Model misspecification sensitivity analysis in estimating causal effects of interventions with non-compliance

Randomized trials often face complications in assessing the effect of treatment because of study participants' non-compliance. If compliance type is observed in both the treatment and control conditions, the causal effect of treatment can be estimated for a targeted subpopulation of interest based on compliance type. However, in practice, compliance type is not observed completely. Given this missing compliance information, the complier average causal effect (CACE) estimation approach provides a way to estimate differential effects of treatments by imposing the exclusion restriction for non-compliers. Under the exclusion restriction, the CACE approach estimates the effect of treatment assignment for compliers, but disallows the effect of treatment assignment for non-compliers. The exclusion restriction plays a key role in separating outcome distributions based on compliance type. However, the CACE estimate can be substantially biased if the assumption is violated. This study examines the bias mechanism in the estimation of CACE when the assumption of the exclusion restriction is violated. How covariate information affects the sensitivity of the CACE estimate to violation of the exclusion restriction assumption is also examined.