A Semiparametric Bayesian Model for Longitudinal Data: The Cluster Memory Dirichlet Process Mixture Model

• Activity Number: 652
• Type: Contributed
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Robert E Weiss*+ and Yuda Zhu
• Companies: University of California, Los Angeles and Genentech
• Keywords: Chinese Restaurant Process ; Markov Process ; Tuberculosis ; Quantile Regression ; Repeated Measures ; Multivariate Data

Abstract

We present a novel extension to the Dirichlet process mixture (DPM) model to model regularly spaced longitudinal data. In longitudinal data, observations are both subject specific and a function of time. It is therefore important to account for these two features: dependence between sampling densities across time and dependence in observations across time within the same subject. To account for both features, we propose the cluster memory DPM (cmDPM) model. In our cmDPM model, subjects are modeled as a DPM model at baseline. Subjects retain their cluster membership from the previous time point with nonzero probability. After baseline subjects are no longer exchangeable and their observed values depend on their previous clustering history. Markers for clusters that are retained over time evolve through a time dependent process. We apply the cmDPM model to model annual tuberculosis (TB) incidence rates across 197 countries from 1990-2010 and examine how the annual distribution of TB incidence rates has changed over time.