Model Semiparametrik Survival Bivariat Copula-Yang Prentice: Studi Kasus Retinopati Diabetik

Itu, Agnes Agatha Renaningtyas (2026) Model Semiparametrik Survival Bivariat Copula-Yang Prentice: Studi Kasus Retinopati Diabetik. Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Retinopati diabetik merupakan komplikasi mikrovaskular diabetes melitus yang menjadi penyebab utama gangguan penglihatan global. Analisis survival pada penyakit ini menghadapi tantangan berupa ketergantungan antar waktu kejadian pada organ berpasangan serta fenomena crossing survival curves yang melanggar asumsi proportional hazards. Penelitian ini mengintegrasikan model regresi semiparametrik Yang-Prentice (YP) dengan Copula Archimedean (Clayton, Frank, dan Gumbel) untuk mengatasi permasalahan tersebut, dengan estimasi parameter menggunakan algoritma BFGS pendekatan dua tahap IFM dan pengujian hipotesis metode jackknife delete-block. Studi kasus menggunakan data pasien Rumah Sakit Mata Undaan Surabaya dengan prediktor jenis terapi, usia, hipertensi, dan jenis kelamin. Hasil simulasi menunjukkan estimasi yang akurat dengan bias dan RMSE menurun seiring bertambahnya ukuran sampel. Pada data nyata, Copula Gumbel terpilih sebagai model terbaik dengan nilai AIC terkecil. Secara serentak, seluruh prediktor berpengaruh signifikan terhadap waktu kebutaan (p<0,001). Secara parsial, jenis terapi, usia, hipertensi, dan jenis kelamin masing-masing berpengaruh signifikan pada setiap mata dan waktu tertentu. Simpulannya, model Copula-Yang Prentice efektif memodelkan data survival bivariat dengan dependensi antar organ berpasangan dan mampu menangkap efek kovariat jangka pendek maupun jangka panjang. Untuk penelitian selanjutnya, disarankan mengeksplorasi keluarga copula lain, memperpanjang periode pengamatan, serta menambah variabel prediktor yang lebih lengkap.
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Diabetic retinopathy is a microvascular complication of diabetes mellitus and a leading global cause of visual impairment. Survival analysis in this context faces challenges of dependency between event times in paired organs and crossing survival curves that violate the proportional hazards assumption. This study integrates the Yang-Prentice (YP) semiparametric regression model with Archimedean Copulas (Clayton, Frank, and Gumbel), using two-stage IFM with BFGS optimization for parameter estimation and jackknife delete-block for hypothesis testing. The case study uses patient data from Undaan Eye Hospital Surabaya, with treatment type, age, hypertension, and sex as predictors. Simulation results confirm accurate estimation with bias and RMSE decreasing as sample size increases. In real data application, the Gumbel Copula was selected as the best model based on minimum AIC. All predictors jointly significantly affect time to blindness (p<0.001), with treatment type, age, hypertension, and sex each showing significant effects on specific eyes and time. In conclusion, the Copula-Yang Prentice model effectively captures bivariate survival dependency and separates short- and long-term covariate effects. Future research is recommended to explore other copula families, extend the observation period, and incorporate additional predictor variables.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	analisis survival, copula, model Yang-Prentice, retinopati diabetik, survival analysis, copula, Yang-Prentice model, retinopati diabetik
Subjects:	Q Science Q Science > QA Mathematics > QA276 Mathematical statistics. Time-series analysis. Failure time data analysis. Survival analysis (Biometry)
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Agnes Agatha Renaningtyas Itu
Date Deposited:	05 Aug 2026 02:18
Last Modified:	05 Aug 2026 02:18
URI:	http://repository.its.ac.id/id/eprint/143782

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