On Transportability of Parameters and Estimation of Risks associated with Metabolic Syndrome

Recently, some studies emphasize the potential problems in using estimated parameter values in an independent study for analysis of the primary study, and introduce the concept of "transportability." As far as we know, however, a mathematical definition and statistical considerations of the transportability have not been fully developed. This paper defines the transportability of a regression model, presents a sufficient condition, describes a necessary assumption, and examines the transportability of the regression model with real data. The motivation of the study comes from the fact that we have to wait for the results of an over ten-year cohort study being conducted at the Radiation Effects Research Foundation to know the epidemiological significance of waist circumference (WC) in the definition of the metabolic syndrome (MS). We considered that it would be possible to estimate the risk associated with WC if an unbiased estimate of WC for each subject ten years earlier could be obtained based on the transportability arguments. Implementing this idea with the cohort database administered by the Radiation Effect Research Foundation, we obtained the relative risk of death from MS-related causes. The results indicated that the risk of death was smaller for a larger WC, which contradicted the suggestion that the risk of death should be higher for a larger WC. The implications of our results are discussed.