Exploring disease mapping models in big data contexts: some new proposals
Authors:   , Orozco Acosta Erick 
Published: September 2023

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.