High-dimensional order-free multivariate spatial disease mapping

• Published in: Statistics and computing Vol. 33; no. 5
• Main Authors: Vicente, Gonzalo, Adin, Aritz, Goicoa, Tomás, Ugarte, María Dolores
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.10.2023; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Computer Science; Mapping; Mortality; Multivariate analysis; Original Paper; Probability and Statistics in Computer Science; Spatial data; Statistical inference; Statistical Theory and Methods; Statistics and Computing/Statistics Programs; High-dimensional data; Scalable models; Spatial epidemiology; Bayesian inference
• ISSN: 0960-3174; 1573-1375
• DOI: 10.1007/s11222-023-10263-x

Despite the amount of research on disease mapping in recent years, the use of multivariate models for areal spatial data remains limited due to difficulties in implementation and computational burden. These problems are exacerbated when the number of areas is very large. In this paper, we introduce an order-free multivariate scalable Bayesian modelling approach to smooth mortality (or incidence) risks of several diseases simultaneously. The proposal partitions the spatial domain into smaller subregions, fits multivariate models in each subdivision and obtains the posterior distribution of the relative risks across the entire spatial domain. The approach also provides posterior correlations among the spatial patterns of the diseases in each partition that are combined through a consensus Monte Carlo algorithm to obtain correlations for the whole study region. We implement the proposal using integrated nested Laplace approximations (INLA) in the R package bigDM and use it to jointly analyse colorectal, lung, and stomach cancer mortality data in Spanish municipalities. The new proposal allows for the analysis of large datasets and yields superior results compared to fitting a single multivariate model. Additionally, it facilitates statistical inference through local homogeneous models, which may be more appropriate than a global homogeneous model when dealing with a large number of areas.