The Mediation Proportion

Abstract

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