A Conditional Approach to Point Process Modelling of Elevated Risk

Abstract

SUMMARY We consider the problem of investigating the elevation in risk for a specified disease in relation to possible environmental factors. Our starting point is an inhomogeneous Poisson point process model for the spatial variation in the incidence of cases and controls in a designated geographic region, as proposed by Diggle. We develop a conditional approach to inference which converts the point process model to a non-linear binary regression model for the spatial variation in risk. Simulations suggest that the usual asymptotic approximations for likelihood-based inference are more reliable in this conditional setting than in the original point process setting. We present an application to some data on the spatial distribution of asthma in relation to three industrial locations.