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

Abstract

Whilst 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 not through or through a mediator variable 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.

Mediation Analysis: A Practitioner's Guide

“…Numerous other methods have been developed (1,2,9,13,24,26,35,58), which we could not address in this article. Some of these are discussed in the book length treatment of mediation (47).…”

“…Sensitivity analysis techniques help one assess, for example, how strong an unmeasured confounder would have to be related to both the mediator and to the outcome to substantially change conclusions being drawn about the direct and indirect effects. Several sensitivity analysis techniques for mediation have been proposed in the literature [12,15,35,42; see chapter 3 of VanderWeele (47) for an overview of many of these methods].…”

Nonparametric estimation of natural direct and indirect effects based on inverse probability weighting

“…We formally show that under the sequential conditional independence assumption and particular regularity conditions, nonparametric IPW is root-n consistent and asymptotically normal. Furthermore, our estimator attains the semiparametric efficiency bounds for mediation analysis derived by Tchetgen Tchetgen and Shpitser (2012). We therefore contribute to a growing literature concerned with assessing direct and indirect effects based on conditional independence under rather flexible model 1 Tchetgen Tchetgen (2013) derives a related result in the context of inverse odds-ratio weighting.…”

“…We therefore contribute to a growing literature concerned with assessing direct and indirect effects based on conditional independence under rather flexible model 1 Tchetgen Tchetgen (2013) derives a related result in the context of inverse odds-ratio weighting. 1 assumptions, 2 see for instance Pearl (2001), Robins (2003), Petersen, Sinisi, and van der Laan (2006), Flores andFlores-Lagunes (2009), VanderWeele (2009), Imai, Keele, and Yamamoto (2010), Hong (2010), Albert and Nelson (2011), Yamamoto (2013), Tchetgen Tchetgen andShpitser (2012), and Vansteelandt, Bekaert, and Lange (2012), among others. In addition to the evaluation of these effects in the total population, we in contrast to Huber (2014) also discuss the identification and estimation of weighted direct and indirect effects.…”

“…Furthermore, we investigate the finite sample performance of nonparametric IPW in a simulation study and compare it to other estimators considered in the literature, namely maximumlikelihood-based g-computation (suggested by Robins (1986) and considered in the context of direct and indirect effects in Zheng and van der Laan (2012)), estimation based on (parametrically) simulating potential mediators and outcomes using the 'mediation' package for R by Tingley, Yamamoto, Hirose, Imai, and Keele (2014), 'multiply robust' estimation based on the efficient influence function as suggested by Tchetgen Tchetgen and Shpitser (2012), and IPW with parametric propensity scores as in Huber (2014). Finally, we apply our estimator (as well as the other methods considered in the simulations) to the experimental evaluation of Chinkhumba, Godlonton, and Thornton (2014) who investigate an information intervention about male circumcisions and HIV risk in urban Malawi.…”