ESTIMASI PARAMETER MODEL COX PROPORTIONAL HAZARD MULTIRESPON DENGAN METODE MAXIMUM PARTIAL LIKELIHOOD ESTIMATION (MPLE)

Abstract

Multirespon Cox proportional hazard models have ratio property, that is the ratio of hazard functions for two individuals with covariate vectors z1 and z2 are constant (time independent). In this study we talk about estimation of prameters on multirespon Cox model by using Maximum Partial Likelihood Estimation (MPLE) method. To determine the appropriate estimators that maximize the lnpartial likelihood function, after a score vector
and a Hessian matrix are found, numerical iteration methods are applied. In this case, we use a Newton Raphson method. This numerical method is used since the solutions of the equation system of the score vector after setting it equal to zero vector are not closed form. Considering the studies about multirespon Cox model are limited, including the parameter estimation methods, but the methods are urgently needed by some fields of study related such as economics, engineering and medical sciences. For this reasons, the goal of this study is designed to develop parameter estimation methods from unirespon to multirespon cases.

Keywords : Multivariate Cox model, Maximum Partial Likelihood Estimation, Parameter Estimator, Newton Raphson Method.