Quantile Regression for Area Disease Counts: Bayesian Estimation using Generalized Poisson Regression
Abstract: Generalized linear models based on Poisson regression are commonly applied to count data for area morbidity outcomes, focused on modelling the conditional mean of the response as a function of a set of risk factors. Mean regression models may be sensitive to outliers and provide no information on other distributional features of the response. We consider instead a Poisson lognormal hierarchical approach to quantile regression of spatially configured count data, allowing for observed risk factors and spatially correlated unobserved risk factors. This technique has the advantage that a profile of the relative outcome risk across quantiles can be obtained, including estimates of uncertainty (e.g. the uncertainty attaching to 2.5% or 5% relative risk quantiles). An application involves counts of emergency hospitalisations for self-harm for 6791 small areas in England. Known risk factors are area deprivation, a measure of social fragmentation and a measure of rural status. It is shown that impact of these predictors varies between quantiles, and that hierarchical quantile regression generally produces narrower risk intervals, except for outlier areas, and leads to a higher number of areas being classed as high risk.Keywords: Hierarchical quantile regression. Relative risk. Risk intervals. Elevated risk. Self-harm.