Latent multivariate log-gamma models for high-dimensional multitype responses with application to daily fine particulate matter and mortality counts

Precise estimation of daily fine particulate matter with a diameter < 2.5 microns (PM2.5) and mortality in the U.S. is an important research challenge in public health because high levels of PM2.5 have been linked to several serious health problems, including lung disease, cardiovascular disease, and stroke. This motivates us to develop a joint Bayesian hierarchical model for bivariate spatial data to obtain precise spatial predictions of two types of re-sponses, continuous skewed PM2.5 levels, and discrete mortality counts over U.S. counties. Our novel modeling framework address several challenges in the area of spatial prediction of mortality counts and PM2.5 levels. Specifi-cally, our model allows for spatial variability and dependence of two types of responses, accommodate an unknown nonlinear spatial relationship between mortality and PM2.5 through basis function expansions, improve the preci-sion of predictions at counties with undisclosed/missing observations, and al-low for different missing data patterns for mortality and PM2.5. Furthermore, we introduce a new local measure of association for the cross-dependence between mortality and PM2.5 level. To address the burden of Bayesian com-putation for large databases, we use the dimension reduction tool and the shared conjugate structure between the Weibull distribution, Poisson distri-bution, and the multivariate log-gamma distribution. We provide a simulation study to illustrate the performance of our method. Our joint spatial model of "multitype responses" (discrete and continuous responses) and associated Bayesian method are used to analyze bivariate spatial data of daily averaged PM2.5 levels in air and mortality counts (due to diseases related to lung, car-diovascular, respiratory, and stroke) from the Centers for Disease Control and Prevention (CDC) database.