A transitional non-parametric maximum pseudo-likelihood estimator for disease mapping

Abstract Non-parametric maximum likelihood estimators of relative risk have been proposed as an alternative to empirical Bayes or full Bayes approaches to disease mapping. They have the advantage of being relatively simple, the EM algorithm assures convergence and area classiÿcation is straightforward. However, they do not take into account spatial autocorrelation and have higher mean square error when the true underlying risk pattern is strongly spatially structured. Furthermore, the EM algorithm is sensible to starting values and could converge to local maxima. We review the transitional generalized linear models and propose a transitional non-parametric maximum pseudo-likelihood estimator for disease mapping. The usual kernel likelihood of the mixture models is replaced by the conditional density of the observed response for a single area given the values observed in adjacent areas. The estimation of the parameters is based on the EM algorithm, appropriately modiÿed to handle the problem of local maxima and to estimate the number of components of the mixture. A simulation study shows that the transitional non-parametric maximum pseudo-likelihood estimator performs similarly to full Bayes estimators