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

Abstract

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.

Keywords:

• Dynamic model
• Hierarchical Bayes
• Joint modeling
• Lasso
• Markov chain Monte Carlo
• Matrix stick-breaking process

Supplementary Materials

The computational details of MCMC algorithm, and some properties of the proposed DH-MSBP are provided in the supplementary materials.

Acknowledgments

The authors sincerely thank the associate editor, and the three anonymous reviewers for their comments and suggestions.

Additional information

Funding

MJD was partially supported by US NIH grants CA85295 and CA183854.