## The Annals of Statistics

- Ann. Statist.
- Volume 40, Number 3 (2012), 1816-1845.

### Semiparametric theory for causal mediation analysis: Efficiency bounds, multiple robustness and sensitivity analysis

Eric J. Tchetgen Tchetgen and Ilya Shpitser

#### Abstract

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.

#### Article information

**Source**

Ann. Statist. Volume 40, Number 3 (2012), 1816-1845.

**Dates**

First available in Project Euclid: 16 October 2012

**Permanent link to this document**

http://projecteuclid.org/euclid.aos/1350394518

**Digital Object Identifier**

doi:10.1214/12-AOS990

**Mathematical Reviews number (MathSciNet)**

MR3015045

**Zentralblatt MATH identifier**

06114731

**Subjects**

Primary: 62G05: Estimation

**Keywords**

Natural direct effects natural indirect effects double robust mediation analysis local efficiency

#### Citation

Tchetgen Tchetgen, Eric J.; Shpitser, Ilya. Semiparametric theory for causal mediation analysis: Efficiency bounds, multiple robustness and sensitivity analysis. Ann. Statist. 40 (2012), no. 3, 1816--1845. doi:10.1214/12-AOS990. http://projecteuclid.org/euclid.aos/1350394518.

#### Supplemental materials

- Supplementary material: Supplemental Appendix to Semiparametric theory for causal mediation analysis. The supplementary material gives the semiparametric efficiency theory for estimation of natural direct effects with a known model for the mediator density. The Appendix also gives the proof of Theorem 3 (stated in the Supplementary Appendix) and of Theorem 4.Digital Object Identifier: doi: 10.1214/12-AOS990SUPPSupplemental files available for subscribers.