SURVIVAL FUNCTION AND HAZARD FUNCTION ANALYSIS OF EXPONENTIAL DISTRIBUTION IN TYPE I CENSORED SURVIVAL DATA: A CASE STUDY OF BREAST CANCER PATIENTS
Breast cancer is the most common cancer in women and the leading cause of cancer-related death in Indonesia. Analysis of survival data is important for improving the treatment and care of breast cancer patients. This study aims to estimate the parameters, find the survival function, and hazard function of breast cancer patients using a parametric method with an exponential distribution. Previous studies have shown that the Maximum Likelihood Estimation (MLE) method is suitable for estimating the survival function from exponential survival data by censoring. In this study, the exponential distribution was found to be the best for data on breast cancer patients from Surabaya Ontology Hospital. The estimated parameters are θ = 33.9157, and the survival function is calculated using The estimated hazard function for patient death or failure is 0.0295. The results of this study can contribute to the development of better treatment and care strategies for breast cancer patients. However, further research is needed because this study only used monthly time units.
Kementerian Kesehatan Republik Indonesia, "Kanker Payudara Paling Banyak di Indonesia, Kemenkes Targetkan Pemerataan Layanan Kesehatan," Kementerian Kesehatan Republik Indonesia, May 2021. [Online]. Available: https://www.kemkes.go.id/article/view/22020400002/kanker-payudara-paling-banyak-di-indonesia-kemenkes-targetkan-pemerataan-layanan-kesehatan.htm. [Accessed 15 April 2023].
iTech Mission, "SDGs Global Dashboard," iTech Mission, 2021. [Online]. Available: https://www.sdgsdashboard.org/. [Accessed 19 June 2023].
T. G. Ieren and P. E. Oguntunde, "A Comparison between Maximum Likelihood and Bayesian Estimation Methods for a Shape Parameter of the Weibull-Exponential Distribution," AJPAS, vol. 1, no. 1, pp. 1-12, May 2018.
A. Wiranto, A. Kurniawan, D. A. Fitria and N. Chamidah, "Estimation of type I censored exponential distribution parameters using objective bayesian and bootstrap methods (case study of chronic kidney failure patients)," Journal of Physics: Conference Series, vol. 1397, no. 1, p. 012060, December 2019.
W. Chen, Y. Zhang and J. He, "Estimating the survival function for exponential distribution with type-I censoring," Journal of Statistical Computation and Simulation, vol. 85, no. 3, pp. 563-574, 2015.
Z. Yu, W. Tang and J. Huang, "Bayesian Survival Analysis For Type-I Censored Data with Exponential Distribution," Journal of Statistical Computation and Simulation, vol. 87, no. 9, pp. 1765-1779, 2017.
A. Budiantoro, "Kajian Data Ketahanan Hidup Tersensor Tipe-I Dengan Distribusi Eksponensia," Neliti, 2016. [Online]. Available: https://media.neliti.com/media/publications/136888-ID-kajian-data-ketahanan-hidup-tersensor-ti.pdf [Accessed: April 15, 2023].. [Accessed 15 April 2023].
D. Collett, Modelling survival data in medical research, Boca Raton: CRC press, 2023.
A. J. Turkson, "Perspectives on Hazard Rate Functions: Concepts; Properties; Theories; Methods; Computations; and Application to Real-Life Data," Open Access Library Journal, vol. 9, no. 1, pp. 1-23, 2022.
A. Kurniawan, "Analisis Data Uji Hidup," Surabaya, Universitas Airlangga, 2023.
A. J. Turkson, F. Ayiah-Mensah and V. Nimoh, "Handling censoring and censored data in survival analysis: a standalone systematic literature review," International journal of mathematics and mathematical sciences, no. 2021, pp. 1-16, 2021.
H. Panahi, "Estimation of the Burr type III distribution with application in unified hybrid censored sample of fracture toughness," Journal of applied Statistics, vol. 44, no. 14, pp. 2575-2592, 2017.
S. Su, "Flexible modelling of survival curves for censored data," Journal of Statistical Distributions and Applications, vol. 3, pp. 1-20, 2016.
N. H, Estimator Bayes Distribusi Eksponensial Terpotong Kiri pada Data Uji Hidup Tersensor Tipe I Berdasarkan Prior Non-Informatif, Skripsi, Universitas Airlangga, 2009.
L. Jäntschi and S. D. Bolboacă, "Computation of probability associated with Anderson–Darling statistic," Mathematics, vol. 6, no. 6, p. 88, 2018.
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