EVALUASI MODEL-MODEL BAYESIAN SPASIAL CONDITIONAL AUTOREGRESSIVE UNTUK PEMODELAN KASUS KEMATIAN CORONA VIRUS DISEASE (COVID-19) DI INDONESIA

Abstract

Covid-19 cases in Indonesia occurred for the first time on 2 March 2020. By 30 September 2022, Indonesia had 158,173 Covid-19 deaths. Several studies have been done in modelling Covid-19 cases. However, research in modelling the number of Covid-19 deaths using the Bayesian Spatial Conditional Autoregressive (CAR) model is still rare. The Bayesian spatial CAR model has high flexibility in relative risk (RR) modeling. CAR models can include various types of spatial effects and can include covariates in the model. RR represents the ratio of the risk of outcome (Covid-19) in the exposed group compared to the population average (the unexposed group). This study aims to evaluate the BYM, Leroux, and Localised models with five hyperpriors, to obtain the best model for estimating the RR of Covid-19 deaths in Indonesia and to create RR maps. This study used aggregate data on Covid-19 deaths (2 March 2020 - 30 September 2022). Data on the total population and population density of each province in 2021 were also used. The best model selection is based on the lowest Watanabe Akaike Information Criterion (WAIC) and Deviance Information Criterion (DIC) values, and Modified Moran's I (MMI) residual values. The result showed that the CAR BYM model with covariates and with Inverse-Gamma IG(0.5; 0.0005) prior distribution had the lowest DIC and WAIC. As the BYM model does not converge, the model cannot be used in determining the RR of Covid-19 deaths in Indonesia. From the other three models that converge, the Bayesian CAR Leroux model without covariate with IG(0,5;0,0005) has the lowest DIC(393,76), and WAIC(400,12), and its MMI value (-0,26) is approximate to zero. Therefore, the Bayesian CAR Leroux model without covariate with IG(0,5;0,0005) is preferred. The province with the highest RR (2,76) and the lowest RR (0,22) are Yogyakarta and Papua, respectively.