Modeling Multiple Time-Varying Related Groups: A Dynamic Hierarchical Bayesian Approach With an Application to the Health and Retirement Study

As the population of the older individuals continues to grow, it is important to study the relationship among the variables measuring financial health and physical health of the older individuals to better understand the demand for healthcare, and health insurance. We propose a semiparametric approach to jointly model these variables. We use data from the Health and Retirement Study which includes a set of correlated longitudinal variables measuring financial and physical health. In particular, we propose a dynamic hierarchical matrix stick-breaking process prior for some of the model parameters to account for the time dependent aspects of our data. This prior introduces dependence among the parameters across different groups which varies over time. A Lasso type shrinkage prior is specified for the covariates with time-invariant effects for selecting the set of covariates with significant effects on the outcomes. Through joint modeling, we are able to study the physical health of the older individuals conditional on their financial health, and vice-versa. Based on our analysis, we find that the health insurance (medicare) provided by the government (of the United States) to the older individuals is very effective, and it covers most of the medical expenditures. However, none of the health insurances conveniently cover the additional medical expenses due to chronic diseases like cancer and heart problem. Simulation studies are performed to assess the operating characteristics of our proposed modeling approach. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.