Pemodelan Survival Cox Copula Bivariat dengan Pendekatan Pseudo Maximum Likelihood

Rahmawati, Wahyu Dwi (2026) Pemodelan Survival Cox Copula Bivariat dengan Pendekatan Pseudo Maximum Likelihood. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Analisis survival merupakan metode statistik yang digunakan untuk mempelajari waktu terjadinya suatu peristiwa. Pada kasus penyakit bilateral seperti katarak, waktu kejadian pada kedua mata berpotensi saling bergantung sehingga pendekatan univariat kurang mampu menangkap struktur dependensi tersebut. Penelitian ini bertujuan memodelkan dependensi antara waktu pencapaian ketajaman penglihatan minimum 6/18 pada mata kanan dan kiri pasien pasca operasi katarak menggunakan regresi survival Cox dengan pendekatan copula bivariat. Data yang digunakan merupakan data pasien yang menjalani operasi katarak pada kedua mata di RS Mata Undaan Surabaya sejak 1 Januari hingga 31 Oktober 2025. Estimasi parameter dilakukan melalui prosedur dua tahap dengan pendekatan maximum pseudo-likelihood dan optimasi numerik menggunakan algoritma BHHH. Empat jenis copula diuji, yaitu Clayton, Frank, Gumbel, dan Joe. Berdasarkan nilai Akaike Information Criterion (AIC), model terbaik adalah copula Joe dengan AIC sebesar 2967,332. Nilai parameter dependensi sebesar 3,934 dan Kendall’s tau sebesar 0,609 menunjukkan adanya dependensi positif yang cukup kuat antara waktu pencapaian visus minimum pada kedua mata. Variabel usia dan riwayat penyakit jantung berpengaruh signifikan pada kedua mata sedangkan riwayat penyakit diabetes dan kolesterol berpengaruh signifikan pada waktu survival mata kanan saja.
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Survival analysis is a statistical method used to study the time until the occurrence of an event. In bilateral diseases such as cataracts, the event times in the two eyes may be dependent, so univariate approaches may not adequately capture this dependence structure. This study aims to model the dependence between the time to achieving a minimum visual acuity of 6/18 in the right and left eyes of patients after cataract surgery using the Cox proportional hazards model combined with a bivariate copula approach. The data consist of patients who underwent cataract surgery in both eyes at RS Mata Undaan Surabaya from January 1 to October 31, 2025. Parameter estimation was conducted using a two-stage procedure with the maximum pseudo-likelihood approach and numerical optimization through the BHHH algorithm. Four copulas were considered: Clayton, Frank, Gumbel, and Joe. Based on the Akaike Information Criterion (AIC), the Joe copula provided the best model with an AIC of 2967.332. The dependence parameter (3.934) and Kendall’s tau (0.609) indicate a relatively strong positive dependence between the times to achieving the visual acuity outcome in both eyes. Age and history of heart disease were found to be significant factors in both eyes. Meanwhile, history of diabetes and cholesterol had a significant effect on the survival time of the right eye only.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Archimedean, Dependensi, Iterasi BHHH, Katarak, Kendall’s Tau
Subjects:	R Medicine > RE Ophthalmology R Medicine > RE Ophthalmology > RE48 Eye--Diseases. Ophthalmoscopy.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Wahyu Dwi Rahmawati
Date Deposited:	20 Jul 2026 02:38
Last Modified:	20 Jul 2026 02:38
URI:	http://repository.its.ac.id/id/eprint/135507

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