Bayesian component selection in multi-response hierarchical structured additive models with an application to clinical workload prediction in patient-centered medical homes

Motivated by a large health care data obtained from the U.S. Veterans Health Administration (VHA), we develop a multivariate version of hierarchical structured additive regression (STAR) models that involves a set of health care responses defined at the lowest level of the hierarchy, a set of patient factors to account for individual heterogeneity, and a set of higher level effects to capture dependence between patients within the same medical home team and facility. We show how a special class of such models can equivalently be represented and estimated in structural equation modeling framework. We then propose a Bayesian component selection with a spike and slab prior structure that allows inclusion or exclusion single effects as well as grouped coefficients representing particular model terms. A simple parameter expansion is used to improve mixing and convergence properties of Markov chain Monte Carlo simulation. The proposed methods are applied to a real-world application of the VHA patient centered medical home (PCMH) data and help to provide a good prediction of clinical workload portfolio for a certain mix of health care professionals based on patient key demographic, diagnostic, and medical attributes.