Application of Weibull Regression to Recurrence Data Kidney Infection Patients

¹ , rea Tri Rian Dani² , Qonita Qurrota A’yun³ , Fachrian Bimantoro Putra⁴ , Meirinda Fauziyah⁵

1. Statistics Study Program, Department of Mathematics, Mulawarman University, Samarinda, Indonesia.
2. Mathematics Study Program, Department of Mathematics, Mulawarman University, Samarinda, Indonesia.
3. Statistics Study Program, Department of Mathematics, Mulawarman University, Samarinda, Indonesia.
4. Statistics Study Program, Department of Mathematics, Mulawarman University, Samarinda, Indonesia.

Section:Research Paper, Product Type: Journal-Paper
Vol.12 , Issue.4 , pp.1-8, Aug-2024

Online published on Aug 31, 2024

Copyright © ,rea Tri Rian Dani, Qonita Qurrota A’yun, Fachrian Bimantoro Putra, Meirinda Fauziyah . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

View this paper at   Google Scholar | DPI Digital Library

XML View     PDF Download

How to Cite this Paper

64 Views    106 Downloads    18 Downloads

Abstract :
The kidneys are the main organ for removing metabolic waste products that are not needed by the body. Kidney infection or pyelonephritis is an infection in the bladder tract that attacks the kidneys and enters through the lower or external urinary tract, spreads to the bladder, to the ureters (upper urinary tract), then finally to the kidneys. This disease is often not detected so it can cause complications of kidney failure. This research discusses survival analysis in kidney infection patients using Weibull survival regression by carrying out descriptive statistical analysis, estimating Weibull regression model parameters, testing hypothesis of regression model parameters simultaneously and partially. The aim of this study was to determine the Weibull survival regression model and determine the factors that influence the length of time for kidney infection patients to relapse. The results of this research obtained the best model is weibill regression , from which it can be seen that frailty, gender, and the patient`s medical history are factors that significantly influence the recovery rate of kidney infection patients.

