Some links between conditional and coregionalized multivariate Gaussian Markov random fields

Multivariate disease mapping models are attracting considerable attention. Many modeling proposals have been made in this area, which could be grouped into three large sets: coregionalization, multivariate conditional and univariate conditional models. In this work we establish some links between these three groups of proposals. Specifically, we explore the equivalence between the two conditional approaches and show that an important class of coregionalization models can be seen as a large subclass of the conditional approaches. Additionally, we propose an extension to the current set of coregionalization models with some new unexplored proposals. This extension is able to reproduce asymmetric cross-spatial covariances for different diseases. This shows that the previously accepted belief that coregionalization was not able to reproduce models with asymmetric cross-covariances was wrong

On the use of adaptive spatial weight matrices from disease mapping multivariate analyses

Conditional autoregressive distributions are commonly used to model spatial dependence between nearby geographic units in disease mapping studies. These distributions induce spatial dependence by means of a spatial weights matrix that quantifies the strength of dependence between any two neighboring spatial units. The most common procedure for defining that spatial weights matrix is using an adjacency criterion. In that case, all pairs of spatial units with adjacent borders are given the same weight (typically 1) and the remaining non-adjacent units are assigned a weight of 0. However, assuming all spatial neighbors in a model to be equally influential could be possibly a too rigid or inappropriate assumption. In this paper, we propose several adaptive conditional autoregressive distributions in which the spatial weights for adjacent areas are random variables, and we discuss their use in spatial disease mapping models. We will introduce our proposal in a multivariate context so that the spatial dependence structure between spatial units is shared and estimated from a sufficiently large set of mortality causes. As we will see, this is a key aspect for making inference on the spatial dependence structure. We show that our adaptive modeling proposal provides more flexible and accurate mortality risk estimates than traditional proposals in which spatial weights for neighboring areas are fixed to a common value

A multiscale method applied to shallow water flow

A flux-limited second order scheme with the C-property is used to solve the one dimensional or two dimensional Saint-Venant system for shallow water flows with non-flat bottom and friction terms, as is introduced in [7] G. Haro, Numerical simulation of shallow water equations amd some physical models in image processing. Ph.D.Thesis, Departament of Technologies, Universitat Pompeu Fabra, Barcelona, 2005. High resolution at low cost can be obtained by applying a point-value multiresolution transform [2, 3, 9] in order to detect regions with singularities. The above method is applied in these regions, while a cheap polynomial interpolation is used in the smooth zones, thus lowering the computational cost

On the convenience of heteroscedasticity in highly multivariate disease mapping

Highly multivariate disease mapping has recently been proposed as an enhancement of traditional multivariate studies, making it possible to perform the joint analysis of a large number of diseases. This line of research has an important potential since it integrates the information of many diseases into a single model yielding richer and more accurate risk maps. In this paper we show how some of the proposals already put forward in this area display some particular problems when applied to small regions of study. Specifically, the homoscedasticity of these proposals may produce evident misfits and distorted risk maps. In this paper we propose two new models to deal with the variance-adaptivity problem in multivariate disease mapping studies and give some theoretical insights on their interpretation

Bayesian modeling of spatial ordinal data from health surveys

Health surveys allow exploring health indicators that are of great value from a public health point of view and that cannot normally be studied from regular health registries. These indicators are usually coded as ordinal variables and may depend on covariates associated with individuals. In this paper, we propose a Bayesian individual-level model for small-area estimation of survey-based health indicators. A categorical likelihood is used at the first level of the model hierarchy to describe the ordinal data, and spatial dependence among small areas is taken into account by using a conditional autoregressive (CAR) distribution. Post-stratification of the results of the proposed individual-level model allows extrapolating the results to any administrative areal division, even for small areas. We apply this methodology to the analysis of the Health Survey of the Region of Valencia (Spain) of 2016 to describe the geographical distribution of a self-perceived health indicator of interest in this region

