The choice of test for detecting raised disease risk near a point source

This paper considers the problem of testing for excess risk near a point source of risk S, as might be postulated to exist near a nuclear installation, for example. The data are assumed to be in the form of counts in small areas for which expected numbers of cases have also been calculated by reference to national rates. It is shown how to derive the most powerful test against any given alternative hypothesis; such 'linear risk score' tests are further considered, particularly that which scores each case according to the reciprocal of the rank of the distance from S. These tests are compared with two tests due to Stone for general ordered alternatives and the important distinction is drawn between conditional and unconditional versions of the tests. Their behaviour is illustrated by application to data on childhood leukaemia in relation to nuclear installations in Britain.