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Parametric Mediational g-Formula Approach to Mediation Analysis with Time-varying Exposures, Mediators, and Confounders

Lin, Sheng-Hsuan; Young, Jessica; Logan, Roger; Tchetgen Tchetgen, Eric J.; VanderWeele, Tyler J.

doi: 10.1097/EDE.0000000000000609

The assessment of direct and indirect effects with time-varying mediators and confounders is a common but challenging problem, and standard mediation analysis approaches are generally not applicable in this context. The mediational g-formula was recently proposed to address this problem, paired with a semiparametric estimation approach to evaluate longitudinal mediation effects empirically. In this article, we develop a parametric estimation approach to the mediational g-formula, including a feasible algorithm implemented in a freely available SAS macro. In the Framingham Heart Study data, we apply this method to estimate the interventional analogues of natural direct and indirect effects of smoking behaviors sustained over a 10-year period on blood pressure when considering weight change as a time-varying mediator. Compared with not smoking, smoking 20 cigarettes per day for 10 years was estimated to increase blood pressure by 1.2 mm Hg (95% CI: −0.7, 2.7). The direct effect was estimated to increase blood pressure by 1.5 mm Hg (95% CI: −0.3, 2.9), and the indirect effect was −0.3 mm Hg (95% CI: −0.5, −0.1), which is negative because smoking which is associated with lower weight is associated in turn with lower blood pressure. These results provide evidence that weight change in fact partially conceals the detrimental effects of cigarette smoking on blood pressure. Our study represents, to our knowledge, the first application of the parametric mediational g-formula in an epidemiologic cohort study (see video abstract at,

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From the aDepartment of Epidemiology, Harvard School of Public Health, Boston, MA; and bDepartment of Biostatistics, Harvard School of Public Health, Boston, MA.

Submitted 17 November 2015; accepted 29 November 2016.

The authors report no conflicts of interest.

The mgformula macro is freely accessible with documentation at The dataset is not publicly available.

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Correspondence: Sheng-Hsuan Lin, Department of Epidemiology and Biostatistics, Harvard School of Public Health, 677 Huntington Avenue, Boston, MA 02115. E-mail:

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