Abstract
Generalized Poisson regression is commonly applied to overdispersed count data, and focused on modelling the conditional mean of the response. However, conditional mean regression models may be sensitive to response outliers and provide no information on other conditional distribution features of the response. We consider instead a hierarchical approach to quantile regression of overdispersed count data. This approach has the benefits of effective outlier detection and robust estimation in the presence of outliers, and in health applications, that quantile estimates can reflect risk factors. The technique is first illustrated with simulated overdispersed counts subject to contamination, such that estimates from conditional mean regression are adversely affected. A real application involves ambulatory care sensitive emergency admissions across 7518 English patient general practitioner (GP) practices. Predictors are GP practice deprivation, patient satisfaction with care and opening hours, and region. Impacts of deprivation are particularly important in policy terms as indicating effectiveness of efforts to reduce inequalities in care sensitive admissions. Hierarchical quantile count regression is used to develop profiles of central and extreme quantiles according to specified predictor combinations.
Highlights
Extensions of Poisson regression are commonly applied to overdispersed count data, focused on modelling the conditional mean of the response
It is shown that the hierarchical median regression via a Poisson log-normal representation (HQRPLN) more accurately reproduces the regression parameters assumed in the simulation than negative binomial or standard PLN regression
We disaggregate the 7518 general practitioner (GP) practices by their region of location, and according to the England-wide deprivation decile of the practice
Summary
Extensions of Poisson regression are commonly applied to overdispersed count data, focused on modelling the conditional mean of the response. We consider instead a Bayesian hierarchical approach to quantile regression of overdispersed count data, based on a Poisson log-normal (PLN) approach to overdispersion. A real application involves counts of ambulatory care sensitive (ACS) emergency admissions in 2014–15 according to 7518 English patient general practitioner (GP) practice. Such admissions are potentially avoidable given effective care and are often used as an index of health performance (Caminal et al 2004). The applied focus of the paper adopts a Bayesian strategy and uses a quantile regression approach that has, as one aspect, the benefit of robustness compared to conditional mean regression, which is demonstrated using simulated data. The remaining sections involve data analysis: a simulation analysis involving contaminated count data (section 5), and the ACS admissions analysis and results applying the HQRPLN method (sections 6 and 7)
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