Open Access
Bayesian inference in multivariate spatio-temporal areal models using INLA: analysis of gender-based violence in small areas
(Springer, 2020) Vicente Fuenzalida, Gonzalo; Goicoa Mangado, Tomás; Ugarte Martínez, María Dolores; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
Multivariate models for spatial count data are currently receiving attention in disease mapping to model two or more diseases jointly. They have been thoroughly studied from a theoretical point of view, but their use in practice is still limited because they are computationally expensive and, in general, they are not implemented in standard software to be used routinely. Here, a new multivariate proposal, based on the recently derived M models for spatial data, is developed for spatio-temporal areal data. The model takes account of the correlation between the spatial and temporal patterns of the phenomena being studied, and it also includes spatio-temporal interactions. Though multivariate models have been traditionally fitted using Markov chain Monte Carlo techniques, here we propose to adopt integrated nested Laplace approximations to speed up computations as results obtained using both fitting techniques were nearly identical. The techniques are used to analyse two forms of crimes against women in India. In particular, we focus on the joint analysis of rapes and dowry deaths in Uttar Pradesh, the most populated Indian state, during the years 2001-2014.
Open Access
Space-time interactions in bayesian disease mapping with recent tools: making things easier for practitioners
(Edward Arnold, 2022) Urdangarin Iztueta, Arantxa; Ugarte Martínez, María Dolores; Goicoa Mangado, Tomás; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
Spatio-temporal disease mapping studies the distribution of mortality or incidence risks in space and its evolution in time, and it usually relies on fitting hierarchical Poisson mixed models. These models are complex for practitioners as they generally require adding constraints to correctly identify and interpret the different model terms. However, including constraints may not be straightforward in some recent software packages. This paper focuses on NIMBLE, a library of algorithms that contains among others a configurable system for Markov chain Monte Carlo (MCMC) algorithms. In particular, we show how to fit different spatio-temporal disease mapping models with NIMBLE making emphasis on how to include sum-to-zero constraints to solve identifiability issues when including spatio-temporal interactions. Breast cancer mortality data in Spain during the period 1990-2010 is used for illustration purposes. A simulation study is also conducted to compare NIMBLE with R-INLA in terms of parameter estimates and relative risk estimation. The results are very similar but differences are observed in terms of computing time.
Open Access
Using mortality to predict incidence for rare and lethal cancers in very small areas
(VCH Publishers, 2022) Etxeberria Andueza, Jaione; Goicoa Mangado, Tomás; Ugarte Martínez, María Dolores; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2
Incidence and mortality figures are needed to get a comprehensive overview of cancer burden. In many countries, cancer mortality figures are routinely recorded by statistical offices, whereas incidence depends on regional cancer registries. However, due to the complexity of updating cancer registries, incidence numbers become available 3 or 4 years later than mortality figures. It is, therefore, necessary to develop reliable procedures to predict cancer incidence at least until the period when mortality data are available. Most of the methods proposed in the literature are designed to predict total cancer (except nonmelanoma skin cancer) or major cancer sites. However, less frequent lethal cancers, such as brain cancer, are generally excluded from predictions because the scarce number of cases makes it difficult to use univariate models. Our proposal comes to fill this gap and consists of modeling jointly incidence and mortality data using spatio-temporal models with spatial and age shared components. This approach allows for predicting lethal cancers improving the performance of individual models when data are scarce by taking advantage of the high correlation between incidence and mortality. A fully Bayesian approach based on integrated nested Laplace approximations is considered for model fitting and inference. A validation process is also conducted to assess the performance of alternative models. We use the new proposals to predict brain cancer incidence rates by gender and age groups in the health units of Navarre and Basque Country (Spain) during the period 2005-2008.
Open Access
Multivariate Bayesian spatio-temporal P-spline models to analyze crimes against women
(Oxford University Press, 2021) Vicente Fuenzalida, Gonzalo; Goicoa Mangado, Tomás; Ugarte Martínez, María Dolores; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
Univariate spatio-temporal models for areal count data have received great attention in recent years for estimating risks. However, models for studying multivariate responses are less commonly used mainly due to the computational burden. In this article, multivariate spatio-temporal P-spline models are proposed to study different forms of violence against women. Modeling distinct crimes jointly improves the precision of estimates over univariate models and allows to compute correlations among them. The correlation between the spatial and the temporal patterns may suggest connections among the different crimes that will certainly benefit a thorough comprehension of this problem that affects millions of women around the world. The models are fitted using integrated nested Laplace approximations and are used to analyze four distinct crimes against women at district level in the Indian state of Maharashtra during the period 2001-2013.
