A hybrid Newton-type method for censored survival data using double weights in linear models
A hybrid Newton-type method for censored survival data using double weights in linear models
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DOI：
10.1007/s10985-006-9014-0
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发表时间：
2006-09-01
影响因子：
1.3
通讯作者：
Nan, Bin
中科院分区：
文献类型：
--
作者：
Yu, Menggang;Nan, Bin
作为 Cox 模型的替代方案，自 Tsiatis [Tsiatis AA (1990) Ann Stat 18:354-372] 等提出以来，用于审查生存数据的基于等级的估计方法已被广泛研究。由于估计函数的不连续性特征，文献中的大量工作都集中在数值问题上。在本文中，我们考虑一系列双加权基于排名的估计函数的计算方面。这个家族足够丰富，包括 Tsiatis (1990) 的随机观测数据估计函数和 Nan 等人的估计函数。 [Nan B, Yu M, Kalbfleisch JD (2006) Biometrika (待发表)] 将病例队列数据作为特殊示例。后者属于有偏抽样问题。我们证明，当使用广义 Gehan 型权重时，基于双加权排序的不连续估计函数是单调的，这是为文献中随机观察的数据建立的属性。虽然估计问题可以表述为线性规划问题，如随机观测数据的估计问题，但由于即使对于中等样本量，其规模也很容易无法控制，因此我们提出了一种牛顿型迭代方法来搜索不连续单调估计方程（系统）的近似解。仿真结果很好地证明了所提出的方法。我们还将我们的方法应用于真实的数据示例。
As an alternative to the Cox model, the rank-based estimating method for censored survival data has been studied extensively since it was proposed by Tsiatis [Tsiatis AA (1990) Ann Stat 18:354-372] among others. Due to the discontinuity feature of the estimating function, a significant amount of work in the literature has been focused on numerical issues. In this article, we consider the computational aspects of a family of doubly weighted rank-based estimating functions. This family is rich enough to include both estimating functions of Tsiatis (1990) for the randomly observed data and of Nan et al. [Nan B, Yu M, Kalbfleisch JD (2006) Biometrika (to appear)] for the case-cohort data as special examples. The latter belongs to the biased sampling problems. We show that the doubly weighted rank-based discontinuous estimating functions are monotone, a property established for the randomly observed data in the literature, when the generalized Gehan-type weights are used. Though the estimating problem can be formulated to a linear programming problem as that for the randomly observed data, due to its easily uncontrollable large scale even for a moderate sample size, we instead propose a Newton-type iterated method to search for an approximate solution of the (system of) discontinuous monotone estimating equation(s). Simulation results provide a good demonstration of the proposed method. We also apply our method to a real data example.