The Bayesian Modeling of Disease Risk in Relation to a Point Source

Abstract

Recently there has been increased interest, from both the media and the public, in the question, “Is there an excess of disease risk close to a prespecified point source?” To address this question, routinely available public health data may be analyzed. In the United Kingdom, as in many countries, health data and the associated population data that are required for comparison, are available as aggregated counts. In this article we propose to analyze such data using a Bayesian disease mapping framework. This framework allows the extra-Poisson variability that is frequently encountered to be accommodated through random effects that may be unstructured or display spatial dependence. The disease risk-spatial location relationship is modeled using a simple but realistic parametric form. The random effects may be used for diagnostic purposes, in particular to assess the appropriateness of the distance-risk model. The choice of prior distribution is extremely important 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 region 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 to occur within a specified distance of the putative source (given a population size, by age and sex, and a time period). The approach is illustrated using data from an investigation into the incidence of stomach cancer close to a municipal solid waste incinerator. The sensitivity to the prior distribution and the presence or absence of spatial random effects is examined. To determine whether the increase in risk detected in the study is persistent, we analyze incidence data from the four-year interval following the study 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 epidemiological question to be answered with greater reliability.

KEY WORDS:

• Disease mapping
• Environmental epidemiology
• Overdispersion
• Predictive distributions
• Prior distributions
• Public health
• Spatial epidemiology