Estimating the Effect of a Treatment When There Is Nonadherence in a Trial

Randomized trials offer a powerful strategy for estimating the effect of a treatment on an outcome. However, interpretation of trial results can be complicated when study subjects do not take the treatment to which they were assigned; this is referred to as nonadherence. Prior authors have described instrumental variable approaches to analyze trial data with nonadherence; under their approaches, the initial assignment to treatment is used as an instrument. However, their approaches require the assumption that initial assignment to treatment has no direct effect on the outcome except via the actual treatment received (i.e., the exclusion restriction), which may be implausible. We propose an approach to identification of a causal effect of treatment in a trial with 1-sided nonadherence without assuming exclusion restriction. The proposed approach leverages the study subjects initially assigned to control status as an unexposed reference population; we then employ a bespoke instrumental variable analysis, where the key assumption is "partial exchangeability" of the association between a covariate and an outcome in the treatment and control arms. We provide a formal description of the conditions for identification of causal effects, illustrate the method using simulations, and provide an empirical application.