Supervised-clustering using a Dirichlet process mixture model to investigate the health effects of the chemical constituents of fine particulate matter (PM$_{2.5}$)

Abstract

Poisson random effects regression model is often used to analyze spatially-varying associations between a count response variable and an exposure variable when multiple observations are available in each location (e.g. multi-site time series data). Also, when location-specific predictors that may explain the spatial variability in the exposure-response association (called effect-modifying variables) are available, a hierarchical regression structure can be added to the Poisson random effects model in a Bayesian frame work. However, in some cases, the effect-modifying variables are highly correlated with each other and multi-colinearity occurs in a hierarchical Poisson regression modeling. With the multi-colinearity, one may fail to detect significant predictors unless enough sample size is ensured. Motivated by this, in this research, avoiding the multi-colinearity, we propose a new statistical approach to associate the highly-correlated effect-modifying variables with the random effects in a hierarchical Poisson regression modeling. The proposed model is based on a Dirichlet process (DP) mixture for the joint model of a Poisson random effects regression and a multivariate normal model for the effect-modifying predictors. The model identifies latent groups that vary jointly by the exposure-response relationship and the effect modifier predictor profiles instead of detecting single predictors as significant. Simulation studies were conducted to examine the performance of our proposed model compared with the conventional regression approach. Also, we apply the proposed model to our motivating example data and compare the results from the conventional method.