Pemetaan Kasus Tuberkulosis di Provinsi Sulawesi Selatan Tahun 2020 Menggunakan Model Bayesian Spasial BYM dan Leroux

A. Aswi(1*), S. Sukarna(2), N. Nurhilaliyah(3),

(1) Program Studi Statistika, Universitas Negeri Makassar
(2) Jurusan Matematika, Universitas Negeri Makassar
(3) Jurusan Fisika, Universitas Negeri Makassar
(*) Corresponding Author



Tuberkulosis (TBC) merupakan penyakit menular yang merupakan salah satu dari sepuluh penyebab utama kematian di dunia. Indonesia merupakan negara yang menempati urutan tertinggi kedua penderita TBC di dunia. Tujuan dari penelitian ini adalah untuk mengidentifikasi area dengan risiko relatif (RR) tinggi TBC maupun rendah dengan menggunakan model Bayesian spasial Conditional Autoregressive (CAR) Besag-York-Molliѐ (BYM) dan Leroux. Data kasus TBC di setiap 24 kabupaten/kota di provinsi Sulawesi Selatan tahun 2020 digunakan. Model terbaik dipilih berdasarkan tiga kriteria yaitu Deviance Information Criteria (DIC) dan Watanabe Akaike Information Criteria (WAIC). Dari hasil analisis, diperoleh bahwa model Bayesian Spasial CAR BYM dan CAR Leroux dengan hyperprior IG (0,5; 0,0005) merupakan model terbaik yang memiliki nilai RR yang sama. Kota Makassar merupakan wilayah dengan nilai RR tertinggi (1,70) yang mengindikasikan bahwa Kota Makassar memiliki risiko TBC 70% lebih tinggi dari rata-rata. Sebaliknya, Kabupaten Toraja memiliki risiko TBC terendah (0,43) yang menunjukkan bahwa Toraja memiliki risiko TBC 43% lebih rendah dari rata-rata.

Kata Kunci: Tuberkulosis, Bayesian, spasial CAR, BYM, Leroux

 Tuberculosis (TB) is an infectious disease that is one of the ten leading causes of death in the world. Indonesia is a country with the second-highest number of TB sufferers in the world. This study aims to identify areas with a high and low relative risk (RR) of TB by using the Bayesian Spatial Conditional Autoregressive (CAR) Besag-York-Molliѐ (BYM) and Leroux models. TB case data in every 24 districts/cities in South Sulawesi province in 2020 is used. The best model was selected based on three criteria, namely Deviance Information Criteria (DIC) and Watanabe Akaike Information Criteria (WAIC). The results show that the Bayesian Spatial CAR BYM and CAR Leroux with hyperprior IG (0.5; 0.0005) are the best models that have the same RR value. Makassar City is the area with the highest RR value (1.70) which indicates that Makassar City has a TB risk 70% higher than the average. On the other hand, the Toraja district has the lowest TB risk (0.43) which indicates that Toraja has a TB risk 43% lower than the average.

Full Text:



Aswi, Zaki, A., & Hijrayanti. (2015). Spatial Analysis of the Spread of Tuberculosis Using Local Indicator of Spatial Association (LISA) in Makassar, Indonesia. Paper presented at the International Conference on Statistics, Mathematics, Teaching, and Research, Makassar.

Aswi, A., Cramb, S., Duncan, E., Hu, W., White, G., & Mengersen, K. (2020). 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, 17(3). doi:10.3390/ijerph17030878

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), 39-39. doi: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), 12098. doi:10.1088/1742- 6596/1899/1/012098

Badan Pusat Statistik. (2021). Sulawesi Selatan in Figures 2021. Makassar: Badan Pusat Statistik.

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

Dinkes, P. S. S. (2021). Profil Dinas Kesehatan Provinsi Sulawesi Selatan Tahun 2020.


Duncan, E. W., & Mengersen, K. L. (2020). Comparing Bayesian spatial models: Goodness-of-smoothing criteria for assessing under- and over-smoothing. PLoS ONE, 15(5), e0233019-e0233019. doi:10.1371/journal.pone.0233019

Florian, G., & Reinhard, F. (2015). Pitfalls in the Implementation of Bayesian Hierarchical Modeling of Areal Count Data: An Illustration Using BYM and Leroux Models. Journal of Statistical Software, 63(1), 1-32. doi:10.18637/jss.v063.c01

Ge, E., Zhang, X., Wang, X., & Wei, X. (2016). Spatial and temporal analysis of tuberculosis in Zhejiang Province, China, 2009-2012. Infectious Diseases of Poverty, 5(11), 11-11. doi:10.1186/s40249-016-0104-2

Gwitira, I., Karumazondo, N., Shekede, M. D., Sandy, C., Siziba, N., & Chirenda, J. (2021). Spatial patterns of pulmonary tuberculosis (TB) cases in Zimbabwe from 2015 to 2018. PLoS ONE, 16(4), e0249523-e0249523.


Iddrisu, A.-K., & Amoako, Y. A. (2016). Spatial Modeling and Mapping of Tuberculosis Using Bayesian Hierarchical Approaches. Open Journal of Statistics, 6, 418-513. doi:

Kemenkes. (2021). Profil Kesehatan Indonesia Tahun 2020. Jakarta.

Lee, D. (2013). CARBayes: an R package for Bayesian spatial modeling with conditional autoregressive priors. Journal of Statistical Software, 55(13), 1-24.

Moran, P. A. P. (1950). Notes on continuous stochastic phenomena. Biometrika, 37(1-2), 17. doi:10.1093/biomet/37.1-2.17

Oliveira, O., Ribeiro, A. I., Krainski, E. T., Rito, T., Duarte, R., & Correia-Neves, M. (2020). Using Bayesian spatial models to map and to identify geographical hotspots of multidrug-resistant tuberculosis in Portugal between 2000 and 2016. Scientific reports, 10(1), 16646-16646. doi:10.1038/s41598-020-73759-w

R Core Team. (2019). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from http://www.R-

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

Waller, L. A., & Gotway, C. A. (2004). Applied spatial statistics for public health data

Hoboken, N.J: John Wiley & Sons.

Watanabe, S. (2010). Asymptotic Equivalence of Bayes Cross Validation and Widely Applicable Information Criterion in Singular Learning Theory. Journal of Machine Learning Research, 11, 3571-3594.

Article Metrics

Abstract view : 165 times | PDF view : 24 times


  • There are currently no refbacks.

Copyright (c) 2022 JMathCos (Journal of Mathematics, Computations, and Statistics)

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Indexed by:


Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.