Investigation of excess environmental risk around putative sources: Stone's test with covariate adjustment

Abstract

Stone (Statistics in Medicine) 7, 649–660 (1988)) proposed a method of testing for elevation of disease risk around a point source. Stone's test is appropriate to data consisting of counts of the numbers of cases, Yi say, in each of n regions which can be ordered in increasing distance from a point source. The test assumes that the Yi are mutually independent Poisson variates, with means μi=Eiλi where the Ei are the expected numbers of cases, for example based on appropriately standardized national incidence rates, and the λi are relative risks. The null hypothesis that the λi are constant is then tested against the alternative that they are monotone non-increasing with distance from the source. We propose an extension to Stone's test which allows for covariate adjustment via a log-linear model, μi=Eiλiexp(Σxijβj), where the xij are the values of each of p explanatory variables in each of the n regions, and the βj are unknown regression parameters. Our methods are illustrated using data on the incidence of stomach cancer near two municipal incinerators. Copyright © 1999 John Wiley & Sons, Ltd.