A Two-Stage Joint Modeling Method for Causal Mediation Analysis in the Presence of Treatment Noncompliance

Abstract Estimating the effect of a randomized treatment and the effect that is transmitted through a mediator is often complicated by treatment noncompliance. In literature, an instrumental variable (IV)-based method has been developed to study causal mediation effects in the presence of treatment noncompliance. Existing studies based on the IV-based method focus on identifying the mediated portion of the intention-to-treat effect, which relies on several identification assumptions. However, little attention has been given to assessing the sensitivity of the identification assumptions or mitigating the impact of violating these assumptions. This study proposes a two-stage joint modeling method for conducting causal mediation analysis in the presence of treatment noncompliance, in which modeling assumptions can be employed to decrease the sensitivity to violation of some identification assumptions. The use of a joint modeling method is also conducive to conducting sensitivity analyses to the violation of identification assumptions. We demonstrate our approach using the Jobs II data, in which the effect of job training on job seekers’ mental health is examined.