The mediation proportion.

To the Editor: We read with interest the recent article by Ditlevsen and colleagues1 on effect decomposition using structural equations models (SEM) in epidemio logic research. Every few years an arti cle appears in an epidemiology journal encouraging greater use of path analysis or SEM methods (eg, Susser et al2), but Ditlevsen et al provide several develop ments of particular interest to epidemi ologists. For example, they compare the SEM approach with some of the existing statistical literature on surrogate out comes, and also describe a model of binary outcomes as realized manifesta tions of latent continuous variables. Unfortunately, the article over looks some important developments in effect definition and decomposition over the last 20 years, as presented else where.36 In particular, Ditlevsen et al provide no interpretation for their pa rameters in terms of an underlying for mal 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 out comes (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 poten tial outcomes, the restrictive assump tions used by Ditlevsen et al (linearity and additivity) can be shown to still be insufficient to give the mediation pro portion an unambiguous causal interpre tation; this interpretation would require the additional assumption of no interac tion 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 decom pose additively into direct and indirect effects.46 In these settings it may still be feasible and substantively interesting to estimate total and direct causal ef fects, recognizing that the latter can be greater than or in the direction opposite to the former.4-6