Bayesian Hierarchical Profile Regression for Categorical Data

In this research we consider problems involving discrete data which are divided into a set of hierarchical groups with each observation in each group believed to be drawn from a mixture model. Our goal is to recover the latent clustering structures for each data group, allow these discovered clusters to be shared among each of the data groups, and assess for associations between the estimated cluster memberships and a clinically relevant outcome. For the clustering model, we assume the number of mixture components within each group is unknown a priori and is to be inferred from the data. To analyze this type of data and accomplish our analytic goals we propose Bayesian Hierarchical Profile Regression (BHPR), a model which utilizes Bayesian Profile Regression (BPR) in conjunction with a Hierarchical Dirichlet Process Mixture Model (HDPMM). The utilization of the HDPMM allows for the discovery of latent clusters within each data group and allows for the identified latent clusters to be shared across the groups, while using the approach of BPR allows for the characterization of the associations between latent cluster memberships and the clinically relevant outcome. Data utilized to recapture cluster memberships within each data group can be either binary or ordinal. For binary data, one of the fundamental assumptions found in similar mixture models called Conditional Independence can either be maintained or relaxed. We demonstrate the utility of our model through applications to two patient populations: 1) a subset of data collected by the Acute Liver Failure Study Group, and 2) a cohort of patients referred for a Modified Barium Swallow Study assessed using the Modified Barium Swallow Impairment Profile. Results from these applications demonstrate that our research results can be used to inform appropriate intervention strategies and provide tools for clinicians to make better multidimensional management and treatment decisions in a variety of disease areas