Some findings on zero-inflated and hurdle Poisson models for disease mapping

Zero excess in the study of geographically referenced mortality data sets has been the focus of considerable attention in the literature, with zero-inflation being the most common procedure to handle this lack of fit. Although hurdle models have also been used in disease mapping studies, their use is more rare. We show in this paper that models using particular treatments of zero excesses are often required for achieving appropriate fits in regular mortality studies since, otherwise, geographical units with low expected counts are oversmoothed. However, as also shown, an indiscriminate treatment of zero excess may be unnecessary and has a problematic implementation. In this regard, we find that naive zero-inflation and hurdle models, without an explicit modeling of the probabilities of zeroes do not fix zero excesses problems well enough and are clearly unsatisfactory. Results sharply suggest the need for an explicit modeling of the probabilities that should vary across areal units. Unfortunately, these more flexible modeling strategies can easily lead to improper posterior distributions as we prove in several theoretical results. Those procedures have been repeatedly used in the disease mapping literature and one should bear these issues in mind in order to propose valid models. We finally propose several valid modeling alternatives according to the results mentioned that are suitable for fitting zero excesses. We show that those proposals fix zero excesses problems and correct the mentioned oversmoothing of risks in low populated units depicting geographic patterns more suited to the data

FluDetWeb: an interactive web-based system for the early detection of the onset of influenza epidemics

<p>Abstract</p> <p>Background</p> <p>The early identification of influenza outbreaks has became a priority in public health practice. A large variety of statistical algorithms for the automated monitoring of influenza surveillance have been proposed, but most of them require not only a lot of computational effort but also operation of sometimes not-so-friendly software.</p> <p>Results</p> <p>In this paper, we introduce <monospace>FluDetWeb</monospace>, an implementation of a prospective influenza surveillance methodology based on a client-server architecture with a thin (web-based) client application design. Users can introduce and edit their own data consisting of a series of weekly influenza incidence rates. The system returns the probability of being in an epidemic phase (via e-mail if desired). When the probability is greater than 0.5, it also returns the probability of an increase in the incidence rate during the following week. The system also provides two complementary graphs. This system has been implemented using statistical free-software (ℝ and WinBUGS), a web server environment for Java code (<it>Tomcat</it>) and a software module created by us (<it>Rdp</it>) responsible for managing internal tasks; the software package <it>MySQL </it>has been used to construct the database management system. The implementation is available on-line from: <url>http://www.geeitema.org/meviepi/fludetweb/</url>.</p> <p>Conclusion</p> <p>The ease of use of <monospace>FluDetWeb</monospace> and its on-line availability can make it a valuable tool for public health practitioners who want to obtain information about the probability that their system is in an epidemic phase. Moreover, the architecture described can also be useful for developers of systems based on computationally intensive methods.</p

Trends in socioeconomic inequalities in amenable mortality in urban areas of Spanish cities, 1996-2007

Background: While research continues into indicators such as preventable and amenable mortality in order to evaluate quality, access, and equity in the healthcare, it is also necessary to continue identifying the areas of greatest risk owing to these causes of death in urban areas of large cities, where a large part of the population is concentrated, in order to carry out specific actions and reduce inequalities in mortality. This study describes inequalities in amenable mortality in relation to socioeconomic status in small urban areas, and analyses their evolution over the course of the periods 1996–99, 2000–2003 and 2004–2007 in three major cities in the Spanish Mediterranean coast (Alicante, Castellón, and Valencia). Methods: All deaths attributed to amenable causes were analysed among non-institutionalised residents in the three cities studied over the course of the study periods. Census tracts for the cities were grouped into 3 socioeconomic status levels, from higher to lower levels of deprivation, using 5 indicators obtained from the 2001 Spanish Population Census. For each city, the relative risks of death were estimated between socioeconomic status levels using Poisson’s Regression models, adjusted for age and study period, and distinguishing between genders. Results: Amenable mortality contributes significantly to general mortality (around 10%, higher among men), having decreased over time in the three cities studied for men and women. In the three cities studied, with a high degree of consistency, it has been seen that the risks of mortality are greater in areas of higher deprivation, and that these excesses have not significantly modified over time. Conclusions: Although amenable mortality decreases over the time period studied, the socioeconomic inequalities observed are maintained in the three cities. Areas have been identified that display excesses in amenable mortality, potentially attributable to differences in the healthcare system, associated with areas of greater deprivation. Action must be taken in these areas of greater inequality in order to reduce the health inequalities detected. The causes behind socioeconomic inequalities in amenable mortality must be studied in depth.This work was partly supported by the FIS-FEDER projects PI040170 and PI080330