Open AccessESTIMASI PARAMETER PADA MODEL COX MULTIVARIAT DENGAN METODE MAXIMUM PARTIAL LIKELIHOOD ESTIMATION
Author(s) -
Irfan Wahyudi,
Purhadi Purhadi,
Sutikno Sutikno,
Irhamah Irhamah
Publication year - 2012
Publication title -
jurnal ilmiah matematika dan pendidikan matematika (jmp)/jurnal ilmiah matematika dan pendidikan matematika
Language(s) - English
Resource type - Journals
eISSN - 2550-0422
pISSN - 2085-1456
DOI - 10.20884/1.jmp.2012.4.1.2954
Subject(s) - multivariate statistics , hessian matrix , univariate , mathematics , covariate , statistics , estimation theory , proportional hazards model , estimator , multivariate analysis , likelihood function , maximum likelihood sequence estimation , estimating equations
Multivariate 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 multivariate Cox model by using Maximum Partial Likelihood Estimation (MPLE) method. To determine the appropriate estimators that maximize the ln-partial 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 multivariate 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 univariate to multivariate cases.