Muhammad Hafizh Shalahuddin Ahsan, - (2024) PEMODELAN COX PROPORTIONAL HAZARD BERDISTRIBUSI GOMPERTZ DENGAN PERTIMBANGAN EFEK ACAK (FRAILTY) SPASIAL GEOSTATISTIK: Studi Kasus Acute Myeloid Leukemia. S1 thesis, Universitas Pendidikan Indonesia.
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Abstract
Kematian berada di luar pengaruh individu dan seringkali timbul kekhawatiran ketika individu menderita suatu penyakit dengan risiko kematian. Tidak terdapat metode pasti dalam menghitung sisa umur pasien, melainkan menghitung besar peluang hidup dari pasien. Distribusi Gompertz pada regresi Cox Proportional Hazard dapat digunakan untuk melihat peluang bertahan hidup individu pada suatu wilayah dengan memperhatikan efek acak (frailty) spasial geostatistik. Estimasi parameter dilakukan dengan metode Estimasi Kemungkinan Maksimum dengan bantuan metode Newton-Raphson untuk melakukan optimisasi. Penelitian diterapkan pada data simulasi berdasarkan kasus Acute Myeloid Leukemia (AML) di Inggris Barat Laut tahun 1982 – 1998. Faktor-faktor yang signifikan memengaruhi waktu tahan hidup pasien adalah usia dan jumlah sel darah putih. Peluang hidup pasien dengan pengaruh spasial yang tinggi lebih rendah dibandingkan model nonfrailty sehingga lokasi pasien tinggal perlu dipertimbangkan dalam suatu model. Death is beyond individual control and often raises concerns when individuals suffer from a disease with a risk of mortality. There is no definitive method to calculate a patient's remaining lifespan; instead, the probability of the patient's survival is assessed. The application of the Gompertz distribution in Cox Proportional Hazard regression can be used to estimate an individual's survival probability in a region, considering the spatial geostatistical random effects (frailty). Parameter estimation is carried out using the Maximum Likelihood Estimation method with the help of the Newton-Raphson method for optimization. The research was applied to simulation data according to Acute Myeloid Leukemia (AML) cases in Northwest England from 1982 to 1998. Significant factors influencing patients' survival time were age and white blood cell count. The survival probability of patients with high spatial influence is lower compared to the nonfrailty model, indicating that the patient's location should be considered in a model.
| Item Type: | Thesis (S1) |
|---|---|
| Additional Information: | ID SINTA Dosen Pembimbing: Bambang Avip Priatna Martadiputra: 6124136 Fitriani Agustina: 5981275 |
| Uncontrolled Keywords: | Distribusi Gompertz, Regresi Cox Proportional Hazard, Spasial Geostatistik, Model Survival, Peluang Hidup. Gompertz Distribution, Cox Proportional Hazard Regression, Spatial Geostatistics, Survival Model, Survival Probability. |
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Fakultas Pendidikan Matematika dan Ilmu Pengetahuan Alam > Jurusan Pendidikan Matematika > Program Studi Matematika (non kependidikan) |
| Depositing User: | Muhammad Hafizh Shalahuddin Ahsan |
| Date Deposited: | 22 Aug 2024 06:38 |
| Last Modified: | 22 Aug 2024 06:38 |
| URI: | http://repository.upi.edu/id/eprint/120523 |
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