Brown B M, Wang You-Gan
Department of Statistics and Applied Probability, National University of Singapore, 6 Science Drive 2, Singapore 117546, Singapore.
Stat Med. 2007 Feb 20;26(4):828-36. doi: 10.1002/sim.2576.
Adaptions of weighted rank regression to the accelerated failure time model for censored survival data have been successful in yielding asymptotically normal estimates and flexible weighting schemes to increase statistical efficiencies. However, for only one simple weighting scheme, Gehan or Wilcoxon weights, are estimating equations guaranteed to be monotone in parameter components, and even in this case are step functions, requiring the equivalent of linear programming for computation. The lack of smoothness makes standard error or covariance matrix estimation even more difficult. An induced smoothing technique overcame these difficulties in various problems involving monotone but pure jump estimating equations, including conventional rank regression. The present paper applies induced smoothing to the Gehan-Wilcoxon weighted rank regression for the accelerated failure time model, for the more difficult case of survival time data subject to censoring, where the inapplicability of permutation arguments necessitates a new method of estimating null variance of estimating functions. Smooth monotone parameter estimation and rapid, reliable standard error or covariance matrix estimation is obtained.
加权秩回归针对删失生存数据的加速失效时间模型进行的调整，在产生渐近正态估计以及能提高统计效率的灵活加权方案方面已取得成功。然而，对于仅一种简单的加权方案，即Gehan或Wilcoxon权重，估计方程才保证在参数分量上是单调的，即便在此情况下它们也是阶梯函数，计算时需要等同于线性规划的方法。缺乏平滑性使得标准误差或协方差矩阵估计变得更加困难。一种诱导平滑技术在各种涉及单调但纯跳跃估计方程的问题中克服了这些困难，包括传统的秩回归。本文将诱导平滑应用于加速失效时间模型的Gehan - Wilcoxon加权秩回归，针对更困难的删失生存时间数据情形，其中排列论证的不可适用性使得必须采用一种新的方法来估计估计函数的零方差。由此获得了平滑的单调参数估计以及快速、可靠的标准误差或协方差矩阵估计。
