A new Bayesian regression model for counts in medicine

TL;DR

This paper introduces the first Bayesian implementation of a discrete Weibull regression model tailored for count data in medicine, enabling flexible modeling of over- and under-dispersion with variable selection.

Contribution

It presents a novel Bayesian approach with a new parameterization for discrete Weibull regression, including variable selection and credible interval computation.

Findings

Effective modeling of medical count data demonstrated

Simulation and real data analyses show promising results

Implementation available in R package BDWreg

Abstract

Discrete data are collected in many application areas and are often characterised by highly skewed and power-lawlike distributions. An example of this, which is considered in this paper, is the number of visits to a specialist, often taken as a measure of demand in healthcare. A discrete Weibull regression model was recently proposed for regression problems with a discrete response and it was shown to possess two important features: the ability to capture over and under-dispersion simultaneously and a closed-form analytical expression of the quantiles of the conditional distribution. In this paper, we propose the first Bayesian implementation of a discrete Weibull regression model. The implementation considers a novel parameterization, where both parameters of the discrete Weibull distribution can be made dependent on the predictors. In addition, prior distributions can be imposed that encourage parameter shrinkage and that lead to variable selection. As with Bayesian procedures, the full posterior distribution of the parameters is returned, from which credible intervals can be readily calculated. A simulation study and the analysis of four real datasets of medical records show promises for the wide applicability of this approach to the analysis of count data. The method is implemented in the R package BDWreg.