Bayesian Quantile Regression for Count Data with Application to Environmental Epidemiology

Abstract

Summary Quantile regression estimates the relationship between covariates and the τth quantile of the response distribution, rather than the mean. We present a Bayesian quantile regression model for count data and apply it in the field of environmental epidemiology, which is an area in which quantile regression is yet to be used. Our methods are applied to a new study of the relationship between long-term exposure to air pollution and respiratory hospital admissions in Scotland. We observe a decreasing relationship between pollution and the τth quantile of the response distribution, with a relative risk ranging between 1.023 and 1.070.