Role of advanced statistical techniques in cancer mapping

Maps are spatial representations of a single-dimensional quantity. When cancer is mapped by geographic region, it is necessary to choose what this quantity is to be. Some cancer atlases have chosen a measure of effect, such as incidence, mortality, or relative risk. These are certainly the quantities which interest us most, but when the number of cases in a given region is small, their estimates can be very imprecise, and unreliable. The usual alternative is to map the statistical significance of departure from the overall map average. This has the advantage of de-emphasizing areas with low precision, but it can conversely highlight areas with high populations, even if they differ only minutely from the overall mean. Attempts to combine the two quantities on one map, for example by starring significant areas with relative risks above a certain level, are clumsy, and detract from the simplicity of the map. The empirical Bayes approach provides an alternative. Rather than plotting rates or risks which are individually estimated, the goal is to plot quantities which are estimated in such a way that those which are imprecise are improved by estimates from other appropriate areas. In the simplest case, this is equivalent to plotting for each map region the weighted average of the estimate for the region and the mean of the whole map, with more weight given to the regional estimate if it is based on a large population, and lower weight given if it is based on a small population. More sophisticated models are also described, and the methods are illustrated by the example of lip cancer in Scotland.