Combined Estimating Equation Approaches for Semiparametric Transformation Models with Length-Biased Survival Data
Combined Estimating Equation Approaches for Semiparametric Transformation Models with Length-Biased Survival Data
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DOI：
10.1111/biom.12170
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发表时间：
2014-09-01
期刊：
影响因子：
1.9
通讯作者：
Huang, Chiung-Yu
中科院分区：
文献类型：
--
作者：
Cheng, Yu-Jen;Huang, Chiung-Yu
当生存时间左截断并且基础截断时间随机变量均匀分布时，生存数据会受到长度偏差采样的影响。通过将有关截断时间分布的信息纳入估计过程中，可以实现显着的效率增益 [Wang (1989) Journal of the American Statistical Association84, 742-748；王（1996）Biometrika83，343-354]。在半参数变换模型下，最大似然法预计是完全有效的，但由于完全似然法以复杂的方式依赖于非参数分量，因此很难实现。此外，其渐近性质尚未确定。在本文中，我们扩展了鞅估计方程方法 [Chen 等人。 (2002) Biometrika89, 659-668;金等人。 (2013) 美国统计协会杂志 108, 217-227] 和伪部分似然方法 [Severini 和 Wong (1992) 统计年鉴 4, 1768-1802； Zucker (2005) Journal of the American Statistical Association100, 1264-1277] 用于使用右删失数据处理左截断和右删失数据的半参数变换模型。本着复合似然法[Huang andqin (2012) Journal of the American Statistical Association107, 946-957]的相同精神，我们利用长度偏差采样的特殊概率结构进一步构造了另一组无偏估计方程。因此，估计方程的数量超过了参数的数量，并且可以通过求解这些估计方程的简单组合来实现效率增益。所提出的方法很容易实现，因为它们不需要额外的编程工作。此外，它们被证明是一致的并且渐近正态分布。痴呆症研究的数据分析说明了这些方法。
Survival data are subject to length-biased sampling when the survival times are left-truncated and the underlying truncation time random variable is uniformly distributed. Substantial efficiency gains can be achieved by incorporating the information about the truncation time distribution in the estimation procedure [Wang (1989) Journal of the American Statistical Association84, 742-748; Wang (1996) Biometrika83, 343-354]. Under the semiparametric transformation models, the maximum likelihood method is expected to be fully efficient, yet it is difficult to implement because the full likelihood depends on the nonparametric component in a complicated way. Moreover, its asymptotic properties have not been established. In this article, we extend the martingale estimating equation approach [Chen et al. (2002) Biometrika89, 659-668; Kim et al. (2013) Journal of the American Statistical Association108, 217-227] and the pseudo-partial likelihood approach [Severini and Wong (1992) The Annals of Statistics4, 1768-1802; Zucker (2005) Journal of the American Statistical Association100, 1264-1277] for semiparametric transformation models with right-censored data to handle left-truncated and right-censored data. In the same spirit of the composite likelihood method [Huang and Qin (2012) Journal of the American Statistical Association107, 946-957], we further construct another set of unbiased estimating equations by exploiting the special probability structure of length-biased sampling. Thus the number of estimating equations exceeds the number of parameters, and efficiency gains can be achieved by solving a simple combination of these estimating equations. The proposed methods are easy to implement as they do not require additional programming efforts. Moreover, they are shown to be consistent and asymptotically normally distributed. A data analysis of a dementia study illustrates the methods.