous because it is restricted to an unknown subpopulation of unknown size. Here we formulate alternative estimands, which allow us to define the conditional separable effects.
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