Abstracts of invited talks

We present dynamic linked graphs for exploratory analysis of spatial marked point processes data. In addition to the usual marked point processes, we are also interested in a special type of marked point process. Namely, we analyse spatial bivariate point processes that are linked: each spatial event of a point process N1 has one or more corresponding events in another spatial point process N2 observed in the same geographical region. Pairs of origin-destination events are the main example of this type of data. We introduce MAPPEA, a graphical tool that displays the spatial point pattern and its marks in linked windows. Brushing over one view creates a linked view of the associated marks within the brush region. Two main applications are presently implemented: first, a dynamically changing cumulative distribution function of the univariate marks; and second, a dynamically changing map of the destination location conditional density distribution function given that the origin-event is within the brushed region. The methods are illustrated with data on car theft location and and the eventual car retrieval location, and ondata of trees' locations and their associated marks.

Rapid developments in geographical information systems (GIS) and advanced spatial statistics continue to generate interest in analyzing complex spatial datasets. One area of activity is in creating smoothed disease maps to describe the geographic variation of disease and generate hypotheses for apparent differences in risk. With multiple diseases, a Multivariate Conditionally Autoregressive (MCAR) model is often used to smooth across space while accounting for associations between the diseases. The MCAR, however, imposes complex covariance structures that are difficult to interpret and estimate. This article develops a much simpler alternative approach building upon the techniques of smoothed ANOVA (SANOVA). Instead of simply shrinking effects without any structure, here we use SANOVA to smooth spatial random effects by taking advantage of the spatial structure. This paper extends SANOVA to cases in which one factor is a spatial lattice, which is smoothed using a CAR model, and a second factor is, for example, type of cancer. Datasets routinely lack enough information to identify the additional structure of MCAR. SANOVA offers a simpler and more intelligible structure than the MCAR while performing as well.
We demonstrate our approach with simulation studies designed to compare SANOVA with different design matrices versus MCAR with different priors. Subsequently a cancer-surveillance dataset, describing incidence of 3 cancers in Minnesota's 87 counties, is analyzed using both approaches, showing the competitiveness of the SANOVA approach.

Population Health profiling is an important phase in Environmental Epidemiology investigations. It consists in identifying altered rate of a disease among many diseases or, for a given disease, of an area within a region. We developed a Bayesian approach to model underlying risk pattern under the null and we used cross-validatory predictive distributions to generate model-based p-values (Ohlssen JRSSA 2007). Alternatively we specified a three level hierarchical Bayesian model and use the posterior classification probabilities as local FDR (Efron JASA 2001). We compare the results with other approaches in the literature (posterior probabilities under different models, simple FDR procedures for Poisson data).

In recent years, spatial and spatio-temporal modelling have become an important area of research in many fields (epidemiology, environmental studies, disease mapping, ...). However, the methodology developed is constrained by the large amount of data available, and most models impose unrealistic constraints on the data in order to be fitted on a reasonable amount of time. We propose the use of Penalized splines (P-splines) in a mixed model framework for smoothing spatio-temporal data. Our approach allows the consideration of interaction terms which can be decomposed as a sum of smooth functions similarly as an ANOVA decomposition. These models are an attractive alternative due to their interpretability in terms of decompositions of smooth functions and basis which are identifiable The properties of the basis allow the use of algorithms that can handle large amount of data.

Integrated nested Laplace approximations (INLA) have been recently proposed for approximate Bayesian inference in latent Gaussian models (Rue, Martino and Chopin, 2009, JRSSB). The INLA approach is applicable to a wide range of commonly used statistical models, including models for spatial and spatio-temporal disease mapping. In this talk I will first review the INLA methodology and contrast it with more established inference approaches such as Markov chain Monte Carlo (MCMC). In the second part of the talk I will illustrate how parametric (Bernardinelli et al., Stats in Med, 1995) and nonparametric (Knorr-Held, Stats in Med, 2000) models for spatio-temporal disease mapping can be fitted using INLA. I will also discuss how the INLA approach can be used for model assessment and model comparison based on leave-one-out cross-validation. The methodology will be applied to case reporting data on BVD (bovine viral diarrhoe) and Salmonellosis in cattle provided by the Swiss federal veterinary office.

In recent years spatial modelling of disease occurrence has become very popular in epidemiological applications. Moreover, the use of Intrinsic Gaussian Markov Random Fields (IGMRF), with a heterogeneous effect for every region, has been the usual procedure to model the underlying risk variability in many of these studies. Nevertheless, the correlation structure in an IGMRF is completely determined by the geographical structure of the lattice under study, therefore it is not possible to adapt the dependence structure of this prior distribution to the geographical pattern of the disease under study. The goal of this study will be to propose an alternative class of spatial correlation structures different to IGMRF and extend its use for the spatio-temporal modelling of diseases. In the same way that IGMRF generalizes random walk processes to the spatial domain, we will resort to moving average ideas in time series to induce spatial dependence in our context. The model proposed will be formulated from a Bayesian perspective and Reversible Jump MCMC will be used to learn about the range (how many neighbouring regions away) of dependence of the spatial pattern studied.