Penaksiran Parameter Cox Proportional Hazard Regression pada Data Besar Menggunakan Stochastic Gradient Descent

Abstract

Parameter estimation of Cox Proportional Hazard (CoxPH) regression models often faces challenges on large datasets. In this study, the Newton-Raphson method is compared with the Stochastic Gradient Descent (SGD) method to evaluate parameter estimation. Log-partial likelihood was utilized to estimate the model parameters, and evaluated using Concordance Index (C-Index) value as the main metric. Results show that SGD is superior in all tested dataset sizes. On a dataset of 10,000 samples, SGD achieved a C-Index of 0.683, while Newton-Raphson was only 0.674. Moreover, on datasets of 50,000 and 100,000, the C-Index values for SGD were 0.679 and 0.684, respectively, while Newton-Raphson experienced a decline in performance with C-Indexes of 0.511 and 0.551. This study demonstrates the effectiveness of SGD in capturing data complexity, making it a better choice for CoxPH parameter estimation on large data.