Spatial Conditional Autoregressive Models in Stan

Modeling data collected by areal units, such as counties or census tracts, is a core component of population health research and public resource distribution. Bayesian inference has both practical and philosophical advantages over classical statistical techniques, and advances in Markov chain Monte Carlo (MCMC) are expanding the range of research questions to which fully Bayesian inference may be applied. This code snippet introduces code for fitting spatial conditional autoregressive (CAR) models with the Stan modeling language. Stan is an expressive programming language that uses a dynamic Hamiltonian Monte Carlo (HMC) algorithm to draw samples from user-specified probability models. This paper discusses various CAR model specifications and introduces computationally efficient implementations for Stan users. The paper demonstrates use of the code by modeling United States county mortality data, including censored observations.

Exploring a multilevel approach with spatial effects to model housing price in San José, Costa Rica

A multilevel model of the housing market for San José Metropolitan Region (Costa Rica) was developed, including spatial effects. The model is used to explore two main questions: the extent to which contextual (of the surroundings) and compositional (of the property itself) effects explain variation of housing prices and how does the relation between price and key covariates change with the introduction of multilevel effects. Hierarchical relations (lower level units nested into higher level) were modeled by specifying multilevel models with random intercepts and a conditional autoregressive term to include spatial effects from neighboring units at the higher level (districts). The random intercepts and conditional autoregressive models presented the best fit to the data. Variation at the higher level accounted for 16% of variance in the random intercepts model and 28% in the conditional autoregressive model. The sign and magnitude of regression coefficients proved remarkably stable across model specifications. Travel time to the city center, which presented a non-linear relation to price, was found to be the most important determinant. Multilevel and conditional autoregressive models constituted important improvements in modeling housing price, despite most of the variation still occurring at the lower level, by improving the overall model fit. They were capable of representing the regional structure and of reducing sampling bias in the data. However, the conditional autoregressive specification only represented a limited advance over the random intercepts formulation.

Association between environmental and climatic risk factors and the spatial distribution of cystic and alveolar echinococcosis in Kyrgyzstan

Background Cystic and alveolar echinococcosis (CE and AE) are neglected tropical diseases caused by Echinococcus granulosus sensu lato and E. multilocularis, and are emerging zoonoses in Kyrgyzstan. In this country, the spatial distribution of CE and AE surgical incidence in 2014-2016 showed marked heterogeneity across communities, suggesting the presence of ecological determinants underlying CE and AE distributions. Methodology/Principal findings For this reason, in this study we assessed potential associations between community-level confirmed primary CE (no.=2359) or AE (no.=546) cases in 2014-2016 in Kyrgyzstan and environmental and climatic variables derived from satellite-remote sensing datasets using conditional autoregressive models. We also mapped CE and AE relative risk. The number of AE cases was negatively associated with 10-year lag mean annual temperature. No associations were detected for CE. We also identified several communities at risk for CE or AE where no disease cases were reported in the study period. Conclusions/Significance Our findings support the hypothesis that CE is linked to an anthropogenic cycle and is less affected by environmental risk factors compared to AE, which is believed to result from spillover from a wild life cycle. As CE was not affected by factors we investigated, hence control should not have a geographical focus. In contrast, AE risk areas identified in this study without reported AE cases should be targeted for active disease surveillance in humans. This active surveillance would confirm or exclude AE transmission which might not be reported with the present passive surveillance system. These areas should also be targeted for ecological investigations in the animal hosts.

Spatiotemporal Heterogeneity in the Distribution of Chikungunya and Zika Virus Case Incidences during their 2014 to 2016 Epidemics in Barranquilla, Colombia

Chikungunya virus (CHIKV) and Zika virus (ZIKV) have recently emerged as globally important infections. This study aimed to explore the spatiotemporal heterogeneity in the occurrence of CHIKV and ZIKV outbreaks throughout the major international seaport city of Barranquilla, Colombia in 2014 and 2016 and the potential for clustering. Incidence data were fitted using multiple Bayesian Poisson models based on multiple explanatory variables as potential risk factors identified from other studies and options for random effects. A best fit model was used to analyse their case incidence risks and identify any risk factors during their epidemics. Neighbourhoods in the northern region were hotspots for both CHIKV and ZIKV outbreaks. Additional hotspots occurred in the southwestern and some eastern/southeastern areas during their outbreaks containing part of, or immediately adjacent to, the major circular city road with its import/export cargo warehouses and harbour area. Multivariate conditional autoregressive models strongly identified higher socioeconomic strata and living in a neighbourhood near a major road as risk factors for ZIKV case incidences. These findings will help to appropriately focus vector control efforts but also challenge the belief that these infections are driven by social vulnerability and merit further study both in Barranquilla and throughout the world’s tropical and subtropical regions.