The Bayesian modeling of disease risk in relation to a point source

Recently there has been increased interest, from both the media and the pub lic, in the question, "Is there an excess of disease risk close to a prespe cified point source?" To address this question, routinely available public health data may be analyzed. In the United Kingdom, as in many countries, h ealth data and the associated population data that are required for compari son, are available as aggregated counts. In this article we propose to anal yze such data using a Bayesian disease mapping framework. This framework al lows the extra-Poisson variability that is frequently encountered to be acc ommodated through random effects that may be unstructured or display spatia l dependence. The disease risk-spatial location relationship is modeled usi ng a simple but realistic parametric form. The random effects may be used f or diagnostic purposes, in particular to assess the appropriateness of the distance-risk model. The choice of prior distribution is extremely importan t in this context and we develop an informative prior distribution that is based on epidemiological considerations and on additional analyses of data that are obtained From a larger "reference" region within which the study r egion is embedded. We argue that a particularly useful inferential summary for public health purposes is the predictive distribution. For example, we may obtain the distribution of the number of cases that would be expected t o occur within a specified distance of the putative source (given a populat ion size, by age and sex, and a time period). The approach is illustrated u sing data from an investigation into the incidence of stomach cancer close to a municipal solid waste incinerator. The sensitivity to the prior distri bution and the presence or absence of spatial random effects is examined. T o determine whether the increase in risk detected in the study is persisten t, we analyze incidence data from the four-year interval following the stud y period. We finally describe a number of extensions including the modeling of data from a number of sites using a four-stage hierarchical model. This model is statistically realistic and, more importantly, allows the epidemi ological question to be answered with greater reliability.