Hierarchical multivariate directed acyclic graph autoregressive models for spatial diseases mapping

Gao, Leiwen; Datta, Abhirup; Banerjee, Sudipto

doi:10.1002/sim.9404

Cited by 8 publications

(2 citation statements)

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“…Simulation studies covering a wide range of scenarios showed that DAGAR models tend to perform better than CAR models for low or moderate spatial correlation in the data, while the performances of the two classes of models are similar in the presence of strong spatial correlation. The model has subsequently been generalized to include multivariate outcomes (Gao et al, 2020, 2021).…”

Section: New Applicationsmentioning

confidence: 99%

Nearest‐neighbor sparse Cholesky matrices in spatial statistics

Datta

2021

WIREs Computational Stats

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Gaussian process (GP) is a staple in the toolkit of a spatial statistician. Well‐documented computing roadblocks in the analysis of large geospatial datasets using GPs have now largely been mitigated via several recent statistical innovations. Nearest neighbor Gaussian process (NNGP) has emerged as one of the leading candidates for such massive‐scale geospatial analysis owing to their empirical success. This article reviews the connection of NNGP to sparse Cholesky factors of the spatial precision (inverse‐covariance) matrix. Focus of the review is on these sparse Cholesky matrices which are versatile and have recently found many diverse applications beyond the primary usage of NNGP for fast parameter estimation and prediction in the spatial (generalized) linear models. In particular, we discuss applications of sparse NNGP Cholesky matrices to address multifaceted computational issues in spatial bootstrapping, simulation of large‐scale realizations of Gaussian random fields, and extensions to nonparametric mean function estimation of a GP using random forests. We also review a sparse‐Cholesky‐based model for areal (geographically aggregated) data that addresses long‐established interpretability issues of existing areal models. Finally, we highlight some yet‐to‐be‐addressed issues of such sparse Cholesky approximations that warrant further research. This article is categorized under: Algorithms and Computational Methods > Algorithms Algorithms and Computational Methods > Numerical Methods

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Section: New Applicationsmentioning

confidence: 99%

Nearest‐neighbor sparse Cholesky matrices in spatial statistics

Datta

2021

WIREs Computational Stats

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“…As stated by the authors, the Cholesky factor has the same level of sparsity as the undirected graph ensuring scalability for analysing very large areal datasets. An extension to deal with multivariate spatial disease mapping models has been developed by Gao et al (2022). This new methodology provides reliable risk estimates with a substantial reduction in A scalable spatial modelling approach for high-dimensional areal data computational time.…”

Section: Introductionmentioning

confidence: 99%

Exploring disease mapping models in big data contexts: some new proposals

Orozco Acosta

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Disease mapping is a highly relevant and significant research area within the field of spatial statistics (areal data), as it offers invaluable support for public health decision-making. Due to the high variability of classical risk estimators, such as the standardized mortality ratio (SMR), the use of statistical models becomes essential to obtain a more consistent representation of the underlying disease risk. During the last decades, several statistical models have been proposed in the disease mapping literature for smoothing risks in space and time, most of them extending the seminal work of Besag et al. (1991) based on conditional autoregressive (CAR) priors. However, the scalability of these models, specifically their utility in scenarios where the number of small areas increases significantly, has not been extensively studied. Thus, the main purpose of this dissertation is to propose new scalable Bayesian modelling methods to smooth incidence/mortality risks (or rates) in high-dimensional spatial and spatio-temporal areal data based on the “divide-and-conquer” approach. The current dissertation is developed with the following main objectives. The first objective is to review the literature about the main contributions of spatial and spatio-temporal disease mapping that are relevant to the research goals. Chapter 1 provides a general overview of model fitting and inference focusing on the widely used integrated nested Laplace approximation (INLA) technique for latent Gaussian models within the Bayesian paradigm (Rue et al., 2009). The chapter also covers the description of how to compute approximations of model selection criteria based on the deviance and the predictive distribution under our scalable model proposals. A brief description of the R package bigDM is also included, which implements all the algorithms and models proposed in this dissertation. The second objective of this dissertation is to propose a scalable Bayesian modelling method for handling high-dimensional spatial count data. In Chapter 2, we provide a comprehensive description of our novel risk smoothing method. We also conduct a multi-scenario simulation study involving nearly 8000 Spanish municipalities to compare our proposed method with the well-known CAR models in terms of goodness of fit and risk estimation accuracy. Additionally, we illustrate the behaviour of the scalable models by analysing male colorectal cancer mortality data from Spanish municipalities using two different partition strategies of the spatial domain. The third objective is to extend our scalable Bayesian modelling approach for smoothing mortality or incidence risks to analyze high-dimensional spatio-temporal count data. In Chapter 3, we present a comprehensive description of the spatiotemporal CAR models originally proposed by Knorr-Held (2000), which are the basis of our new modelling proposal for analyzing spatio-temporal areal data. The chapter also explains the parallel and distributed strategies implemented in the bigDM package to speed up computations by using the R package future (Bengtsson, 2021). A simulation study is conducted to compare our new scalable proposal with two different merging strategies against traditional spatio-temporal CAR models using the map of the Spanish municipalities as a template. Additionally, we evaluate our proposal in terms of computational time. Finally, we illustrate and compare all the approaches described in this chapter by analyzing the spatio-temporal evolution for male lung cancer mortality data in Spanish continental municipalities during the period 1991-2015. The fourth objective is to assess the suitability of the method developed in Chapter 3 for short-term forecasting in high spatial resolution data. In Chapter 4, we present the spatio-temporal CAR model, which incorporates missing observations in the response variable for the time periods to be forecasted. Additionally, a validation study is conducted to assess the predictive ability of the models for one, two and three periods ahead forecasting using real lung cancer mortality data in Spanish municipalities. In this chapter, we also compare the predictive performance of the models using scoring rules based on leave-one-out and leave-group-out cross-validation strategies (Liu and Rue, 2022). The fifth objective is transversal to all chapters. The aim was to develop an open-source R language package named bigDM (Adin et al., 2023b) that consolidates all the methods proposed in this dissertation making them readily available for use by the scientific community. The dissertation ends with the main conclusions and future research lines.

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