Effects conditional on post-treatment events generated by independent mechanisms

TL;DR

This paper demonstrates that certain causal effects involving post-treatment events can be identified without measuring common causes, provided treatment and causes generate events through independent mechanisms.

Contribution

It introduces a novel identification strategy for causal effects involving post-treatment events without needing to measure common causes, under an independence assumption.

Findings

Conditional separable effects are identifiable without adjustment for common causes.

Identification relies on the assumption that treatment and causes generate post-treatment events via independent mechanisms.

The approach applies to studies with truncation, nonadherence, and birth weight paradox.

Abstract

In both observational studies and randomized trials, post-treatment events such as dropout, nonadherence, and truncation by death occur frequently. In some studies, conditioning on post-treatment variables is a deliberate strategy to isolate particular treatment effects on the outcome. However, naive comparisons of outcomes conditional on post-treatment events generally lack a causal interpretation, even when treatment is randomly assigned. There exist causal estimands that account for post-treatment events, including survivor average causal effects and conditional separable effects, but identification usually requires measurement of common causes of the post-treatment event and the outcome. In this article, we show that such measurements are not always necessary. Conceptually, what we require is that the treatment and other unmeasured causes of the outcome generate the post-treatment event through "independent mechanisms". Then, conditional separable effects and survivor average causal effects are identified without adjustment for common causes of the post-treatment event and the outcome. We illustrate the results in studies with truncating events, differential nonadherence, and the birth weight paradox.