Bayesian classification and regression trees for predicting incidence of cryptosporidiosis

Abstract

Background: Classification and regression tree (CART) models are tree-based exploratory data analysis methods which have been shown to be very useful in identifying and estimating complex hierarchical relationships in ecological and medical contexts. In this paper, a Bayesian CART model is described and applied to the problem of modelling the cryptosporidiosis infection in Queensland, Australia.

Methodology/principal findings: We compared the results of a Bayesian CART model with those obtained using a Bayesian spatial conditional autoregressive (CAR) model. Overall, the analyses indicated that the nature and magnitude of the effect estimates were similar for the two methods in this study, but the CART model more easily accommodated higher order interaction effects.

Conclusions/significance: A Bayesian CART model for identification and estimation of the spatial distribution of disease risk is useful in monitoring and assessment of infectious diseases prevention and control.

Figure 1. The best tree identified from Bayesian regression trees.

At each terminal node the mean (μ) and number of individuals (n) are displayed.

Figure 2. The observed spatial distribution of SEIFA, temperature, rainfall and annual average incidence rates of cryptosporidiosis.

Figure 3. The best tree identified from Bayesian classification trees.

At each terminal node the predicted category of presence or absence is denoted respectively by pres or abs. The two numbers directly below this are in general a/b (e.g. 16/0) which denotes the number of observed absences “a” and presences “b” that are classified into this particular node.