On fitting spatio-temporal disease mapping models using approximate Bayesian inference

Abstract

Spatio-temporal disease mapping comprises a wide range of models used to describe the distribution of a disease in space and its evolution in time. These models have been commonly formulated within a hierarchical Bayesian framework with two main approaches: an empirical Bayes (EB) and a fully Bayes (FB) approach. The EB approach provides point estimates of the parameters relying on the well-known penalized quasi-likelihood (PQL) technique. The FB approach provides the posterior distribution of the target parameters. These marginal distributions are not usually available in closed form and common estimation procedures are based on Markov chain Monte Carlo (MCMC) methods. However, the spatio-temporal models used in disease mapping are often very complex and MCMC methods may lead to large Monte Carlo errors and a huge computation time if the dimension of the data at hand is large. To circumvent these potential inconveniences, a new technique called integrated nested Laplace approximations (INLA), based on nested Laplace approximations, has been proposed for Bayesian inference in latent Gaussian models. In this paper, we show how to fit different spatio-temporal models for disease mapping with INLA using the Leroux CAR prior for the spatial component, and we compare it with PQL via a simulation study. The spatio-temporal distribution of male brain cancer mortality in Spain during the period 1986-2010 is also analysed.

Penalising Model Component Complexity: A Principled, Practical Approach to Constructing Priors

“…However, they did not assume a scaled structured spatial effect, which is essential for controlling the influence of the corresponding hyperprior (Sørbye and Rue, 2014). Leroux, Lei and Breslow (2000) proposed a slightly different reparameterisation, which has been widely promoted as an alternative formulation to the standard BYM model, see for example Lee (2011); Ugarte et al (2014). The structured spatial effect is however again not scaled and it is assumed that the precision matrix of the new spatial model component is a weighted average of the precisions of the structured and unstructured spatial components, whereas here as well as in Dean, Ugarte and Militino (2001) this assumption is posed on the variance scale.…”

Spatial modeling with R‐INLA: A review

“…Very recently, the Shiny app SSTCDapp ( http://www.unavarra.es/spatial-statistics-group/shiny-app ) has been introduced, which allows the estimation of different discrete space and space–time models using R‐INLA in a user‐friendly way without R‐code Ugarte et al (); Goicoa et al (); and Adin, Martínez‐Beneito, Botella‐Rocamora, Goicoa, and Ugarte (). The app provides different descriptive statistics and supports several spatial and temporal model components.…”

Bayesian Computing with INLA: A Review

“…Recent examples of applications using the R-INLA package for statistical analysis, include disease mapping (Schrödle and Held, 2011b,a;Ugarte et al, 2014Ugarte et al, , 2016Papoila et al, 2014;Goicoa et al, 2016;, age-period-cohort models (Riebler and Held, 2016), evolution of the Ebola virus (Santermans et al, 2016), studies of relationship between access to housing, health and well-being in cities (Kandt et al, 2016), study of the prevalence and correlates of intimate partner violence against men in Africa (Tsiko, 2015), search for evidence of gene expression heterosis (Niemi et al, 2015), analysis of traffic pollution and hospital admissions in London (Halonen et al, 2016), early transcriptome changes in maize primary root tissues in response to moderate water deficit conditions by RNA-Sequencing (Opitz et al, 2016), performance of inbred and hybrid genotypes in plant breeding and genetics (Lithio and Nettleton, 2015), a study of Norwegian emergency wards (Goth et al, 2014), effects of measurement errors (Kröger et al, 2016;Muff and Keller, 2015), network meta-analysis (Sauter and Held, 2015), time-series analysis of genotyped human campylobacteriosis cases from the Manawatu region of New Zealand (Friedrich et al, 2016), modeling of parrotfish habitats (Roos et al, 2015b), Bayesian outbreak detection (Salmon et al, 2015), studies of long-term trends in the number of Monarch butterflies (Crewe and Mccracken, 2015), long-term effects on hospital admission and mortality of road traffic noise (Halonen et al, 2015), spatio-temporal dynamics of brain tumours (Iulian et al, 2015), ovarian cancer mortality (García-Pérez et al, 2015), the effect of preferential sampling on phylodynamic inference (Karcher et al, 2016), analysis of the impact of climate change on abundance trends in central Europe (Bowler et al, 2015), investigation of drinking patterns in US Counties from 2002 to 2012 …”