Binomial cokriging for estimating and mapping the risk of childhood cancer

The incidences of human diseases vary from place to place, and this is also likely to be so for the risk of people developing many of them. We have analysed the spatial distribution of childhood cancer in the West Midland Health Authority Region of England from 1980 to 1984. This is a rare disease which is considered to be noncontagious. The observed frequencies of the disease in the electoral wards have been converted to proportions that estimate the risk of a child's developing it. The spatial autocorrelation of the risk, expressed in the variogram, was determined in a novel way from the proportions within electoral wards by treating them as binomial variables dependent on the risk and the numbers of children in the wards. The observed variogram was modelled by Whittle's elementary two-dimensional correlation. Covariances of the proportion and cross covariances between the proportion and the risk were derived, and from the latter and the proportions the risk was estimated in two ways by a form of cokriging: ordinary and conditional unbiased cokriging. The variogram of the risk shows strong autocorrelation, and the kriged estimates, when mapped, have a distribution that is far from even. There are patches where the estimated risk is large, especially in the rural south west and the suburban north east; and there are other patches, notably the more densely populated areas, where it is small.