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

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 Castellón, a province in Spain.

Bayesian age-stratified joinpoint regression model: an application to lung and brain cancer mortality

“…For application, we rather choose to study the mortality trends only and the reason is discussed earlier in paragraph one. Our work in this paper extends the work of Martinez-Beneito et al [29], Ghosh et al [15,16], and Tiwari et al [37] in different dimensions. Being rare events, the observed mortality counts are assumed to follow the Poisson probability distributions.…”

“…The assumption of the breakpoints in our proposed model is random and applying the Bayesian approach to detect them is a reasonable choice (see [15,16,29,37]). For k = K fixed, we develop a Bayesian model selection procedure to select the best model among K + 1 nested models in the model space…”

“…We can only assign same priors to all common parameters in all competing models only if they have the same meaning [2]. Martinez-Beneito et al [29] proposed an alternative parametrization arguing that the hypothesis of common parameters have the same meaning across the models. We have adopted their reparametrization method in [20] and we follow the same procedure here.…”

“…Although this technique is in extensive use, its limitations are prominent [29]. In 2005, Tiwari et al [37] developed a Bayesian model selection approach for discrete joinpoint regression.…”

“…Also, they assumed a mixture distribution with point mass at zero for the slope that changes at the joinpoint. Martinez-Beneito et al [29] proposed a joinpoint regression model based on the Poisson assumption in which they find a suitable reparametrization method to handle the joinpoints. They claimed that the developed model is sophisticated enough to handle the uncertainty related to the model and its parameters.…”