Research Team: Robert Haining and Jane Law
Abstract
The incidence of lung cancer at the ward level in Cambridgeshire, 1988, is mapped using the standardized incidence ratios (SIR) and Bayes adjusted ratios. SIR is the ratio of the observed to expected counts. Expected counts are based on indirect standardization. The county’s population is taken as the standard population. This is the maximum likelihood estimate of relative risk under the assumption that the counts are independently Poisson distributed, each with intensity parameter that is the product of the expected count for the given data and the area-specific relative risk. The map suggests considerable heterogeneity of these ratios but this may in part be an artefact of population size variation and the fact that if a ward has no cases in the interval of time then the relative risk for that ward is 0. For better estimates of the relative risks, we use a Bayesian approach with the models of (i) the Poisson-gamma, (ii) the log normal with spatially unstructured extra-Poisson variation, and (iii) the convolution prior with spatially structured and unstructured extra-Poisson variation, and compare their results.
Illustrations
Lung cancer incidence maps of Cambridgeshire 1988: (i) Standardized Incidence Ratio (SIR), (ii) Bayes-adjusted: Poisson-Gamma, (3) Bayes-adjusted: Poisson-log normal with spatially unstructured variation, and (iv) Bayes-adjusted: Poisson-log normal with spatially structured and unstructured variation.
Further reading
- Haining, R. (2003). Spatial Data Analysis: Theory and Practice. Cambridge: Cambridge University Press.