Score tests for detecting excess risks around putative sources.

Focused clustering studies examine raised disease risk around prespecified point sources. As statistical methods to detect such clusters, Stone's maximum likelihood ratio test is popular, against the general ordered alternatives and score tests which score each case the reciprocal of the distance from a point source as a surrogate exposure. This paper considers extensions of score tests in that (i) they can allow us to select the best among prespecified parametric exposure functions to avoid multiple testing problems and (ii) they can be applied to a possible situation where the hazardous substance levels have a peak at some distance from a point source. Simulation studies show that the powers of the proposed tests are higher than that of Stone's test over all the alternatives considered. The proposed tests are illustrated with hypothetical data as well as simulated data to be expected in an epidemiological study currently in progress regarding an excess risk of perinatal undesirable outcomes near municipal solid waste incinerators in Japan.