Defining and Identifying Per-protocol Effects in Randomized Trials

In trials with noncompliance to assigned treatment, researchers might be interested in estimating a per-protocol effect-a comparison of two counterfactual outcomes defined by treatment assignment and (often time-varying) compliance with a well-defined treatment protocol. Here, we provide a general counterfactual definition of a per-protocol effect and discuss examples of per-protocol effects that are of either substantive or methodologic interest. In doing so, we seek to make more concrete what per-protocol effects are and highlight that one can estimate per-protocol effects that are more than just a comparison of always taking treatment in two distinct treatment arms. We then discuss one set of identifiability conditions that allow for identification of a causal per-protocol effect, highlighting some potential violations of those conditions that might arise when estimating per-protocol effects.