Institutional members access full text with Ovid®

Share this article on:

Distribution-Free Mediation Analysis for Nonlinear Models with Confounding

Albert, Jeffrey M.

doi: 10.1097/EDE.0b013e31826c2bb9

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.

Supplemental Digital Content is available in the text.

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).

Supplemental digital content is available through direct URL citations in the HTML and PDF versions of this article (

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:

© 2012 Lippincott Williams & Wilkins, Inc.