Pemodelan Kasus Tuberkulosis di Jawa Barat Menggunakan Metode Generalized Poisson Regression
DOI:
https://doi.org/10.29313/bcss.v6i2.24314Keywords:
Generalized Poisson Regression, Overdispersi, TuberculosisAbstract
Abstract. Poisson regression is widely used to model count data, but this method assumes the variance and the mean are equal, known as equidispersion. In practice, this assumption is often not met due to overdispersion, a condition where the variance is much greater than the mean, making parameter estimates less accurate when ordinary Poisson regression is used. This study applies the Generalized Poisson Regression (GPR) method, an extension of Poisson regression with an added dispersion parameter to handle overdispersion, to model tuberculosis (TB) cases in 27 regencies/cities in West Java Province in 2024. The data used are secondary data from Statistics Indonesia and West Java Open Data, with population density, poverty percentage, sanitation access, number of HIV/AIDS cases, and number of health facilities as predictors. Parameters were estimated using Maximum Likelihood Estimation with the Newton-Raphson iteration, while significance testing used the Likelihood Ratio Test and the Wald test. The Pearson Chi-Square dispersion test showed a value of 682.744, far above 1, meaning the data experienced overdispersion so GPR was appropriately used. Simultaneous testing showed all predictors had a significant joint effect, while partial testing showed only population density and health facilities had a significant effect on tuberculosis cases in West Java.
Abstrak. Regresi poisson umum digunakan untuk memodelkan data cacah, namun metode ini mengasumsikan nilai varians dan rata-rata sama, atau disebut equidispersi. Pada praktiknya, asumsi tersebut sering tidak terpenuhi karena terjadi overdispersi, yaitu kondisi ketika nilai varians jauh lebih besar dari rata-ratanya, sehingga estimasi parameter menjadi kurang akurat apabila tetap menggunakan regresi poisson biasa. Oleh karena itu, penelitian ini menerapkan metode Generalized Poisson Regression (GPR) yaitu pengembangan dari regresi poisson dengan tambahan parameter dispersi untuk mengatasi overdispersi, guna memodelkan jumlah kasus tuberkulosis (TB) di 27 kabupaten/kota Provinsi Jawa Barat tahun 2024. Data yang digunakan adalah data sekunder dari Badan Pusat Statistik dan Open Data Provinsi Jawa Barat, dengan variabel prediktor berupa kepadatan penduduk, persentase penduduk miskin, akses sanitasi layak, jumlah penderita HIV/AIDS, dan jumlah sarana kesehatan. Estimasi parameter dilakukan menggunakan Maximum Likelihood Estimation dengan iterasi Newton-Raphson, sedangkan pengujian signifikansi dilakukan menggunakan Likelihood Ratio Test dan uji Wald. Hasil uji dispersi Pearson Chi-Square menunjukkan nilai 682,744, jauh di atas 1, berarti data mengalami overdispersi sehingga GPR tepat digunakan. Hasil pengujian simultan menunjukkan seluruh variabel prediktor berpengaruh signifikan secara bersama-sama, sedangkan hasil pengujian parsial menunjukkan hanya variabel kepadatan penduduk dan variabel sarana kesehatan yang berpengaruh signifikan terhadap jumlah kasus tuberkulosis di Jawa Barat.
References
Berk, R., & MacDonald, J. M. (2008). Overdispersion and Poisson Regression. Journal of Quantitative Criminology, 24(3), 269–284. https://doi.org/10.1007/s10940-008-9048-4
BPS. (2024). Provinsi Jawa Barat dalam Angka 2024.
Consul, P. C., & Famoye, F. (1992). Generalized poisson regression model. Communications in Statistics - Theory and Methods, 21(1), 89–109. https://doi.org/10.1080/03610929208830766
Demidenko, E. (2020). Approximations of the power functions for Wald, likelihood ratio, and score tests and their applications to linear and logistic regressions. Model Assisted Statistics and Applications, 15(4), 335–349. https://doi.org/10.3233/MAS-200505
Jannah, R. Z., Azizah, R., Jalaludin, J. B., Sulistyorini, L., & Lestari, K. S. (2023). Meta-Analysis Study: Environmental Risk Factors of Tuberculosis (TB). JURNAL KESEHATAN LINGKUNGAN, 15(2), 84–91. https://doi.org/10.20473/jkl.v15i2.2023.84-91
Otok, B. W., Rachmawati, D. S., Purhadi, Purnami, S. W., & Mahpolah, M. (2021). Poisson Regression Modeling of Diarrhea Events in Pasuruan Regency with Maximum Likelihood Estimates and Generalized Method Moment. International Journal of Preventive Medicine, 12(1). https://doi.org/10.4103/ijpvm.IJPVM_79_20
Sriningsih, M., Hatidja, D., & Prang, J. D. (2018). Multicollinierity Handling Using Principal Components Refression on Imported Rice Case in North Sulawesi Province. Statmat : Jurnal Statistika Dan Matematika, 18(01), 18–24.
Suryani, F. T., & Ibad, M. (2022). Analisis Faktor Kepadatan Penduduk, Cakupan Rumah Sehat Dan Sanitasi Rumah Tangga Terhadap Kejadian Tuberkulosis Tahun 2018. Jurnal Sosial Dan Sains, 2(10), 1086–1095. https://doi.org/10.59188/jurnalsosains.v2i10.468
WHO. (2024). Global Tuberculosis Report 2024. Geneva: WHO; 2024. Licence: CC BY-NC-SA 3.0 IGO. In Global tuberculosis report. https://www.who.int/publications/i/item/9789240101531
