Parameter estimation of Cox Proportional Hazard regression model with Newton-Raphson

Survival analysis is a method for analyzing survival time data, starting from the first observation an event happens. A model to analyze survival is the Cox Proportional Hazard (CPH) regression model. The interesting thing about the CPH regression model is to estimate the parameter, apart from the maximum likelihood method, it can be done by using a numerical approach, namely the Newton-Raphson (NR) algorithm. This study aims to estimate the parameter of the CPH regression model with the NR algorithm. The research method used is a literature review of reference books and journals related to the CPH regression model and the NR algorithm. NR is a solution method of nonlinear equations by one starting point approach and approach it by look carefully at to the gradient. NR is best known as a method for finding the solution set of the roots of a real function and fast to reach the convergence, especially when the iteration starts quite close to the desired root. However, if the iteration starts far away from the sought root, this method may miss without warning. This method has an implementation that is usually notices and resolves convergence failures. Based on the results of the research, we get the constraint of the NR estimation, namely the approach point cannot be used if it’s an extreme point, because the value of the first derivative is zero. We get the CPH model estimator which is an iterative iteration until the desired convergence is achieved.