Jiang Fei, Haneuse Sebastien
Department of Statistics, University of South Carolina.
Department of Biostatistics, Harvard University.
Scand Stat Theory Appl. 2017 Mar;44(1):112-129. doi: 10.1111/sjos.12244. Epub 2016 Aug 31.
In the analysis of semi-competing risks data interest lies in estimation and inference with respect to a so-called non-terminal event, the observation of which is subject to a terminal event. Multi-state models are commonly used to analyse such data, with covariate effects on the transition/intensity functions typically specified via the Cox model and dependence between the non-terminal and terminal events specified, in part, by a unit-specific shared frailty term. To ensure identifiability, the frailties are typically assumed to arise from a parametric distribution, specifically a Gamma distribution with mean 1.0 and variance, say, σ. When the frailty distribution is misspecified, however, the resulting estimator is not guaranteed to be consistent, with the extent of asymptotic bias depending on the discrepancy between the assumed and true frailty distributions. In this paper, we propose a novel class of transformation models for semi-competing risks analysis that permit the non-parametric specification of the frailty distribution. To ensure identifiability, the class restricts to parametric specifications of the transformation and the error distribution; the latter are flexible, however, and cover a broad range of possible specifications. We also derive the semi-parametric efficient score under the complete data setting and propose a non-parametric score imputation method to handle right censoring; consistency and asymptotic normality of the resulting estimators is derived and small-sample operating characteristics evaluated via simulation. Although the proposed semi-parametric transformation model and non-parametric score imputation method are motivated by the analysis of semi-competing risks data, they are broadly applicable to any analysis of multivariate time-to-event outcomes in which a unit-specific shared frailty is used to account for correlation. Finally, the proposed model and estimation procedures are applied to a study of hospital readmission among patients diagnosed with pancreatic cancer.
在对半竞争风险数据的分析中，关注点在于对所谓的非终端事件进行估计和推断，对该事件的观察受到终端事件的影响。多状态模型通常用于分析此类数据，协变量对转移/强度函数的影响通常通过Cox模型指定，非终端事件和终端事件之间的依赖性部分通过单位特定的共享脆弱项指定。为确保可识别性，通常假设脆弱性来自参数分布，具体而言是均值为1.0且方差为σ（比如说）的伽马分布。然而，当脆弱性分布被错误指定时，所得估计量不能保证是一致的，渐近偏差的程度取决于假设的和真实的脆弱性分布之间的差异。在本文中，我们提出了一类用于半竞争风险分析的新型变换模型，该模型允许对脆弱性分布进行非参数指定。为确保可识别性，该类模型限制为变换和误差分布的参数指定；不过，后者具有灵活性，涵盖了广泛的可能指定。我们还推导了完全数据设置下的半参数有效得分，并提出了一种非参数得分插补方法来处理右删失；推导了所得估计量的一致性和渐近正态性，并通过模拟评估了小样本操作特性。尽管所提出的半参数变换模型和非参数得分插补方法是由半竞争风险数据分析推动的，但它们广泛适用于任何多变量事件发生时间结果的分析，其中使用单位特定的共享脆弱性来考虑相关性。最后，将所提出的模型和估计程序应用于一项对诊断为胰腺癌患者的医院再入院研究。
