Evaluation of reduced rank semiparametric models to assess excess of risk in cluster analysis

The existence of multiple environmental hazards is obviously a threat to human health and, from a statistical point of view, the modeling and the detection of disease clusters potentially related to those hazards offer challenging tasks. In this paper, we consider low rank thin plate spline (TPS) models within a semiparametric approach to focused clustering for small area health data. Both the distance from a putative source and a general, unspecified clustering process are modeled in the same fashion and they are entered log-additively in mixed Poisson-Normal models. Some issues related to the identification of the random effects arising from this approach are investigated. Under different simulated scenarios, we evaluate the proposed models using conditional Akaike's weights and tests for variance components, providing a comprehensive model selection methodology easy to implement. We examine observations of lung cancer deaths taken in Ohio between 1987 and 1988. These data were analyzed on several occasions to investigate the risk associated with a putative source in Hamilton county. In our analysis, we found a strong south-eastward spatial trend which is confounded with a significant radial distance effect decreasing between 0 and 150 km from the point source. © 2008 John Wiley & Sons, Ltd.