📝 SummarXiv

Abstract

The average causal mediation effect (ACME) and the natural direct effect (NDE) are two parameters of primary interest in causal mediation analysis. However, the two causal parameters are not identifiable from randomized experimental data in the presence of outcome-mediator confounding and treatment-assignment noncompliance. Sj\"{o}lander (2009) addressed the partial identification issue and derived nonparametric bounds of the NDE in randomized controlled trials under a set of monotonicity assumptions based on the Balke-Pearl algorithm. These bounds provide partial information on the parameters and can be used for sensitivity analysis. In this paper, we extend Sj\"{o}lander's bounds on the NDE as well as the ACME to randomized controlled trials in the presence of noncompliance when the treatment assignment serves as an instrumental variable. Nonparametric sharp bounds for the local causal parameters defined on the subpopulation of treatment-assignment compliers are also established. We demonstrate the practical usefulness of the proposed upper and lower bounds through an application to the randomized experimental dataset on Job Search Intervention Study.