The Role of Assignment in Defining and Identifying Causal Effects in Randomized Trials

In randomized trials, the per-protocol effect is defined as the effect of being assigned a treatment strategy and receiving treatment according to the assigned strategy; therefore, it encompasses the effect of the treatment strategy and any effect of assignment that does not operate through the received treatment. However, the per-protocol effect is sometimes interpreted as reflecting the effect of the treatment strategy itself, regardless of assignment. Here, we argue by example that this is not necessarily the case. We examine causal structures for randomized trials where these two causal estimands - the per-protocol effect and the effect of the treatment strategy - are not equal, and where their corresponding identifying observed data functionals are not the same, but both require information on assignment for identification. Our examples clarify the conceptual difference between these estimands and the conditions that guarantee their equality. Our examples also highlight that in some cases identification of these estimands requires information on assignment, even when assignment is randomized, unless one makes additional assumptions - informally, that assignment does not affect the outcome except through treatment (i.e., an exclusion-restriction assumption), and that assignment is not a confounder of the treatment-outcome association conditional on other variables in the analysis. These assumptions may not be plausible, particularly when the treatment assignment process in the trial differs materially from routine practice in outcome-relevant ways (e.g., "blinding" investigators and participants to treatment assignment). Our examination emphasizes the important role of assignment in defining and estimating causal effects in randomized trials, with implications for statistical analysis and the interpretation of trial results.