A Bayesian Joinpoint regression model with an unknown number of break-points

TL;DR

This paper introduces a Bayesian joinpoint regression model with an unknown number of break-points, enabling uncertainty quantification and application to epidemiological data, exemplified by breast cancer mortality trends in Castellón, Spain.

Contribution

It presents a novel Bayesian approach with reparameterization and priors for joinpoint detection, addressing model selection challenges in epidemiological trend analysis.

Findings

Successfully applied to breast cancer mortality data from 1980-2007.

Provides a flexible Bayesian framework for count data with unknown change-points.

Enhances uncertainty quantification in joinpoint regression models.

Abstract

Joinpoint regression is used to determine the number of segments needed to adequately explain the relationship between two variables. This methodology can be widely applied to real problems, but we focus on epidemiological data, the main goal being to uncover changes in the mortality time trend of a specific disease under study. Traditionally, Joinpoint regression problems have paid little or no attention to the quantification of uncertainty in the estimation of the number of change-points. In this context, we found a satisfactory way to handle the problem in the Bayesian methodology. Nevertheless, this novel approach involves significant difficulties (both theoretical and practical) since it implicitly entails a model selection (or testing) problem. In this study we face these challenges through (i) a novel reparameterization of the model, (ii) a conscientious definition of the prior distributions used and (iii) an encompassing approach which allows the use of MCMC simulation-based techniques to derive the results. The resulting methodology is flexible enough to make it possible to consider mortality counts (for epidemiological applications) as Poisson variables. The methodology is applied to the study of annual breast cancer mortality during the period 1980--2007 in Castell\'{o}n, a province in Spain.