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The Mediation Proportion

Kaufman, Jay S.; MacLehose, Richard F.; Kaufman, Sol; Greenland, Sander

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doi: 10.1097/01.ede.0000171282.54664.71
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To the Editor:

We read with interest the recent article by Ditlevsen and colleagues1 on effect decomposition using structural equations models (SEM) in epidemiologic research. Every few years an article appears in an epidemiology journal encouraging greater use of path analysis or SEM methods (eg, Susser et al2), but Ditlevsen et al provide several developments of particular interest to epidemiologists. For example, they compare the SEM approach with some of the existing statistical literature on surrogate outcomes, and also describe a model of binary outcomes as realized manifestations of latent continuous variables.

Unfortunately, the article overlooks some important developments in effect definition and decomposition over the last 20 years, as presented elsewhere.3–6 In particular, Ditlevsen et al provide no interpretation for their parameters in terms of an underlying formal causal model. Indeed, the strategy of focusing attention on an arbitrarily scaled latent continuous variable makes it difficult to give causal interpretations to the estimated regression coefficients or to the mediation proportion derived from these coefficients.7 Furthermore, because of identification problems, a variety of causal structures can give rise to the same value for parameters such as the mediation proportion, even when the causal implications of these various structures would be entirely different.6 Finally, for many epidemiologic outcomes (eg, spontaneous abortion or mortality), focusing attention on the causal effect of the exposure on the latent continuous outcome, rather than on the observed discrete event, seems to lack clear public-health meaning.

When examined in terms of potential outcomes, the restrictive assumptions used by Ditlevsen et al (linearity and additivity) can be shown to still be insufficient to give the mediation proportion an unambiguous causal interpretation; this interpretation would require the additional assumption of no interaction at the unit level.8 Under a more general set of circumstances, the total effect (defined causally as a contrast of hypothetical actions) will not decompose additively into direct and indirect effects.4–6 In these settings it may still be feasible and substantively interesting to estimate total and direct causal effects, recognizing that the latter can be greater than or in the direction opposite to the former.4–6

Jay S. Kaufman

Richard F. MacLehose

Department of Epidemiology

University of North Carolina, Chapel Hill

Chapel Hill, NC

[email protected]

Sol Kaufman

Department of Otolaryngology

University at Buffalo, State University of

New York

Buffalo, NY

Sander Greenland

Department of Epidemiology

University of California, Los Angeles

Los Angeles, CA


1. Ditlevsen S, Christensen U, Lynch J, et al. The mediation proportion: a structural equation approach for estimating the proportion of exposure effect on outcome explained by an intermediate variable. Epidemiology. 2005;16:114–120.
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3. Greenland S. An overview of methods for causal inference from observational studies. In: Gelman A, Meng X-L, eds. Applied Bayesian Modeling and Casual Inference from Incomplete-Data Perspectives. Hoboken, NJ: John Wiley & Sons; 2004:3–13.
4. Robins JM, Greenland S. Identifiability and exchangeability for direct and indirect effects. Epidemiology. 1992;3:143–155.
5. Joffe MM, Colditz GA. Restriction as a method for reducing bias in the estimation of direct effects. Stat Med. 1998;17:2233–2249.
6. Pearl J. Causality: Models, Reasoning and Inference. Cambridge, UK: Cambridge University Press; 2000.
7. Wooldridge JW. Econometric Analysis of Cross Sectional and Panel Data. Cambridge, MA: MIT Press; 2002;458.
8. Kaufman JS, Maclehose RF, Kaufman S. A further critique of the analytic strategy of adjusting for covariates to identify biologic mediation. Epidemiol Perspect Innov. 2004;1:4.Available at:
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