Hierarchical bivariate time series models: a combined analysis of the effects of particulate matter on morbidity and mortality

In this paper we develop a hierarchical bivariate time series model to characterize the relationship between particulate matter less than 10 microns in aerodynamic diameter (PM10) and both mortality and hospital admissions for cardiovascular diseases. The model is applied to time series data on mortality and morbidity for 10 metropolitan areas in the United States from 1986 to 1993. We postulate that these time series should be related through a shared relationship with PM10. At the first stage of the hierarchy, we fit two seemingly unrelated Poisson regression models to produce city-specific estimates of the log relative rates of mortality and morbidity associated with exposure to PM10 within each location. The sample covariance matrix of the estimated log relative rates is obtained using a novel generalized estimating equation approach that takes into account the correlation between the mortality and morbidity time series. At the second stage, we combine information across locations to estimate overall log relative rates of mortality and morbidity and variation of the rates across cities. Using the combined information across the 10 locations we find that a 10 mug/m(3) increase in average PM10 at the current day and previous day is associated with a 0.26% increase in mortality (95% posterior interval -0.37, 0.65), and a 0.71% increase in hospital admissions (95% posterior interval 0.35, 0.99).