Emanuela Dreassi

Disease mapping in veterinary epidemiology: a Bayesian geostatistical approach

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 hierarchical Bayesian model for space-time variation of disease risk

In this paper we propose a hierarchical Bayesian model to study the variation in space and time of disease risk. We represent spatial effects following the usual Bayesian specification of a Gaussian convolution of unstructured and structured components, while we adopt the birth cohort (instead of the commonly used period of death) as the main time scale. The model also includes space-time interaction terms to take into account structured inseparable space-time variability. The model is applied to lung cancer death certificate data in Tuscany, for males during the period 1971-94. While a calendar period analysis points out a general increase of mortality levelling off in the last period (1990-94), the cohort model shows a general and substantial decrease of the relative risk for the youngest cohorts born after 1930. Moreover, the pattern of the epidemic by birth cohort presents a maximum which varies by municipalities, with a strong north-west/south-east gradient.

Small area estimation for semicontinuous skewed spatial data: An application to the grape wine production in Tuscany

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.

Robust small area prediction for counts

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.

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

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 classification 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 modified 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.

The epidemic of lung cancer in Tuscany (Italy): a joint analysis of male and female mortality by birth cohort.

Lung cancer epidemic among males and females was studied at small geographical level in Tuscany Region (Italy), about 3.5 million inhabitants over almost 30 years (1971-1999). The joint analysis of the space-time pattern of relative risk for a given cause on males and females was conducted specifying a series of Hierarchical Bayesian models. Goodness-of-fit, parsimony and robustness under misspecification were used to identify candidate models. We chose birth cohort as relevant time axis and restricted our attention to birth cohorts born between 1905 and 1940. We found very different pattern by gender: the epidemic curve among males had a peak for the birth cohort born around 1930, the younger cohorts being at lower risk. Among females the relative risk was rising almost linearly on the log scale, the younger birth cohorts being at higher risk. Both curves showed two accelerations corresponding to the post-war periods (1915-1929 and 1945-1959), assuming an average age at first exposure of 20 years old. The spatial distribution among the 287 municipalities investigated was characterized by high risks in all industrial areas in males, and limited to large towns in females. The shared spatial clustering component highlighted the historically developed part of the Tuscany Region.

Bayesian Ecological Regression with Latent Factors: Atmospheric Pollutants Emissions and Mortality for Lung Cancer

In this work we propose a Bayesian ecological analysis in which a latent variable summarizes data on emissions of atmospheric pollutants. We specified a hierarchical Bayesian model with spatially structured and unstructured random terms with a nested latent factor model. This can be considered a combination of the convolution spatial model of Besag et al. (1991) and an ecological regression analysis in which a latent variable plays the role of the covariate. The unified approach allows to proper account for the uncertainty in the latent score estimation in the regression analysis. The Bayesian Latent Factor model is used to summarize the information on environmental pressure derived from three stressors: Carbon Monoxide, Nitrogen Oxides and Inhalable Particles. We found evidence of positive correlation between Lung cancer mortality and environmental pressure indicators, in males, Tuscany (Italy), 1995–1999. Environmental pressure seems to be restricted to fourteen municipalities (top 5% of the Latent Factor distribution). The model identified two areas with high point source emissions.

Disease Mapping via Negative Binomial Regression M- quantiles

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 with a disease mapping approach based on a random effects model. This suggests that the M-quantile approach leads to predicted relative risks with smaller root mean square error. 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.

A consistency theorem for regular conditional distributions

Let be a measurable space, a sub- -field and a random probability measure on , . In various frameworks, one looks for a probability P on such that is a regular conditional distribution for P given for all n. Conditions for such a P to exist are given. The conditions are quite simple when is a compact Hausdorff space equipped with the Borel or the Baire -field (as well as under similar assumptions). Applications to Gibbs measures and Bayesian statistics are given as well.

A Bayesian approach to model interdependent event histories by graphical models

In event history analysis, the problem of modeling two interdependent processes is still not completely solved. In a frequentist framework, there are two most general approaches: the causal approach and the system approach. The recent growing interest in Bayesian statistics suggests some interesting works on survival models and event history analysis in a Bayesian perspective. In this work we present a possible solution for the analysis of dynamic interdependence by a Bayesian perspective in a graphical duration model framework, using marked point processes. Main results from the Bayesian approach and the comparison with the frequentist one are illustrated on a real example: the analysis of the dynamic relationship between fertility and female employment.