MEDIATIONAL MODELS WITH MULTIPLE OUTCOMES IN CROSS-SECTIONAL AND LONGITUDINAL STUDIES

Mediational analysis is used to explain how a predictor affects the outcome through an intervening variable called a mediator. In a cross-sectional study, the predictor, the mediator, and the outcome are measured at single time points and these time points need to be chronologically in the same order. In longitudinal mediational models, the outcome and the mediator are measured over the follow-up period also in the chronological order while the predictor is measured at a single time point.The role of a mediator in cross-sectional mediational models with single outcomes is mostly assessed by two parametric tests, Sobel test and Clogg test. We have extended these tests to multiple outcomes. The extensions also include two bootstrap approaches. Simulation results show that in the presence of moderate correlation between the predictor and the mediator, the extended Clogg test has the most reliable Type I error rate and the highest power.For longitudinal mediational models, we have discussed one scenario where the outcome process and the mediational process are described by linear growth curves. The total indirect effect of the predictor is defined as the effect of the predictor on the initial status and the growth rate of the outcome after accounting for the mediating effect of the initial status and the growth rate of the mediator. Inferential methods for the total indirect effect are proposed, using a formulation by random coefficient models. Results indicate the reliability of the proposed methods with large samples. An illustrative example using University of Pittsburgh Physical Activity Study (PittPAS) is given. The study seeks to investigate an important question about the differential effect of gender, if any, on the exercise behavior in young adulthood in relation to the exercise behavior in adolescence. Using the mediational model, we found the differential effect of gender on physical activity in young adulthood was mediated by the previous physical activities experience in adolescence.The public health significance of the present work lies in the development of statistical procedures using cutting-edge methodologies to handle irregularly observed data, small samples and a finer characterization of the longitudinal outcome and mediational processes.