Case-control isotonic regression for investigation of elevation in risk around a point source

Stone's isotonic regression method for analysing count data to estimate dis ease risk in relation to a point source of environmental pollution is now r outinely used. This paper develops the corresponding procedure for case-con trol data consisting of the locations of individual cases with controls wit h associated covariate information. In this setting, the generalized likeli hood ratio statistic to test the null hypothesis of constant risk against t he alternative that risk is a monotone non-increasing function of distance from the point source is intractable. An approximate Monte Carlo test is de scribed, extending an exact test proposed by Bithell for the situation in w hich there are no covariates. Interval estimates of risk as a function of d istance from the point source are constructed by simulation of the sampling distribution of the isotonic regression estimator. The methodology is illu strated by two applications: one to the relative risk of larynx cancers and lung cancers near a now-disused industrial incinerator; the other to the r isk of asthma in children in relation to distance of residence from the nea rest main road. Copyright (C) 1999 John Wiley & Sons, Ltd.