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American Journal of Epidemiology Advance Access published online on October 22, 2009
American Journal of Epidemiology, doi:10.1093/aje/kwp283
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American Journal of Epidemiology © The Author 2009. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

Practice of Epidemiology

"Proportion Explained": A Causal Interpretation for Standard Measures of Indirect Effect?

Danella M. Hafeman*

* Correspondence to Dr. Danella M. Hafeman, Western Psychiatric Institute and Clinic, 3811 O'Hara Street, Pittsburgh, PA 15213 (e-mail: dmh2002{at}columbia.edu).

Received for publication April 30, 2009. Accepted for publication August 12, 2009.

The assessment of indirect effects is an important tool for epidemiologists interested in exploring the mechanisms of exposure-disease relations. A standard way of expressing an indirect effect is in terms of the "proportion explained"; this is the proportion of the total effect that is explained by a particular mediator (or set of mediators). There are several ways to calculate the proportion explained, based on both additive and multiplicative models. However, these standard methods (particularly those based on multiplicative models) have been criticized for lacking a causal interpretation. To address this issue, the author uses a framework of potential outcomes to define the indirect effects of interest (natural effects) and assess the correspondence between the natural effects and standard measures. The author finds that standard additive measures represent an unbiased weighted average of the effects of interest; standard multiplicative measures, on the other hand, yield a biased weighted average of these effects. If the investigator is primarily interested in whether or not an indirect effect exists, standard measures for mediation will often yield the correct answer. In contrast, if valid quantification of the indirect effect is desired, counterfactual-based methods should be used.

causality; effect size; epidemiologic methods; indirect effects; mediation; statistics

Abbreviations: BMI, body mass index; HR, hazard ratio; OR, odds ratio; PE, proportion explained; PIE, pure indirect effect; RD, risk difference; RR, risk ratio; TIE, total indirect effect


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