EVALUASI MODEL-MODEL BAYESIAN SPASIAL CONDITIONAL AUTOREGRESSIVE UNTUK PEMODELAN KASUS KEMATIAN CORONA VIRUS DISEASE (COVID-19) DI INDONESIA
Keywords: conditional autoregressive (CAR), covid-19 death, bayesian method, relative risk, spatial
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.
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References
Aprianti, W., & Maliha U. (2016). Sistem Informasi Kepadatan Penduduk atau Desa Studi kasus pada Kecamatan Bati-Bati.2(2013), 21–28.
Aswi, A., Cramb, S., Duncan, E., & Mengersen, K. (2020). Evaluating the impact of a small number of areas on spatial estimation. International Journal of Health Geographics, 19(1), 1–14. https://doi.org/10.1186/s12942-020-00233-1
Aswi, A., Cramb, S., Duncan, E., & Mengersen, K. (2021). Detecting Spatial Autocorrelation for a Small Number of Areas: A practical example. Journal of Physics: Conference Series, 1899(1). https://doi.org/10.1088/1742-6596/1899/1/012098
Aswi, A., Tiro, M. A., Sudarmin, S., Sukarna, S., & Cramb, S. (2022). the Interplay Between Clusters, Covariates, and Spatial Priors in Spatial Modelling of Covid-19 in South Sulawesi Province, Indonesia. Media Statistika, 15(1), 48–59. https://doi.org/10.14710/medstat.15.1.48-59
Badan Pusat Statistik. (2022). Jumlah Penduduk Setiap Provinsi Di Indonesia.
Besag, J., York, J., & Mollié, A. (1991). Bayesian image restoration, with two applications in spatial statistics. Annals of The Institute of Statistical Mathematics, 43(1), 1-20.
BPMI Setpres. (2020). Pemerintah Tetapkan Status Kedaruratan Kesehatan Masyarakat. https://www.presidenri.go.id/siaran-pers/pemerintah-tetapkan-status-kedaruratan-kesehatan-masyarakat/.
Carrijo, T. B., & Da Silva, A. R. (2017). Modified Moran’s I for Small Samples. Geographical Analysis, 49(4), 451-467. doi:10.1111/gean.12130.
Kemenkes RI. (2022). Situasi Covid-19 Di Indonesia (per tanggal 12 April 2022).
Khaerati, R., Thamrin, S. A., & Jaya, A. K. (2020). Bayesian Conditional Autoregressive (CAR) dengan Model Localised dalam Menaksir Risiko Relatif DBD di Kota Makassar. ESTIMASI: Journal of Statistics and Its Application, 1(1), 21. https://doi.org/10.20956/ejsa.v1i1.9298
Lee, D., & Sarran, C. (2015). Controlling for unmeasured confounding and spatial misalignment in long‐term air pollution and health studies. Environmetrics, 26(7), 477-487.
Leroux, B. G., Lei, X., & Breslow, N. (2000). Estimation of Disease Rates in Small Areas: A new Mixed Model for Spatial Dependence. Statistical models in epidemiology, the environment, and clinical trials, 116, 179-191. doi:10.1007/978-1-4612-1284-3_4.
Lutfi, A., Aidid, M. K., & Sudarmin, S. (2019). Identifikasi Autokorelasi Spasial Angka Partisipasi Sekolah di Provinsi Sulawesi Selatan Menggunakan Indeks Moran. Journal of Statistics and Its application on Teaching and Research, 1(2), 1–8. https://doi.org/10.35580/variansi.v1i2.9354.
M. Gayo, U. C., Rusdi, M., Fazlina, D., Studi, P., Sumber, P., Lahan, D., Pertania, F., & Kuala, U. S. (2018). Distribusi Spasial Lahan Kopi Eksisting Berdasarkan Ketinggian dan Arahan Fungsi Kawasan di Kabupaten Aceh Tengah Spatial Distribution of Existing Coffee Land Based on Altitude and Direction of Function Area in Central Aceh Regency * corresponding author. Jurnal Ilmiah Mahasiswa Pertanian Unsyiah, 3(4), 1–7.
Simatauw, A., Sediyono, E., & Prasetyo, S. Y. J. (2019). Autokorelasi Spasial Untuk Analisis Pola Pengawasan Kawasan Lindung Di Kota Ambon Maluku. Teknika, 8(1), 36–43. https://doi.org/10.34148/teknika.v8i1.144.
Spiegelhalter, D. J., Best, N. G., Carlin, B. P., & Van Der Linde, A. (2002). Bayesian measures of model complexity and fit. Journal of the Royal Statistical Society. Series B, Statistical methodology, 64(4), 583-639. doi:10.1111/1467-9868.00353.
Sunengsih, N., Nyoman, I. G., Jaya, M., & Tantular, B. (2016). Bayesian Conditional Autoregressive (CAR) Dalam Menaksir Resiko Relative Diare di Kota Bandung. 21–26.
Susilo, A., Rumende, C. M., Pitoyo, C. W., Santoso, W. D., Yulianti, M., Herikurniawan, H., Sinto, R., Singh, G., Nainggolan, L., Nelwan, E. J., Chen, L. K., Widhani, A., Wijaya, E., Wicaksana, B., Maksum, M., Annisa, F., Jasirwan, C. O. M., & Yunihastuti, E. (2020). Coronavirus Disease 2019: Tinjauan Literatur Terkini. Jurnal Penyakit Dalam Indonesia, 7(1), 45. https://doi.org/10.7454/jpdi.v7i1.415.
Tiro, M. A., Aswi, A., & Rais, Z. (2021a). Association of Population Density and Distance to the City with the Risks of COVID-19: A Bayesian Spatial Analysis. Journal of Physics: Conference Series, 2123(1). https://doi.org/10.1088/1742-6596/2123/1/012001
Tiro, M. A., Aswi, A., & Rais, Z. (2021b). Perbandingan Model Bayesian Spasial Conditional Autoregressive (CAR): Kasus Covid-19 di Kota Makassar, Indonesia. Seminar Nasional LP2M UNM, 2019, 1026–1034.
Whittle, R. S., & Diaz-Artiles, A. (2020). An ecological study of socioeconomic predictors in detection of COVID-19 cases across neighborhoods in New York City. BMC Medicine, 18(1), 1–17. https://doi.org/10.1186/s12916-020-01731-6.
Yu, X., Wong, M. S., Kwan, M. P., Nichol, J. E., Zhu, R., Heo, J., Chan, P. W., Chin, D. C. W., Yin, C., Kwok, T., & Kan, Z. (2021). COVID-19 Infection and Mortality : Association with PM 2 . 5 Concentration and Population Density — An Exploratory Study.
Yuriantari, N. P., Hayati, M. N., & Wahyuningsih, S. (2017). Analisis Autokorelasi Spasialtitik Panas Di Kalimantan Timur Menggunakan Indeks Moran dan Local Indicator Of Spatial Autocorrelation (LISA) Analysis Spatial Autocorrelation Hotspot in East Kalimantan Using Index Moran and Local Indicator of Spatial Autoco. Eksponensial, 8(1), 63–70.
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