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Estimation of Natural Indirect Effects Robust to Unmeasured Confounding and Mediator Measurement Error

Fulcher, Isabel R.a; Shi, Xua; Tchetgen Tchetgen, Eric J.b

doi: 10.1097/EDE.0000000000001084

The use of causal mediation analysis to evaluate the pathways by which an exposure affects an outcome is widespread in the social and biomedical sciences. Recent advances in this area have established formal conditions for identification and estimation of natural direct and indirect effects. However, these conditions typically involve stringent assumptions of no unmeasured confounding and that the mediator has been measured without error. These assumptions may fail to hold in many practical settings where mediation methods are applied. The goal of this article is two-fold. First, we formally establish that the natural indirect effect can in fact be identified in the presence of unmeasured exposure–outcome confounding provided there is no additive interaction between the mediator and unmeasured confounder(s). Second, we introduce a new estimator of the natural indirect effect that is robust to both classical measurement error of the mediator and unmeasured confounding of both exposure–outcome and mediator–outcome relations under certain no interaction assumptions. We provide formal proofs and a simulation study to illustrate our results. In addition, we apply the proposed methodology to data from the Harvard President’s Emergency Plan for AIDS Relief (PEPFAR) program in Nigeria.

From the aDepartment of Biostatistics, Harvard T.H. Chan School of Public Health, Boston, MA

bWharton Statistics Department, University of Pennsylvania, Philadelphia, PA.

Submitted August 10, 2018; accepted July 28, 2019.

This study was funded by the NIH NIAID with award numbers R01AI27271 and R01AI104459.

The authors report no conflicts of interest.

The code for the simulation can be found on the corresponding author’s GitHub page: The data are not publicly available, but anyone interested can make a request with Dr. Phyllis Kanki (

Supplemental digital content is available through direct URL citations in the HTML and PDF versions of this article (

Correspondence: Isabel R. Fulcher, Department of Global Health and Social Medicine, Harvard Medical School, 641 Huntington Avenue, 4th floor, Boston, MA 02115. E-mail:

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