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We present a novel approach for the analysis of multivariate case-control georeferenced data using Bayesian inference in the context of disease mapping, where the spatial distribution of different types of cancers is analyzed. Extending other methodology in point pattern analysis, we propose a log-Gaussian Cox process for point pattern of cases and the controls, which accounts for risk factors, such as exposure to pollution sources, and includes a term to measure spatial residual variation. For each disease, its intensity is modeled on a baseline spatial effect (estimated from both controls and cases), a disease-specific spatial term and the effects on covariates that account for risk factors. By fitting these models the effect of the covariates on the set of cases can be assessed, and the residual spatial terms can be easily compared to detect areas of high risk not explained by the covariates. Three different types of effects to model exposure to pollution sources are considered. First of all, a fixed effect on the distance to the source. Next, smooth terms on the distance are used to model non-linear effects by means of a discrete random walk of order one and a Gaussian process in one dimension with a Matern covariance. Models are fit using the integrated nested Laplace approximation (INLA) so that the spatial terms are approximated using an approach based on solving Stochastic Partial Differential Equations (SPDE). Finally, this new framework is applied to a dataset of three different types of cancer and a set of controls from Alcala de Henares (Madrid, Spain). Covariates available include the distance to several polluting industries and socioeconomic indicators. Our findings point to a possible risk increase due to the proximity to some of these industries.
We propose a framework for Bayesian non-parametric estimation of the rate at which new infections occur assuming that the epidemic is partially observed. The developed methodology relies on modelling the rate at which new infections occur as a functi
Models defined by stochastic differential equations (SDEs) allow for the representation of random variability in dynamical systems. The relevance of this class of models is growing in many applied research areas and is already a standard tool to mode
It has become increasingly common to collect high-dimensional binary data; for example, with the emergence of new sampling techniques in ecology. In smaller dimensions, multivariate probit (MVP) models are routinely used for inferences. However, algo
This paper introduces a framework for speeding up Bayesian inference conducted in presence of large datasets. We design a Markov chain whose transition kernel uses an (unknown) fraction of (fixed size) of the available data that is randomly refreshed
Variational approaches to approximate Bayesian inference provide very efficient means of performing parameter estimation and model selection. Among these, so-called variational-Laplace or VL schemes rely on Gaussian approximations to posterior densit