Recently, researchers have used a potential-outcome framework to estimate causally interpretable direct and indirect effects of an intervention or exposure on an outcome. One approach to causal-mediation analysis uses the so-called mediation formula to estimate the natural direct and indirect effects. This approach generalizes the classical mediation estimators and allows for arbitrary distributions for the outcome variable and mediator. A limitation of the standard (parametric) mediation formula approach is that it requires a specified mediator regression model and distribution; such a model may be difficult to construct and may not be of primary interest. To address this limitation, we propose a new method for causal-mediation analysis that uses the empirical distribution function, thereby avoiding parametric distribution assumptions for the mediator. To adjust for confounders of the exposure-mediator and exposure-outcome relationships, inverse-probability weighting is incorporated based on a supplementary model of the probability of exposure. This method, which yields the estimates of the natural direct and indirect effects for a specified reference group, is applied to data from a cohort study of dental caries in very-low-birth-weight adolescents to investigate the oral-hygiene index as a possible mediator. Simulation studies show low bias in the estimation of direct and indirect effects in a variety of distribution scenarios, whereas the standard mediation formula approach can be considerably biased when the distribution of the mediator is incorrectly specified.
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From the Department of Epidemiology and Biostatistics, School of Medicine, Case Western Reserve University, Cleveland, OH.
Submitted 18 October 2011; accepted 19 April 2012; posted 21 September 2012.
Supported by the National Institute of Dental and Craniofacial Research/NIH (grant numbers R03DE018391 and R01DE022674).
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Editors’ note: A commentary on this article appears on page 889.
Correspondence: Jeffrey M. Albert, Department of Epidemiology and Biostatistics, School of Medicine WG-43, Case Western Reserve University, 10900 Euclid Ave, Cleveland, OH 44120. E-mail: firstname.lastname@example.org.