Key-Words / Index Term :
Kidneys, Kidney Infection, Weibull Survival Regression

References :
[1] A. P. D. Alamsyah and Normalisa, “Sistem Pakar Diagnosa Penyakit Ginjal,” International Journal of Artificial Inteligence, vol. 6, no. 1, pp. 53-74, 2019.
[2] L. Geografi and N. M. Y. D. Wahyani, “Duration of Antibiotic Treatment for Urinary Tract Infection,” Jurnal Manajemen dan Pelayanan Farmasi, vol. 4, no. 1, 2014.
[3] P. D. Allison, Survival Analysis Using the SAS System: A Practical Guide, Cary , NC: SAS Institute, Inc., 1995.
[4] A. Solehah and M. Fatekurohman, “Analisis Ketahanan Hidup Pasien Kanker Paru Menggunakan Regresi Weibull,” Indonesian Journal of Applied Statistics, vol. 1, no. 2, pp. 79-87, 2018.
[5] N. Safitri, Syafriandi and Helma, “faktor Dominan yang Mempengaruhi Penyakit Gagal Ginjal dengan Menggunakan Regresi Cox (Studi Kasus di RZUP Dr. M. Djamil Padang),” Journal of Mathematics UNP, vol. 1, no. 1, pp. 47-53, 2013.
[6] N. Safitri and Helma, “Faktor-Faktor Penyebab Penyakit Gagal Ginjal pada Pasien di RSUP Dr. M. Djamil Padang dengan Menggunakan Regresi Cox,” EKSAKTA, pp. 60-66, 2016.
[7] Y. I. Z. Afni, M. Fatekurhoman and D. Anggraeni, “Perbandingan Model Cox Proportional Hazard dan Regresi Weibull untuk Menganalisis Ketahanan bank Syariah,” Indonesian Journal of Applied Statistics, vol. 6, no. 1, pp. 53-74, 2019.
[8] Y. S. A. Monica and Purhadi, “Analisis Faktor yang Memengaruhi Laju Kesembuhan Pasien Tuberkulosis Paru di RSUD dr. Soetomo Tahun 2015 Menggunakan Regresi Weibull dan Regresi Cox Proportional Hazard,” JURNAL SAINS & SENI ITS, vol. 5, no. 2, 2016.
[9] Mayawi, Nurhayati, N. S. Laamen, A. W. Bustan, M. Salmin and T. Talib, “Perbandingan Model Regresi Weibull dan Regresi Cox Proportional Hazard,” Science Map Journal, vol. 4, no. 2, 2022.
[10] I. K. Hasan, W. A. Pakarya, N. Achamd and D. R. Isa, “Analisis Survival Menggunakan Regresi Weibull pada Laju Kesembuhan Pasien Tuberkulosis Paru di RSUD Aloei Saboe Kota Gorontalo,” EULER: Jurnal Ilmiah Matematika, Sains, dan teknologi, vol. 9, pp. 40-51, 2021.
[11] Hasmiati, Suyitno and Nasution, “Model Regresi Weibull pada Data Waktu Rawat Inap Pasien Penderita Penyakit Jantung Koroner dengan Event Kematian di RSUD Abdul Wahab Sjahranie Samarinda,” Prosiding Seminar Nasional Matematika, Statistika, dan Aplikasinya, vol. 2, pp. 369-376, 2022.
[12] H. D. Panduwinata, Suyitno and M. N. Huda, “Model Regresi Weibull pada Daa Kontinu yang Diklasifikasikan (Studi Kasus: Indikator Pencemaran Air BOD di DAS Mahakam Tahun 2016),” EKSPONENSIAL, vol. 13, no. 2, pp. 123-130, 2022.
[13] Suyitno, “Penaksiran Parameter dan Pengujian Hipotesis Model Regresi Weibull Univariat,” Jurnal EKSPONENSIAL, vol. 8, pp. 179-184, 2017.
[14] Suyitno, Purhadi, Sutikno and Irhamah, “Multivariate Weibull Regression Model,” Far East Journal of Mathematical Sciences, vol. 101, pp. 1977-1992, 2017.
[15] S. F. Khairunnisa, Suyitno and S. Mahmuda, “Weibull Regression Model on Hospitalization Time Data of COVID-19 Patients at Abdul Wahab Sjahranie Hospital Samarinda,” Jurnal Matematika, Statistika, dan Komputasi, vol. 19, no. 2, pp. 286-303, 2023.
[16] J. F. Lawless, Statistical Models and Methods for Lifetime Data, New York: John Willey and Sons, Inc, 1982.
[17] D. D. Hanagal, “Parametric Bivariate Regression Analysis Based on Censored Samples: A Weibull Model,” Stochastics and Quality Control, vol. 19, no. 1, pp. 83-90, 2004.
[18] H. Rinnie, The Weibull Distribution A Handbook, New York: CRC Press Taylor and Francis Group, 2009.
[19] H. Rehman, N. Chandra, T. Emura and M. Pandey, “Estimation of The Modified Weibull Additive Hazard Regression Model under Competing Risks,” Symmetry, vol. 15, p. 485, 2023.
[20] Y. Pawitan, In All Likelihood Statistical Modelling and Inference using Likelihood, Sweden: Claredon Press-Oxford, 2001.
[21] N. Draper and H. Smith, Analisis Regresi Terapan Edisi Kedua, Jakarta: PT. Gramedia Pustaka Utama, 1992.
[22] A. C. Renchar, Linier Model in Statistics, New York: John Wiley and Sons, Inc, 2000.
[23] E. Liu, R. Y. Liu and K. Lim, “Using the Weibull Accelerated Failure Time Regression Model to Predict Time to Health Events,” Applied Sciences, vol. 13, no. 24, 2023.
[24] P. Gauthami, K. D. Mariyamma and P. Kavya, “A Modified Inverse Weibull Distribution Using KM Transformation,” Reliability: Theory & Applications, vol. 18, pp. 35-42, 2023.
[25] T. Cavalcante, R. Ospina, V. Leiva, X. Cabezas and C. M. Barreiro, “Weibull Regression and Machine Learning Survival Models: Methodology, Comparison, adn Application to Biomedical Data Related to cardiac Surgery,” Biology, vol. 12, no. 3, p. 442, 2023