RELATIVE RISK OF CORONAVIRUS DISEASE (COVID-19) IN SOUTH SULAWESI PROVINCE, INDONESIA: BAYESIAN SPATIAL MODELING

The Covid-19 has exploded in the world since late 2019. South Sulawesi Province has the highest number of Covid-19 cases outside Java Island in Indonesia. This paper aims to determine the most suitable Bayesian spatial conditional autoregressive (CAR) localised models in modeling the relative risk (RR) of Covid-19 in South Sulawesi Province, Indonesia. Bayesian spatial CAR localised models with different hyperpriors were performed adopting a Poisson distribution for the confirmed Covid-19 counts to examine the grouping of Covid-19 cases. All confirmed cases of Covid-19 (19 March 2020-18 February 2021) for each district were included. Overall, Bayesian CAR localised model with G = 5 with a hyperprior IG (1, 0.1) is the preferred model to estimate the RR based on the two criteria used. Makassar and Toraja Utara have the highest and the lowest RR, respectively. The group formed in the localised model is influenced by the magnitude of the mean and variance in the count data between areas. Using suitable Bayesian spatial CAR localised models enables the identification of high-risk areas of Covid-19 cases. This localised model could be applied in other case studies.

Comparison of Bayesian Spatio-temporal Models of Tuberculosis in Makassar, Indonesia

South Sulawesi province ranks sixth-highest in tuberculosis (TB) in Indonesia. Makassar ranks the highest in South Sulawesi. Spatio-temporal modelling can identify the areas with high risk as well as the temporal relative risk of disease. We analysed the tuberculosis cases data from Makassar City Health Office for 15 districts over seven years from 2012 to 2018. Seven models of Bayesian Spatio-temporal (BST) Conditional Autoregressive (CAR) were applied by using the measures of goodness of fit (GOF) namely, DIC and WAIC. The results showed that BST CAR localised model with G = 3 has the lowest DIC and BST CAR adaptive has the lowest WAIC. Based on the preferred model (Bayesian ST CAR localised with G=3), Panakukang district had the highest relative risk of TB in 2012, 2013, and 2014, while Makassar district had the highest relative risk of TB in 2015, 2016, and 2017. Mamajang had the highest relative risk of TB in 2018.

A joint hierarchical model for the number of cases and deaths due to COVID-19 across the boroughs of Montreal

Montreal is the epicentre of the COVID-19 pandemic in Canada with highest number of deaths. The cumulative numbers of cases and deaths in the 33 areas of Montreal are modelled through bivariate hierarchical Bayesian models using Poisson distributions. The Poisson means are decomposed in the log scale as the sums of fixed effects and latent effects. The areal median age, the educational level, and the number of beds in long-term care homes are included in the fixed effects. To explore the correlation between cases and deaths inside and across areas, three bivariate models are considered for the latent effects, namely an independent one, a conditional autoregressive model, and one that allows for both spatially structured and unstructured sources of variability. As the inclusion of spatial effects change some of the fixed effects, we extend the Spatial+ approach to a Bayesian areal set up to investigate the presence of spatial confounding.

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.

Analysis of risk spillover effect of copper option in China

Purpose The purpose of this paper is to compare the changes in the risk spillover effects between the copper spot and futures markets before and after the issuance of copper options, analyze the risk spillover effects between the three markets after the issuance of the options and can provide effective suggestions for regulators and investors who hedge risks. Design/methodology/approach The MV-CAViaR model is an extended form of the vector autoregressive model (VAR) to the quantile model, and it is also a special form of the MVMQ-CAViaR model. Based on the VAR quantile model, this model has undergone continuous promotion of the Conditional Autoregressive Value-at-Risk Model (CAViaR) and the Multi-quantile Conditional Autoregressive Value-at-Risk Model (MQ-CAViaR), and finally got the current form of the model. Findings The issuance of options has led to certain changes in the risk spillover effect between the copper spot and its derivative markets, and the risk aggregation effect in the futures market has always been significant. Therefore, when supervising the copper product market and investors using copper derivatives to avoid market risks, they need to pay attention to the impact of futures on the spot market, the impact of options on the futures market and the risk spillover effects of spot and futures on the options market. Practical implications The empirical results of this paper can be used to hedge market risk investment strategies, and the changes in market relationships also provide an effective basis for the supervision of the copper product market by the supervisory authority. Originality/value It is the first literature research to discuss the risk and the impact of spillover effects of copper options on China copper market and its derivative markets. The MV-CAViaR model can capture the mutual risk influence between markets by modeling multiple markets simultaneously.

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.

Markov modelling of viral load adjusting for CD4 orthogonal variable and multivariate conditional autoregressive mapping of the HIV immunological outcomes among ART patients in Zimbabwe

Background This study aimed to jointly model HIV disease progression patterns based on viral load (VL) among adult ART patients adjusting for the time-varying “incremental transients states” variable, and the CD4 cell counts orthogonal variable in a single 5-stage time-homogenous multistate Markov model. We further jointly mapped the relative risks of HIV disease progression outcomes (detectable VL (VL ≥ 50copies/uL) and immune deterioration (CD4 < 350cells/uL) at the last observed visit) conditional not to have died or become loss to follow-up (LTFU). Methods Secondary data analysis of individual-level patients on ART was performed. Adjusted transition intensities, hazard ratios (HR) and regression coefficients were estimated from the joint multistate model of VL and CD4 cell counts. The mortality and LTFU transition rates defined the extent of patients’ retention in care. Joint mapping of HIV disease progression outcomes after ART initiation was done using the Bayesian intrinsic Multivariate Conditional Autoregressive prior model. Results The viral rebound from the undetectable state was 1.78times more likely compared to viral suppression among patients with VL ranging from 50-1000copies/uL. Patients with CD4 cell counts lower than expected had a higher risk of viral increase above 1000copies/uL and death if their VL was above 1000copies/uL (state 2 to 3 (λ23): HR = 1.83 and (λ34): HR = 1.42 respectively). Regarding the time-varying effects of CD4 cell counts on the VL transition rates, as the VL increased, (λ12 and λ23) the transition rates increased with a decrease in the CD4 cell counts over time. Regardless of the individual’s VL, the transition rates to become LTFU decreased with a decrease in CD4 cell counts. We observed a strong shared geographical pattern of 66% spatial correlation between the relative risks of detectable VL and immune deterioration after ART initiation, mainly in Matabeleland North. Conclusion With high rates of viral rebound, interventions which encourage ART adherence and continual educational support on the barriers to ART uptake are crucial to achieve and sustain viral suppression to undetectable levels. Area-specific interventions which focus on early ART screening through self-testing, behavioural change campaigns and social support strategies should be strengthened in heavily burdened regions to sustain the undetectable VL. Sustaining undetectable VL lowers HIV transmission in the general population and this is a step towards achieving zero HIV incidences by 2030.

Analysis of spatial determinants of poverty in Kelantan

This study examines socio-demographic effects on poverty and measures spatial patterns in poverty risk looking for high risk of areas. The poverty data were counts of the numbers of poverty cases occurring in each 66 districts of Kelantan. A Poisson Log Linear Leroux Conditional Autoregressive model with different neighbourhood matrices was fitted to the data. The results show that the contiguity neighbour was performed nearly similar to Delaunay triangulation neighbourhood matrix in estimate poverty risk. Apart from that, the variables average age, number of non-education of household head and number of female household head significantly associated with the number of poor households head. Kursial was found as the highest risk area of poverty among 66 districts in Kelantan.