Estimasi Fungsi Baseline Hazard dengan B-Spline pada Model Additive Hazard (Studi Kasus: Kanker Payudara di RSUD NTB)

Ariyadi, Lalu Yuhda (2025) Estimasi Fungsi Baseline Hazard dengan B-Spline pada Model Additive Hazard (Studi Kasus: Kanker Payudara di RSUD NTB). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Analisis survival merupakan cabang statistik yang berfokus pada analisis data waktu hingga terjadinya suatu peristiwa, seperti kematian atau kekambuhan penyakit. Salah satu tantangan utama dalam analisis ini adalah menangani data tersensor, terutama sensor kanan, di mana waktu kejadian hanya diketahui melebihi suatu titik waktu tertentu. Model Cox Proportional Hazard merupakan pendekatan yang paling umum digunakan, namun memiliki keterbatasan ketika asumsi proportional hazard tidak terpenuhi. Sebagai alternatif, model Additive Hazard menawarkan fleksibilitas tanpa memerlukan asumsi tersebut. Penelitian ini bertujuan untuk mengestimasi fungsi baseline hazard dalam model additive hazard dengan pendekatan maximum penalized likelihood (MPL) menggunakan B-spline. Pendekatan ini memungkinkan pengendalian terhadap kehalusan fungsi estimasi serta menjamin hasil yang non-negatif. Model yang dikembangkan diterapkan pada data pasien kanker payudara di RSUD Provinsi Nusa Tenggara Barat. Hasil analisis menunjukkan bahwa fungsi baseline hazard yang di aproximasi menggunakan fungsi B-spline derajat nol, satu dan dua menunjukkan pola peningkatan laju kejadian seiring bertambahnya waktu. Variabel stadium, pendidikan dan status kemoterapi memiliki pengaruh signifikan terhadap laju kematian pasien. Hasil ini menunjukkan bahwa model additive hazard berbasis B-spline dengan pendekatan MPL dapat digunakan sebagai alternatif yang andal dalam analisis survival, khususnya ketika asumsi proportional hazard tidak terpenuhi
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Survival analysis is a branch of statistics that focuses on analyzing data on the time until an event occurs, such as death or disease recurrence. One of the main challenges in this analysis is handling censored data, particularly right censoring, where the time of the event is only known to exceed a certain point in time. The Cox Proportional Hazard model is the most commonly used approach, but it has limitations when the proportional hazard assumption is not met. As an alternative, the Additive Hazard model offers flexibility without requiring such assumptions. This study aims to estimate the baseline hazard function in the additive hazard model using the maximum penalized likelihood (MPL) approach with B-splines. This approach allows control over the smoothness of the estimated function and ensures non-negative results. The developed model was applied to data from breast cancer patients at the West Nusa Tenggara Provincial Hospital. The analysis results showed that the baseline hazard function approximated using B-splines of degrees zero, one, and two exhibited a pattern of increasing incidence rates over time. The variables of stage, education, and chemotherapy status have a significant influence on the mortality rate of patients. These results indicate that the B-spline-based additive hazard model with the MPL approach can be used as a reliable alternative in survival analysis, especially when the proportional hazard assumption is not met

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Additive Hazard, Analisis Survival, B-Spline, Maximum Penalized Likelihood, Kanker Payudara; Additive Hazard, Survival Analysis, B-Spline, Maximum Penalized Likelihood, Breast Cancer.
Subjects:	Q Science > QA Mathematics > QA276 Mathematical statistics. Time-series analysis. Failure time data analysis. Survival analysis (Biometry) R Medicine > R Medicine (General) > R853.S7 Survival analysis (Biometry)
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Lalu Yuhda Ariyadi
Date Deposited:	07 Aug 2025 02:08
Last Modified:	07 Aug 2025 02:08
URI:	http://repository.its.ac.id/id/eprint/127864

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