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Study Objective: To describe the advantages of using Poisson regression methods as an alternative to standardisation when computing expected numbers of disease occurrences adjusted for possible confounding factors. The problem of assessing the adequacy of model fit when the expectations are small is addressed by analytical calculations and by simulation. The method is illustrated with data from the national register of childhood tumours., Design: The tumour data are recorded in a national register., Setting: England, Scotland, and Wales., Subjects: The cases considered are all children registered with leukaemia or non-Hodgkin lymphoma under the age of 15 years between 1966-87., Main Results: The methods show a significant variation of leukaemia incidence in relation to the Register General's standard region and a negative association with socioeconomic deprivation, as measured by the Townsend index. After allowing for these variables, the incidence seems to be reasonably homogeneous throughout the population, in the sense that the residual deviance does not seem to be much larger than would be expected by chance., Conclusions: The methods described have major advantages over standardisation in controlling for confounding, both in terms of flexibility of factor selection and assessment and also in the ability to determine whether there is residual variability of incidence after allowing for these factors.

A recent study by Knox concludes that cases and "clusters" of two or more cases of childhood leukaemia and non-Hodgkin's lymphoma occur closer to many kinds of industrial installation than to supposedly comparable control locations. It is argued that these findings could be largely or entirely artefactual, the apparent differences arising out of the inappropriateness of the control data. Knox used randomly selected postcode units as controls, a procedure that leads to the comparison of individuals located in areas with typically quite different population densities from those for the cases. The resulting potential for bias is explored and the arguments are exemplified by analysing household data based on postcodes.

There is great public concern, often based on anecdotal reports, about risks from ionising radiation. Recent interest has been directed at an excess of leukaemia cases in the locality of civil nuclear installations at Sellafield and Sizewell, and epidemiologists have a duty to pursue such information vigorously. This paper sets out to show that the epidemiological methods most commonly used can be improved upon. When analysing geographical data it is necessary to consider location. The most obvious quantification of location is ranked distance, though other measures which may be more meaningful in relation to aetiology may be substituted. A test based on distance ranks, the "Poisson maximum test", depends on the maximum of observed relative risk in regions of increasing size, but with significance level adjusted for selection. Applying this test to data from Sellafield and Sizewell shows that the excess of leukaemia incidence observed at Seascale, near Sellafield, is not an artefact due to data selection by region, and that the excess probably results from a genuine, if as yet unidentified cause (there being little evidence of any other locational association once the Seascale cases have been removed). So far as Sizewell is concerned, geographical proximity to the nuclear power station does not seem particularly important.