SEMIPARAMETRIC THEORY FOR CAUSAL MEDIATION ANALYSIS: EFFICIENCY BOUNDS, MULTIPLE ROBUSTNESS AND SENSITIVITY ANALYSIS
BY ERIC J. TCHETGEN TCHETGEN¹ AND ILYA SHPITSER
Harvard School of Public Health
While estimation of the marginal (total) causal effect of a point exposure on an outcome is arguably the most common objective of experimental and observational studies in the health and social sciences, in recent years, investigators have also become increasingly interested in mediation analysis. Specifically, upon evaluating the total effect of the exposure, investigators routinely wish to make inferences about the direct or indirect pathways of the effect of the exposure, through a mediator variable or not, that occurs subsequently to the exposure and prior to the outcome. Although powerful semiparametric methodologies have been developed to analyze observational studies that produce double robust and highly efficient estimates of the marginal total causal effect, similar methods for mediation analysis are currently lacking. Thus, this paper develops a general semiparametric framework for obtaining inferences about so-called marginal natural direct and indirect causal effects, while appropriately accounting for a large number of pre-exposure confounding factors for the exposure and the mediator variables. Our analytic framework is particularly appealing, because it gives new insights on issues of efficiency and robustness in the context of mediation analysis. In particular, we propose new multiply robust locally efficient estimators of the marginal natural indirect and direct causal effects, and develop a novel double robust sensitivity analysis framework for the assumption of ignorability of the mediator variable.
1. Introduction. The evaluation of the total causal effect of a given point exposure, treatment or intervention on an outcome of interest is arguably the most common objective of experimental and observational studies in the fields of epidemiology, biostatistics and in the social sciences. However, in recent years, investigators in these various fields have become increasingly interested in making inferences about the direct or indirect pathways of the exposure effect, through a mediator variable or not, that occurs subsequently to the exposure and prior to the outcome. Recently, the counterfactual language of causal inference has proven particularly useful for formalizing mediation analysis. Indeed, causal inference
Received March 2011; revised March 2012. ¹Supported by NIH Grant R21ES019712. MSC2010 subject classifications. 62G05. Key words and phrases. Natural direct effects, natural indirect effects, double robust, mediation analysis, local efficiency.