The Effects of Air Pollution on Health: A Study of Los Angeles County

This study aims to develop and implement a Poisson regression model with measurement error using a Bayesian framework, with model fitting performed in Stan. The focus is on examining the relationship between air pollution exposure and health outcomes, such as respiratory and cardiovascular disease counts, while accounting for inaccuracies in pollution measurements. Air pollution data is often subject to measurement error due to imperfect monitoring or averaging, which, if ignored, can lead to biased estimates and incorrect conclusions. The Poisson regression will model count data, where the response variable, such as disease counts, follows a Poisson distribution. Covariates including pollution levels, demographic factors, and meteorological conditions will be incorporated to control for confounders. To address measurement error in the exposure data, a Bayesian hierarchical model will be used, where observed pollution levels are treated as noisy measurements of the true underlying exposure. Priors will be specified for both the regression coefficients and the measurement error parameters, and posterior distributions will be estimated via Markov Chain Monte Carlo (MCMC) sampling. This approach ensures that both the count nature of the response and the uncertainty in exposure measurements are properly accounted for, leading to more accurate estimates of the health risks associated with air pollution.