A Comparison of Bayesian Spatial Models for Cancer Incidence at a Small Area Level: Theory and Performance

Abstract

The increase in Bayesian models available for disease mapping at a small area level can pose challenges to the researcher: which one to use? Models may assume a smooth spatial surface (termed global smoothing), or allow for discontinuities between areas (termed local spatial smoothing). A range of global and local Bayesian spatial models suitable for disease mapping over small areas are examined, including the foundational and still most popular (global) Besag, York and Mollié (BYM) model through to more recent proposals such as the (local) Leroux scale mixture model. Models are applied to simulated data designed to represent the diagnosed cases of (1) a rare and (2) a common cancer using small-area geographical units in Australia. Key comparative criteria considered are convergence, plausibility of estimates, model goodness-of-fit and computational time. These simulations highlighted the dramatic impact of model choice on posterior estimates. The BYM, Leroux and some local smoothing models performed well in the sparse simulated dataset, while centroid-based smoothing models such as geostatistical or P-spline models were less effective, suggesting they are unlikely to succeed unless areas are of similar shape and size. Comparing results from several different models is recommended, especially when analysing very sparse data.