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Abstract:
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Mediation analysis has become a statistical topic of much interest, particularly for epidemiology and public health. The general problem is that a variable X will affect variables Y and Z, but also Z affects Y. We call Y the outcome, X the exposure, and Z the mediator. Mediation analysis seeks to determine what part of the effect of X on Y is mediated by Z, and what part is direct. In many public health studies, data is gathered for many variables. An obvious set of potential mediators would be biomarkers of effect. However, while outcomes and exposures may be relatively easy to measure, biomarkers must generally be measured by assays that are more expensive; therefore biomarker data may be available for only a fraction of all observations. To deal with the multiplicity of variables and lack of data for mediator variables, we propose a ``unified model". To do this, take all regression models (X -> Z; X,Z -> Y) and joining them into one likelihood. For missing mediator values, use imputation by modeling. The unified model allows estimation of all coefficients with increased acccuracy. As an example, the method is applied to data from a public health study.
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