The role of assignment in defining and identifying causal effects in randomized trials

Abstract

In randomized trials, the per-protocol effect, that is, the effect of being assigned a treatment strategy and receiving treatment according to the assigned strategy, is sometimes thought to reflect the effect of the treatment strategy itself, without intervention on assignment. Here, we argue by example that this is not necessarily the case. We examine a causal structure for a randomized trial 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 example highlights the conceptual difference between the per-protocol effect and the effect of the treatment strategy, the conditions under which these causal estimands are equal, and suggests that in some cases their identification requires information on assignment, even when assignment is randomized. Furthermore, both per-protocol effects and effects of treatment may be unidentifiable without information on treatment assignment, 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. Our analyses suggest a need to more clearly define the role of assignment when specifying causal effects of interest in randomized trials, which has implications for identification, analysis methods, and the interpretation of trial results.