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 W est Midland Health Authority Region of England from 1980 to 1984. This is a rare disease which is considered to be noncontagious. The observ ed frequencies of the disease in the electoral wards have been convert ed to proportions that estimate the risk of a child's developing it. T he spatial autocorrelation of the risk, expressed in the variogram, wa s determined in a novel way from the proportions within electoral ward s 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 t he proportion and cross covariances between the proportion and the ris k were derived, and from the latter and the proportions the risk was e stimated in two ways by a form of cokriging: ordinary and conditional unbiased cokriging. The variogram of the risk shows strong autocorrela tion, 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 t here are other patches, notably the more densely populated areas, wher e it is small.