Approximate inference for disease mapping

Disease mapping is an important area of statistical research. Contributions to the area over the last twenty years have been instrumental in helping to pinpoint potential causes of mortality and to provide a strategy for effective allocation of health funding. Because of the complexity of spatial analyses, new developments in methodology have not generally found application at Vital Statistics agencies. Inference for spatio-temporal analyses remains computationally prohibitive, for routine preparation of mortality atlases. This paper considers whether approximate methods of inference are reliable for mapping studies, especially in terms of providing accurate estimates of relative risks, ranks of regions and standard errors of risks. These approximate methods lie in the broader realm of approximate inference for generalized linear mixed models. Penalized quasi-likelihood is specifically considered here. The main focus is on assessing how close the penalized quasi-likelihood estimates are to target values, by comparison with the more rigorous and widespread Bayesian Markov Chain Monte Carlo methods. No previous studies have compared these two methods. The quantities of prime interest are small-area relative risks and the estimated ranks of the risks which are often used for ordering the regions. It will be shown that penalized quasi-likelihood is a reasonably accurate method of inference and can be recommended as a simple, yet quite precise method for initial exploratory studies. (C) 2005 Elsevier B.V. All rights reserved.