比例风险模型下参数估计的两种MM算法的一些应用

Some Applications of Two Minorization-Maximization Algorithms for the Maximum Likelihood Estimator under the Proportional Hazards Model

对于带有删失机制的生存数据的研究,比例风险模型是应用最为广泛的统计模型之一。实际中,为得到其参数的极大似然估计需要采用数值方法计算得分方程的解。MinorizationMaximization算法(以下简称"MM算法")将求解复杂的目标函数的极值问题转化为求解简单的代理函数的极值问题。本文主要探讨,在比例风险模型下通过两种不同的思想为偏似然函数构造代理函数,从而得到的两种MM算法。通过数值模拟和实际数据分析实现这两种MM算法在比例风险模型下的一些应用。

The proportional hazards model has been widely used to study survival data with censoring.In practice, numerical methods are required for the calculation of the maximum likelihood estimators ofthe regression parameter. More and more researches and applications on the minorization-maximizationalgorithm （MM algorithm） have been widely developed due to the stability of the algorithm. The key ofthe MM algorithm is to transfer the optimization to a surrogate function. This paper studies two MMalgorithms by building different surrogate functions for the likelihood of the proportional hazards model.The simulation studies are conducted and real data sets are analyzed to study applications of these twoMM algorithms to the proportional hazards model.