Kwak Minjung, Kim Jinseog, Jung Sin-Ho
a Department of Statistics , Yeungnam University , Gyeongsan , Gyeongbuk , ROK.
J Biopharm Stat. 2015;25(3):539-47. doi: 10.1080/10543406.2014.923726.
A logistic regression method can be applied to regressing the [Formula: see text]-year survival probability to covariates, if there are no censored observations before time [Formula: see text]. But if some observations are incomplete due to censoring before time [Formula: see text], then the logistic regression cannot be applied. Jung (1996) proposed to modify the score function for logistic regression to accommodate the right-censored observations. His modified score function, motivated for a consistent estimation of regression parameters, becomes a regular logistic score function if no observations are censored before time [Formula: see text]. In this article, we propose a modification of Jung's estimating function for an optimal estimation for the regression parameters in addition to consistency. We prove that the optimal estimator is more efficient than Jung's estimator. This theoretical comparison is illustrated with a real example data analysis and simulations.
如果在时间[公式：见正文]之前没有删失观测值，那么逻辑回归方法可用于将[公式：见正文]年生存概率对协变量进行回归。但如果由于在时间[公式：见正文]之前的删失导致一些观测值不完整，那么就不能应用逻辑回归。荣格（1996）提出修改逻辑回归的得分函数以适应右删失观测值。他修改后的得分函数，出于对回归参数进行一致估计的目的，如果在时间[公式：见正文]之前没有观测值被删失，就会变成常规的逻辑得分函数。在本文中，我们除了一致性之外，还提出对荣格估计函数进行修改以对回归参数进行最优估计。我们证明最优估计量比荣格的估计量更有效。这种理论比较通过一个实际例子的数据分析和模拟来说明。
