Non-parametric maximum likelihood estimators for disease mapping

A Non-Parametric Maximum Likelihood approach to the estimation of relative risks in the context of disease mapping is discussed and a NPML approximati on to conditional autoregressive models is proposed. NPML estimates have be en compared to other proposed solutions (Maximum Likelihood via Monte Carlo Scoring, Hierarchical Bayesian models) using real examples. Overall, the N PML autoregressive estimates (with weighted term) were closer to the Bayesi an estimates. The exchangeable NPML model ranked immediately after, even if it implied a greater shrinkage, while the truncated auto-Poisson showed in adequate for disease mapping. The coefficients of the autoregressive term f or the different mixtures have clear interpretations: in the breast cancer example, the larger cities in the region showed high rates and very low cor relation with the neighbouring areas, while the less populated rural areas with low rates were strongly positively correlated each other. This pattern is expected since breast cancer is strongly correlated with parity and age at first birth, and the female population of the rural areas experienced a decline in fertility much later than those living in the larger cities. Th e leukemia example highlighted the failure of the Poisson-Gamma model and o ther general overdispersion tests to detect high risk areas under specific conditions. The NPML approach in Aitkin is very general, simple and flexibl e. However the user should be warned against the possibility of local maxim a and the difficulty in detecting the optimal number of components. Special software (such as CAMAN or DismapWin) had been developed and should be rec ommended mainly to not experienced users. Copyright (C) 2000 John Wiley & S ons, Ltd.