To the Editor:
Subsequent to the publication of our paper1 in the January 2005 issue of Epidemiology, relevant references2–4 to the problem of mediation analysis have been brought to our attention from the discipline of drug abuse prevention.
Using the framework of the multivariate normal distribution, MacKinnon2 explained mediation analysis in the context of prevention and intervention studies with an abundance of examples of problems of mediation. He proposed to measure the intermediate effect by the product of the regression coefficients in the relevant regression equations and denoted the fraction of the intermediate effect to the total effect for the proportion mediated. When the intermediate and response variables are jointly normally distributed, the analysis is straightforward and intuitive, and in this case, MacKinnon's proportion mediated coincides with our proposed mediation proportion, as do the measures of both Freedman et al5 and Wang and Taylor,6 as we have pointed out earlier.1
In psychology, it is standard to apply structural equations models. Finch et al3 studied a model of 3 latent variables, each with 3 indicator variables, and through simulations, analyzed the effects of nonnormality of the indicator variables on the estimates of the intermediate effect. The nonnormality was represented by continuous variables with positive skewness and kurtosis. Nonnormal data are common in epidemiology such as when constructing scales on some measured items or indicators. The data may be analyzed (possibly transformed) assuming normality or by grouping into a smaller number of categories, maybe all the way to binary variables. Unfortunately, the statistical conclusions are sensitive to the construction of scales and choice of cut points. Our main motivation for using structural equations models was to provide a fresh approach to defining and estimating the mediation proportion for the discrete or ordered categorical variables commonly met in epidemiology. Such observations may often be embedded in the structural equations framework through threshold models.1 The threshold model approach is particularly useful when handling ordered categorical data, in which it will often be natural to assume an underlying continuous variable governing the observed data.
MacKinnon et al4 discussed the concepts of mediation, confounding, and suppression effects in the context of causality.
Department of Biostatistics
University of Copenhagen
Mogens Trab Damsgaard
Department of Social Medicine
Institute of Public Health
University of Copenhagen
Department of Epidemiology
University of Michigan
Ann Arbor, MI
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
2. MacKinnon DP. Analysis of mediating variables in prevention and intervention research. In: Cazares A, Beatty LA, eds. Scientific methods for prevention intervention research. NIDA Res Monogr
3. Finch JH, West SG, MacKinnon DP. Effects of sample size and nonnormality on the estimation of mediated effects in latent variables models. Structural Equation Modeling
4. MacKinnon DP, Krull JL, Lockwood CM. Equivalence of the mediation, confounding and suppression effect. Prev Sci
5. Freedman LS, Graubard BI, Schatzkin A. Statistical validation of intermediate endpoints for chronic disease. Stat Med
6. Wang Y, Taylor JMG. A measure of the proportion of treatment effect explained by a surrogate marker. Biometrics