PEMODELAN BAYESIAN SPASIAL CONDITIONAL AUTOREGRESSIVE (CAR) PADA KASUS DEMAM BERDARAH DENGUE DI INDONESIA
Abstract
Demam Berdarah Dengue (DBD) merupakan salah satu penyakit menular yang masih merupakan masalah utama dalam kesehatan masyarakat di Indonesia. Total kasus DBD di Indonesia pada tahun 2020 masih cukup tinggi yaitu 108.303 kasus. Beberapa penelitian terkait pemodelan DBD telah menggunakan metode Bayesian spasial. Akan tetapi, penelitian tersebut masih fokus pada salah satu provinsi yang ada di Indonesia. Penelitian ini bertujuan untuk memodelkan risiko relatif (RR) kasus DBD tahun 2020 di Indonesia dengan 34 provinsi dan menghasilkan peta tematik RR. Data yang digunakan data kasus DBD serta data jumlah penduduk di Indonesia tahun 2020 yang diperoleh dari Publikasi Kementerian Kesehatan Republik Indonesia 2021. Model Bayesian spasial Conditional Autoregressive (CAR) Leroux digunakan dengan pemilihan model terbaik didasarkan pada Deviance Information Criteria (DIC), Watanabe Akaike Information Criteria (WAIC), dan Modifikasi Moran’s I (MMI) untuk residual. Hasil yang diperoleh menunjukkan bahwa model Bayesian spasial CAR Leroux dengan hyperprior IG(1; 0,1) merupakan model terbaik dalam pemodelan kasus DBD tahun 2020 di Indonesia. Sekitar 53% provinsi yang ada di Indonesia merupakan wilayah dengan RR tinggi, dimana Provinsi Bali memiliki nilai RR tertinggi (6,84), diikuti oleh Provinsi Nusa Tenggara Timur (RR=2,70), dan Daerah Istimewa Yogyakarta (RR=2,33). Sebaliknya, provinsi dengan RR terendah adalah Provinsi Maluku (RR=0,11), diikuti oleh Provinsi Papua (RR = 0,13), dan Provinsi Kalimantan Barat (RR =0,38).
References
[2] M. Jaya and H. Folmer, "Bayesian spatiotemporal mapping of relative dengue disease risk in Bandung, Indonesia," Journal of geographical systems, vol. 22, no. 1, pp. 105-142, 2020.
[3] F. Kristiani, Y. Claudia, B. Yong, and A.-M. Hilsdon, "A comparative analysis of frequentist and Bayesian approaches to estimate dengue disease transmission in Bandung-Indonesia," Journal of statistics & management systems, vol. 23, no. 8, pp. 1543-1559, 2020.
[4] D. Rantini, N. Iriawan, and Irhamah, "Bayesian Mixture Generalized Extreme Value Regression with Double-Exponential CAR Frailty for Dengue Haemorrhagic Fever in Pamekasan, East Java, Indonesia," Journal of physics. Conference series, vol. 1752, no. 1, p. 12022, 2021.
[5] A. Aswi, S. Cramb, E. Duncan, W. Hu, G. White, and K. Mengersen, "Bayesian spatial survival models for hospitalisation of Dengue: A case study of Wahidin hospital in Makassar, Indonesia," International Journal of Environmental Research and Public Health, vol. 17, no. 3, 2020.
[6] S. A. Thamrin, Aswi, Ansariadi, A. K. Jaya, and K. Mengersen, "Bayesian spatial survival modelling for dengue fever in Makassar, Indonesia," Gaceta sanitaria, vol. 35, pp. S59-S63, 2021.
[7] R. Khaerati, S. A. Thamrin, and A. K. Jaya, "Bayesian Conditional Autoregressive (CAR) dengan model localised dalam menaksir risiko DBD di Kota Makassar," Estimasi, vol. 1, no. 1, pp. 21-31, 2020.
[8] A. Aswi, S. Cramb, W. Hu, G. White, and K. Mengersen, "Spatio-temporal analysis of dengue fever in Makassar Indonesia: A comparison of models based on CARBayes," in In Case Studies in Applied Bayesian Data Science, vol. 2259, K. Mengersen, P. Pudlo, and C. Robert, Eds. Switzerland: Springer, 2020, pp. 229-244.
[9] A. Aswi, S. Cramb, E. Duncan, and K. Mengersen, "Evaluating the impact of a small number of areas on spatial estimation," International journal of health geographics, vol. 19, no. 1, pp. 39-39, 2020.
[10] A. Aswi, S. Cramb, E. Duncan, and K. Mengersen, "Climate variability and dengue fever in Makassar, Indonesia: Bayesian spatio-temporal modelling," Spatial and spatio-temporal epidemiology, vol. 33, p. 100335, 2020.
[11] A. Aswi, Sukarna, S. Cramb, and K. Mengersen, "Effects of Climatic Factors on Dengue Incidence: A Comparison of Bayesian Spatio-Temporal Models," Journal of Physics: Conference Series, vol. 1863, p. 12050, 2021 2020.
[12] W. Winardi et al., Statistik Indonesia 2021. Jakarta: Badan Pusat Statistik Indonesia, 2021, p. 758.
[13] B. G. Leroux, X. Lei, and N. Breslow, "Estimation of Disease Rates in Small Areas: A new Mixed Model for Spatial Dependence," Statistical Models in Epidemiology, the Environment, and Clinical Trials, vol. 116, pp. 179-191, 2000.
[14] D. Lee, "CARBayes: an R package for Bayesian spatial modeling with conditional autoregressive priors," Journal of Statistical Software, vol. 55, no. 13, pp. 1-24, 2013.
[15] R Core Team, "R: A language and environment for statistical computing," ed. Vienna, Austria: R Foundation for Statistical Computing, 2019.
[16] D. J. Spiegelhalter, N. G. Best, B. P. Carlin, and A. Van Der Linde, "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society. Series B, Statistical methodology, vol. 64, no. 4, pp. 583-639, 2002.
[17] S. Watanabe, "Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory," Journal of Machine Learning Research vol. 11, pp. 3571-3594, 2010.
[18] T. B. Carrijo and A. R. Da Silva, "Modified Moran's I for Small Samples," Geographical Analysis, vol. 49, no. 4, pp. 451-467, 2017.
[19] A. Aswi, S. Cramb, E. Duncan, and K. Mengersen, "Detecting Spatial Autocorrelation for a Small Number of Areas: a practical example," Journal of physics. Conference series, vol. 1899, no. 1, p. 12098, 2021.
Copyright (c) 2022 Jurnal MSA ( Matematika dan Statistika serta Aplikasinya )
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
