POISSON REGRESSION MODELS TO ANALYZE FACTORS THAT INFLUENCE THE NUMBER OF TUBERCULOSIS CASES IN JAVA

• Zalfa Alifah Budiawan Statistics Study Program, Faculty of Mathematics and Natural Sciences, University of Indonesia, Indonesia
• Yekti Widyaningsih Statistics Study Program, Faculty of Mathematics and Natural Sciences, University of Indonesia, Indonesia http://orcid.org/0000-0002-1309-6916
Keywords: Generalized Poisson Regression, Geographically weighted negative binomial regression, Geographically weighted generalized poisson regression, Negative binomial regression

Abstract

Tuberculosis is an infectious disease and one of the world's top 10 highest causes of mortality in Indonesia. Based on this fact, it is necessary to study what factors affect number of tuberculosis cases. The number of tuberculosis cases as dependent variable is a count data that generally analyzed using Poisson regression. However, equidispersion assumption must be met, so Generalized Poisson Regression and Negative Binomial Regression are applied if the assumption is not met. Spatial aspects can be considered so Geographically Weighted Generalized Poisson Regression and Geographically Weighted Negative Binomial Regression were also conducted. Four models were built to evaluate relationship between number of tuberculosis cases and factors affecting it in Java in 2020. The explanatory variables are population density, percentage of children receiving BCG immunization, percentage of poor people, percentage of eligible drinking water facilities, percentage of family cards with access to proper sanitation, percentage of public places meet health requirements, and percentage of food management places meet hygienic requirements. This study shows that the best model for modeling the data is GWNBR with 2 groups of significant explanatory variables. Seven explanatory variables are statistically significant in 88 districts and six explanatory variables statistically significant in 12 districts.

References

Kemenkes RI, “InfoDATIN Tuberkulosis 2018,” Pusat Data dan Informasi Kementerian Kesehatan RI, Jakarta, 2018. [Online]. Available: https://pusdatin.kemkes.go.id/article/view/18101500001/infodatin-tuberkulosis-2018.html

Kompaspedia, “Sebaran Kasus Tuberkulosis di Indonesia,” 2021. https://kompaspedia.kompas.id/baca/infografik/peta-tematik/sebaran-kasus-tuberkulosis-di-indonesia

B. Irawati, “Perbandingan Analisis Generalized Poisson Regression (GPR) dan Regresi Binomial Negatif untuk Mengatasi Overdispersi Studi Kasus: Pemodelan Jumlah Kasus Kanker Serviks di Jawa Timur,” Jurnal Matematika, vol. 2, no. 2, pp. 13–24, 2012.

E. U. L. Fitri, “Pemodelan Faktor-Faktor yang Mempengaruhi Jumlah Kasus Tuberkulosis di Jawa Timur Menggunakan Metode Geographically Weighted Generalized Poisson Regression dan Geographically Weighted Negative Binomial Regression,” Institut Teknologi Sepuluh Nopember, Surabaya, 2017.

S. Indahwati and M. Salamah, “Analisis Faktor-Faktor yang Memengaruhi Jumlah Kasus Tuberculosis di Surabaya Tahun 2014 Menggunakan Geographically Weighted Negative Binomial Regression,” Jurnal Sains dan Seni ITS, vol. 5, no. 2, 2016.

A. S. N. Zaina, R. S. Pontoh, and B. Tantular, “Pemodelan Dan Pemetaan Penyakit TB Paru di Kota Bandung Menggunakan Geographically Weighted Negative Binomial Regression: Studi Kasus Dinas Kesehatan Kota Bandung,” in E-Prosiding Seminar Nasional Statistika| Departemen Statistika FMIPA Universitas Padjadjaran, 2021, p. 8.

S. Noorcintanami, Y. Widyaningsih, and S. Abdullah, “Geographically weighted models for modelling the prevalence of tuberculosis in Java,” J Phys Conf Ser, vol. 1722, no. 1, p. 012089, Jan. 2021, doi: 10.1088/1742-6596/1722/1/012089.

Dinas Kesehatan Provinsi Jawa Barat, Profil Kesehatan Provinsi Jawa Barat. Bandung, 2020. [Online]. Available: https://diskes.jabarprov.go.id/assets/unduhan/Profil%20Kesehatan%20Jawa%20Barat%20Tahun%202020.pdf

Dinas Kesehatan Provinsi Jawa Tengah, Profil Kesehatan Provinsi Jawa Tengah. Semarang, 2020. [Online]. Available: https://dinkesjatengprov.go.id/v2018/dokumen/Profil2020/mobile/index.html

Dinas Kesehatan Provinsi Jawa Timur, Profil Kesehatan Provinsi Jawa Timur. Surabaya, 2020. [Online]. Available: https://dinkes.jatimprov.go.id/userfile/dokumen/PROFIL%20KESEHATAN%202020.pdf

BPS Provinsi Jawa Barat, “Persentase Penduduk Miskin (Persen), 2019-2021,” Badan Pusat Statistik Provinsi Jawa Barat, 2021. https://jabar.bps.go.id/indicator/23/51/1/persentase-penduduk-miskin.html

BPS Provinsi Jawa Tengah, “Kemiskinan, 2019-2021,” Badan Pusat Statistika Provinsi Jawa Tengah, 2021. https://jateng.bps.go.id/indicator/23/34/1/kemiskinan.html

BPS Provinsi Jawa Timur, “Jumlah dan Persentase Penduduk Miskin di Provinsi Jawa Timur Menurut Kabupaten/Kota, 2017-2021,” Badan Pusat Statistika Provinsi Jawa Timur, 2021. https://jatim.bps.go.id/indicator/23/421/1/jumlah-penduduk-miskin-menurut-kabupaten-Kota-di-jawa-timur.html

D. C. Montgomery, E. A. Peck, and G. G. Vining, Introduction to linear regression analysis. John Wiley & Sons, 2021.

P. McCullagh, Generalized linear models. Routledge, 2019.

F. Famoye, J. T. Wulu, and K. P. Singh, “On the generalized Poisson regression model with an application to accident data,” Journal of Data Science, vol. 2, no. 3, pp. 287–295, 2004.

F. Famoye, “Restricted generalized poisson regression model,” Commun Stat Theory Methods, vol. 22, no. 5, pp. 1335–1354, Jan. 1993, doi: 10.1080/03610929308831089.

J. M. Hilbe, Negative binomial regression. Cambridge University Press, 2011.

L. Anselin, Spatial econometrics: methods and models, vol. 4. Springer Science & Business Media, 1988.

A. R. da Silva and T. C. V. Rodrigues, “Geographically weighted negative binomial regression—incorporating overdispersion,” Stat Comput, vol. 24, pp. 769–783, 2014.

H. Akaike, “Information theory and an extension of the maximum likelihood principle,” Selected papers of hirotugu akaike, pp. 199–213, 1998.

Published
2023-09-30
How to Cite
[1]
Z. Budiawan and Y. Widyaningsih, “POISSON REGRESSION MODELS TO ANALYZE FACTORS THAT INFLUENCE THE NUMBER OF TUBERCULOSIS CASES IN JAVA”, BAREKENG: J. Math. & App., vol. 17, no. 3, pp. 1761-1772, Sep. 2023.
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Articles