Open Access
Alleviating confounding in spatio-temporal areal models with an application on crimes against women in India
(SAGE Publications, 2021) Adin Urtasun, Aritz; Goicoa Mangado, Tomás; Hodges, James S.; Schnell, Patrick M.; Ugarte Martínez, María Dolores; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2; Estadística, Informática y Matemáticas
Assessing associations between a response of interest and a set of covariates in spatial areal models is the leitmotiv of ecological regression. However, the presence of spatially correlated random effects can mask or even bias estimates of such associations due to confounding effects if they are not carefully handled. Though potentially harmful, confounding issues have often been ignored in practice leading to wrong conclusions about the underlying associations between the response and the covariates. In spatio-temporal areal models, the temporal dimension may emerge as a new source of confounding, and the problem may be even worse. In this work, we propose two approaches to deal with confounding of fixed effects by spatial and temporal random effects, while obtaining good model predictions. In particular, restricted regression and an apparently—though in fact not—equivalent procedure using constraints are proposed within both fully Bayes and empirical Bayes approaches. The methods are compared in terms of fixed-effect estimates and model selection criteria. The techniques are used to assess the association between dowry deaths and certain socio-demographic covariates in the districts of Uttar Pradesh, India.
Open Access
A two-stage approach to estimate spatial and spatio-temporal disease risks in the presence of local discontinuities and clusters
(SAGE, 2018-04-13) Adin Urtasun, Aritz; Lee, Duncan; Goicoa Mangado, Tomás; Ugarte Martínez, María Dolores; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2
Disease risk maps for areal unit data are often estimated from Poisson mixed models with local spatial smoothing, for example by incorporating random effects with a conditional autoregressive prior distribution. However, one of the limitations is that local discontinuities in the spatial pattern are not usually modelled, leading to over-smoothing of the risk maps and a masking of clusters of hot/coldspot areas. In this paper, we propose a novel two-stage approach to estimate and map disease risk in the presence of such local discontinuities and clusters. We propose approaches in both spatial and spatio-temporal domains, where for the latter the clusters can either be fixed or allowed to vary over time. In the first stage, we apply an agglomerative hierarchical clustering algorithm to training data to provide sets of potential clusters, and in the second stage, a two-level spatial or spatio-temporal model is applied to each potential cluster configuration. The superiority of the proposed approach with regard to a previous proposal is shown by simulation, and the methodology is applied to two important public health problems in Spain, namely stomach cancer mortality across Spain and brain cancer incidence in the Navarre and Basque Country regions of Spain.
Open Access
In spatio-temporal disease mapping models, identifiability constraints affect PQL and INLA results
(Springer, 2018) Goicoa Mangado, Tomás; Adin Urtasun, Aritz; Ugarte Martínez, María Dolores; Hodges, James S.; Institute for Advanced Materials and Mathematics - INAMAT2
Disease mapping studies the distribution of relative risks or rates in space and time, and typically relies on generalized linear mixed models (GLMMs) including fixed effects and spatial, temporal, and spatio-temporal random effects. These GLMMs are typically not identifiable and constraints are required to achieve sensible results. However, automatic specification of constraints can sometimes lead to misleading results. In particular, the penalized quasi-likelihood fitting technique automatically centers the random effects even when this is not necessary. In the Bayesian approach, the recently-introduced integrated nested Laplace approximations computing technique can also produce wrong results if constraints are not wellspecified. In this paper the spatial, temporal, and spatiotemporal interaction random effects are reparameterized using the spectral decompositions of their precision matrices to establish the appropriate identifiability constraints. Breast cancer mortality data from Spain is used to illustrate the ideas.
Open Access
Flexible Bayesian P-splines for smoothing age-specific spatio-temporal mortality patterns
(SAGE, 2019) Goicoa Mangado, Tomás; Adin Urtasun, Aritz; Etxeberria Andueza, Jaione; Militino, Ana F.; Ugarte Martínez, María Dolores; Estadística, Informática y Matemáticas; Estatistika, Informatika eta Matematika; Institute for Advanced Materials and Mathematics - INAMAT2
In this paper age-space-time models based on one and two-dimensional P-splines with B-spline bases are proposed for smoothing mortality rates, where both xed relative scale and scale invariant two-dimensional penalties are examined. Model tting and inference are carried out using integrated nested Laplace approximations (INLA), a recent Bayesian technique that speeds up computations compared to McMC methods. The models will be illustrated with Spanish breast cancer mortality data during the period 1985-2010, where a general decline in breast cancer mortality has been observed in Spanish provinces in the last decades. The results reveal that mortality rates for the oldest age groups do not decrease in all provinces.