The association between levels of air pollution and mortality rate is well-established, but quantifying the magnitude of the effect is sometimes complicated by limitations in the data. In this paper, a joint Bayesian hierarchical model is developed to identify significant predictor factors and quantify their impacts on mortalities. To account for potential measurement error in the pollution data, the observed pollutant levels were treated as noisy proxies for the true exposure, therefore requiring a measurement error structure. We illustrate the developed model by performing an analysis of the association between weekly air pollution levels and cardiovascular and respiratory mortality in Los Angeles (LA) County over five years from January 2018 to December 2022. The purpose of the study was to quantify the impact of the main air pollutants (PM2.5, PM10, SO2, NO2, CO, and O3) and of temperature on weekly mortality from four causes: chronic obstructive pulmonary diseases, pneumonia, heart failures, and malignant neoplasms. The results, supported by Bayesian model comparison criteria, indicated that weekly county-level cause-specific mortalities were significantly associated with certain ranges of air pollutants, and that some of these cause-specific mortalities had significant associations with ambient temperature levels. The analysis revealed that several pollutants appeared to be associated with lower mortality; we interpreted this counterintuitive finding from various perspectives.

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