Dengue fever (DF) is one of the world's most disabling mosquito-borne diseases, with a variety of approaches available to model its spatial and temporal dynamics. This paper aims to identify and compare the different spatial and spatio-temporal Bayesian modelling methods that have been applied to DF and examine influential covariates that have been reportedly associated with the risk of DF. A systematic search was performed in December 2017, using Web of Science, Scopus, ScienceDirect, PubMed, ProQuest and Medline (via Ebscohost) electronic databases. The search was restricted to refereed journal articles published in English from January 2000 to November 2017. Thirty-one articles met the inclusion criteria. Using a modified quality assessment tool, the median quality score across studies was 14/16. The most popular Bayesian statistical approach to dengue modelling was a generalised linear mixed model with spatial random effects described by a conditional autoregressive prior. A limited number of studies included spatio-temporal random effects. Temperature and precipitation were shown to often influence the risk of dengue. Developing spatio-temporal random-effect models, considering other priors, using a dataset that covers an extended time period, and investigating other covariates would help to better understand and control DF transmission.

Spatial models are becoming more popular in time-to-event data analysis. Commonly, the intrinsic conditional autoregressive prior is placed on an area level frailty term to allow for correlation between areas. We considered a range of Bayesian Weibull and Cox semiparametric spatial models to describe a dataset on hospitalisation of dengue. This paper aimed to extend these two models, to evaluate the suitability of these models for estimation and prediction of the length of stay, compare different spatial priors, and determine factors that significantly affect the duration of hospital stay for dengue fever patients in the case study location, namely Wahidin hospital in Makassar, Indonesia. We compared two different models with three different spatial priors with respect to goodness of fit and generalisability. For all models considered, the Leroux prior was preferred over the intrinsic conditional autoregressive and independent priors, but Cox and Weibull versions had similar predictive performance, model fit, and results. Age and platelet count were negatively associated with the length of stay, while red blood cell count was positively associated with the length of stay of dengue patients at this hospital. Using appropriate Bayesian spatial survival models enables identification of factors that substantively affect the length of stay.

Background There is an expanding literature on different representations of spatial random effects for different types of spatial correlation structure within the conditional autoregressive class of priors for Bayesian spatial models. However, little is known about the impact of these different priors when the number of areas is small. This paper aimed to investigate this problem both in the context of a case study of spatial analysis of dengue fever and more generally through a simulation study. Methods Both the simulation study and the case study considered count data aggregated to a small area level in a region. Five different conditional autoregressive priors for a simple Bayesian Poisson model were considered: independent, Besag-York-Mollié, Leroux, and two variants of a localised clustering model. Data were simulated with eight different sizes of areal grids, ranging from 4 to 2500 areas, and two different levels of both spatial autocorrelation and disease counts. Model goodness-of-fit measures and model estimates were compared. A case study involving dengue fever cases in 14 local areas in Makassar, Indonesia, was also considered. Results The simulation study showed that model performance varied under different scenarios. When areas had low autocorrelation and high counts, and the number of areas was at most 25, the BYM, Leroux and localised $$G = 2$$ G = 2 models performed similarly and better than the independent and localised $$G = 3$$ G = 3 models. However, when the number of areas were at least 100, all models performed differently, and the Leroux model performed the best. Overall, the Leroux model performed the best for every scenario especially when there were at least 16 areas. Based on the case study, the comparative performance of spatial models may also vary for a small number of areas, especially when the data have a relatively large mean and variance over areas. In this case, the localised model with G = 3 was a better choice. Conclusion Detecting spatial patterns can be difficult when there are very few areas. Understanding the characteristics of the data and the relative influence of alternative conditional autoregressive priors is essential in selecting an appropriate Bayesian spatial model.

A range of Bayesian models have been used to describe spatial and temporal patterns of disease in areal unit data. In this study, we applied two Bayesian spatio-temporal conditional autoregressive (ST CAR) models, one of which allows discontinuities in risk between neighbouring areas (creating 'groups'), to examine dengue fever patterns. Data on annual (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017) and monthly (January 2013 -December 2017) dengue cases and climatic factors over 14 geographic areas were obtained for Makassar, Indonesia. Combinations of covariates and model formulations were compared considering credible intervals, overall goodness of fit, and the grouping structure. For annual data, an ST CAR localised model incorporating average humidity provided the best fit, while for monthly data, a single-group ST CAR autoregressive model incorporating rainfall and average humidity was preferred. Using appropriate Bayesian spatio-temporal models enables identification of different groups of areas and the impact of climatic covariates which may help inform policy decisions.

Moran’s I is commonly used to detect spatial autocorrelation in spatial data. However, Moran’s I may lead to underestimating spatial dependence when used for a small number of areas. This led to the development of Modified Moran’s I, which is designed to work when there are few areas. In this paper, both methods will be presented. Many R programs enable calculating Moran’s I, but to date, none have been available for calculating Modified Moran’s I. This paper aims to present both methods and provide the R code for calculating Modified Moran’s I, with an application to a case study of dengue fever across 14 regions in Makassar, Indonesia.

The transmission of Coronavirus diseases 2019 (Covid-19) grows continuously around the world. Although a number of researches of modelling Covid-19 cases have been conducted, there was limited research implementing the Bayesian Spatial Conditional Autoregressive (CAR) model. Factors affecting the Covid-19 risk especially population density and distance to the capital city have been studied, but the results are inconsistent and limited research has been done in Indonesia. This study aims to assess the most appropriate Bayesian spatial CAR Leroux models and examine factors that affect the risk of Covid-19 in South Sulawesi Province. Data on the number of Covid-19 cases (19 March 2020 -31 January 2022), population density, and distance to the capital city were used for every 24 districts. Several criteria were used in choosing the most appropriate model. The results depict that Bayesian spatial CAR Leroux with hyperprior IG (1, 0.01) model with the inclusion of population density were preferred. It is concluded that a factor that significantly affects the number of Covid-19 cases is population density. There was a positive correlation between the population density and Covid-19 risk. Makassar city has the highest relative risk (RR) among other districts while Bone has the lowest RR of Covid-19.

No abstract

Considering only the spatial component of diseases can identify areas with reduced or elevated risk, but not capture anything about temporal variation of risk which could be more or equally crucial. Hence, both spatial and temporal components of diseases need to be considered. Bayesian methods are useful due to the ease of specifying additional information, including temporal or spatial structure, through prior distributions. Here, we examine a range of different Bayesian spatio-temporal models available using CARBayes. Combinations of model formulations and climatic covariates were compared using goodness-of-fit measures, such as Watanabe Akaike Information Criterion (WAIC). Comparisons were made in the context of a substantive case study, namely monthly dengue fever incidence from January 2013 to December 2017 and climatic covariates in 14 geographic areas of Makassar, Indonesia. A spatio-temporal conditional autoregressive adaptive model combining rainfall and average humidity provided the most suitable model.