No abstract

In many causal inference problems, one is interested in the direct causal effect of an exposure on an outcome of interest that is not mediated by certain intermediate variables. Robins and Greenland (1992) and Pearl (2001) formalized the definition of two types of direct effects (natural and controlled) under the counterfactual framework. The efficient scores (under a nonparametric model) for the various natural effect parameters and their general robustness conditions, as well as an estimating equation based estimator using the efficient score, are provided in Tchetgen Tchetgen and Shpitser (2011b). In this article, we apply the targeted maximum likelihood framework of van der Laan and Rubin (2006) and van der Laan and Rose (2011) to construct a semiparametric efficient, multiply robust, substitution estimator for the natural direct effect which satisfies the efficient score equation derived in Tchetgen Tchetgen and Shpitser (2011b). We note that the robustness conditions in Tchetgen Tchetgen and Shpitser (2011b) may be weakened, thereby placing less reliance on the estimation of the mediator density. More precisely, the proposed estimator is asymptotically unbiased if either one of the following holds: i) the conditional mean outcome given exposure, mediator, and confounders, and the mediated mean outcome difference are consistently estimated; (ii) the exposure mechanism given confounders, and the conditional mean outcome are consistently estimated; or (iii) the exposure mechanism and the mediator density, or the exposure mechanism and the conditional distribution of the exposure given confounders and mediator, are consistently estimated. If all three conditions hold, then the effect estimate is asymptotically efficient. Extensions to the natural indirect effect are also discussed.

In this study, oral contraceptives were not associated with HIV acquisition. There is substantial uncertainty in the effect of injectable hormonal contraception on HIV risk. These findings underscore the importance of dual protection with condoms and the need for diverse contraceptive options for women at risk of HIV infection.

In this paper, we study the effect of a time-varying exposure mediated by a time-varying intermediate variable. We consider general longitudinal settings, including survival outcomes. At a given time point, the exposure and mediator of interest are influenced by past covariates, mediators and exposures, and affect future covariates, mediators and exposures. Right censoring, if present, occurs in response to past history. To address the challenges in mediation analysis that are unique to these settings, we propose a formulation in terms of random interventions based on conditional distributions for the mediator. This formulation, in particular, allows for well-defined natural direct and indirect effects in the survival setting, and natural decomposition of the standard total effect. Upon establishing identifiability and the corresponding statistical estimands, we derive the efficient influence curves and establish their robustness properties. Applying Targeted Maximum Likelihood Estimation, we use these efficient influence curves to construct multiply robust and efficient estimators. We also present an inverse probability weighted estimator and a nested non-targeted substitution estimator for these parameters.

Background: Causal mediation analysis can improve understanding of the mechanisms underlying epidemiologic associations. However, the utility of natural direct and indirect effect estimation has been limited by the assumption of no confounder of the mediator-outcome relationship that is affected by prior exposure-an assumption frequently violated in practice.Methods: We build on recent work that identified alternative estimands that do not require this assumption and propose a flexible and double robust semiparametric targeted minimum loss-based estimator for data-dependent stochastic direct and indirect effects. The proposed method treats the intermediate confounder affected by prior exposure as a time-varying confounder and intervenes stochastically on the mediator using a distribution which conditions on baseline covariates and marginalizes over the intermediate confounder. In addition, we assume the stochastic intervention is given, conditional on observed data, which results in a simpler estimator and weaker identification assumptions.Results: We demonstrate the estimator's finite sample and robustness properties in a simple simulation study. We apply the method to an example from the Moving to Opportunity experiment. In this application, randomization to receive a housing voucher is the treatment/instrument that influenced moving to a low-poverty neighborhood, which is the intermediate confounder. We estimate the data-dependent stochastic direct effect of randomization to the voucher group on adolescent marijuana use not mediated by change in school district and the stochastic indirect effect mediated by change in school district. We find no evidence of mediation.Conclusions: Our estimator is easy to implement in standard statistical software, and we provide annotated R code to further lower implementation barriers.