This article analyzes the performance of different smoothing methods by comparing the robustness of the fitted models to changes in the underlying true risk. The models include empirical Bayes (EB), linear Bayes (LB), non-parametric smoothing, marginal mixture methods and full Bayes (FB). The goodness-of-fit of these models is assessed using global methods. The authors simulated several sets of data with different possible relative risk models using the former East Germany as a base map with counts of lip cancer deaths from 1980 to 1989.

With these data as a starting point, the authors apply several models to simulate the risk, and simulate 100 data sets from each model. Among the models used to define the true risk the authors use the following: Two fixed effect models, one constant risk and two linear trend models; among the random effects models the authors include one linear trend model, one quadratic trend; BYM exponential covariance model as well as the uncorrelated case; mixture models with and without spatial structure; BYM with non-general clusters; and a global gamma model.

Several alternatives of each model, for example, using different parameters, are also estimated. The measures of goodness of fit were all obtained as an average of the measures for each of the 100 simulated data. Different measures of goodness of fit were used to evaluate the models; the Bayesian information criterion was used for all models that had associated likelihoods. The difference between the true risk and the fitted risk was also considered as well as the comparison between the observed and fitted counts. For this, the authors used Pearson and Spearman correlation coefficients relating the fitted and the simulated counts and relative risk; Pearson chi-squared measure is also applied to the counts and relative risks and the Moran's I autocorrelation coefficient is applied to the residuals from the fit.

The main results of the article show that the gamma-Poisson exchangeable model and the BYM model are the most robust methods from the ones analyzed, and mixture models are the least robust. Non-parametric smoothing methods are shown to perform badly in general.

Last updated March 9, 2006