We introduce a semi-parametric approach to ecological regression for disease mapping, based on modelling the regression M-quantiles of a Negative Binomial variable. The proposed method is robust to outliers in the model covariates, including those due to measurement error, and can account for both spatial heterogeneity and spatial clustering. A simulation experiment based on the well-known Scottish lip cancer data set is used to compare the M-quantile modelling approach and a random effects modelling approach for disease mapping. This suggests that the Mquantile approach leads to predicted relative risks with smaller root mean square error than standard disease mapping methods. The paper concludes with an illustrative application of the M-quantile approach, mapping low birth weight incidence data for English Local Authority Districts for the years 2005-2010.

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SUMMARYJoint modelling of space and time variation of the risk of disease is an important topic in descriptive epidemiology. Most of the proposals in this field deal with at most two time scales (age-period or age-cohort). We propose a hierarchical Bayesian model that can be used as a general framework to jointly study the evolution in time and the spatial pattern of the risk of disease. The rates are modelled as a function of purely spatial terms (local effects of risk factors that do not vary in time), time effects (on the three time axes: age, calendar period and birth cohort) and space-time interactions that describe area specific time patterns.

Linear-mixed models are frequently used to obtain model-based estimators in small area estimation (SAE) problems. Such models, however, are not suitable when the target variable exhibits a point mass at zero, a highly skewed distribution of the nonzero values and a strong spatial structure. In this paper, a SAE approach for dealing with such variables is suggested. We propose a two-part random effects SAE model that includes a correlation structure on the area random effects that appears in the two parts and incorporates a bivariate smooth function of the geographical coordinates of units. To account for the skewness of the distribution of the positive values of the response variable, a Gamma model is adopted. To fit the model, to get small area estimates and to evaluate their precision, a hierarchical Bayesian approach is used. The study is motivated by a real SAE problem. We focus on estimation of the per-farm average grape wine production in Tuscany, at subregional level, using the Farm Structure Survey data. Results from this real data application and those obtained by a model-based simulation experiment show a satisfactory performance of the suggested SAE approach.

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Model-based geostatistics and Bayesian approaches are useful in the context of veterinary epidemiology when point data have been collected by appropriate study design. We take advantage of an example of Epidemiological Surveillance on urban settings where a two-stage sampling design with first stage transects is applied to study the risk of dog parasite infection in the city of Naples, 2004-2005. We specified Bayesian Gaussian spatial exponential models and Bayesian kriging were performed to predict the continuous risk surface of parasite infection on the study region. We compared the results with those obtained by the application of hierarchical Bayesian models on areal data (proportion of positive specimens by transect). The models results were consistent with each other and the Bayesian geostatistical approach proved to be more accurate in identifying areas at risk of zoonotic parasitic diseases. In general, larger risk areas were identified at the city border where wild dogs mixed with domestic dogs and human or urban barriers were less present.

A new semiparametric approach to model-based small area prediction for counts is proposed and used for estimating the average number of visits to physicians for Health Districts in Central Italy. The proposed small area predictor can be viewed as an outlier robust alternative to the more commonly used empirical plug-in predictor that is based on a Poisson generalized linear mixed model with Gaussian random effects. Results from the real data application and from a simulation experiment confirm that the proposed small area predictor has good robustness properties and in some cases can be more efficient than alternative small area approaches.

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