Lung cancer risk modelling, from poisson regression to spatial Bayes

Abstract

Over the years, as national medical records pile up and widen in scope, more horizons are being opened up for studies to be conducted about cancer incidence rates taken in conjunction with a number of other related factors. Poisson regression provides a relatively robust, easily computed model to capture salient features of the relationship between incident rates, gender and age, amongst others. However, Poisson regression models suffer from a number of deficiencies when confronting the problem of fitting suitable models to the data. Overdispersion and lack of independence between observations are the more serious sources of concern. Also, it is quite difficult to force in more details within its structure to include a spatial dimension which is wide enough. Bayesian techniques offer a powerful remedy to these problems. Based on the Hammersley-Clifford theorem, a lot of work has been done by many researchers to provide the basis and validity for a powerfully expressive spatial interaction model underwritten by a system of consistent conditional probabilities. Within the Bayesian context, these are taken into account by conditional autoregressive models (CAR), which are able to incorporate the complications of geographical considerations into a correlation structure on a hierarchical pyramid of random variables, out of which a random field can be defined. A number of Poisson regression models and Bayesian random field models are employed for the analysis of lung cancer incidences in Malta during the period 1995- 2012. The Bayesian models are computed with the use of Markov Chain Monte Carlo (MCMC) algorithms which are easily computed by software available nowadays. The aim is to first establish significant links to the disease, and then analyse spatially and temporally the risks in the Maltese localities.