Prentice R L, Kalbfleisch J D, Peterson A V, Flournoy N, Farewell V T, Breslow N E
Biometrics. 1978 Dec;34(4):541-54.
Distinct problems in the analysis of failure times with competing causes of failure include the estimation of treatment or exposure effects on specific failure types, the study of interrelations among failure types, and the estimation of failure rates for some causes given the removal of certain other failure types. The usual formation of these problems is in terms of conceptual or latent failure times for each failure type. This approach is criticized on the basis of unwarranted assumptions, lack of physical interpretation and identifiability problems. An alternative approach utilizing cause-specific hazard functions for observable quantities, including time-dependent covariates, is proposed. Cause-specific hazard functions are shown to be the basic estimable quantities in the competing risks framework. A method, involving the estimation of parameters that relate time-dependent risk indicators for some causes to cause-specific hazard functions for other causes, is proposed for the study of interrelations among failure types. Further, it is argued that the problem of estimation of failure rates under the removal of certain causes is not well posed until a mechanism for cause removal is specified. Following such a specification, one will sometimes be in a position to make sensible extrapolations from available data to situations involving cause removal. A clinical program in bone marrow transplantation for leukemia provides a setting for discussion and illustration of each of these ideas. Failure due to censoring in a survivorship study leads to further discussion.
在分析具有竞争失效原因的失效时间时，存在一些独特的问题，包括估计治疗或暴露对特定失效类型的影响、研究失效类型之间的相互关系，以及在去除某些其他失效类型的情况下估计某些原因的失效率。这些问题通常是根据每种失效类型的概念性或潜在失效时间来形成的。这种方法因存在无端假设、缺乏物理解释和可识别性问题而受到批评。本文提出了一种替代方法，该方法利用针对可观测数量（包括随时间变化的协变量）的特定原因风险函数。特定原因风险函数被证明是竞争风险框架中的基本可估计量。本文提出了一种方法，用于研究失效类型之间的相互关系，该方法涉及估计将某些原因的随时间变化的风险指标与其他原因的特定原因风险函数相关联 的参数。此外，本文认为，在指定原因去除机制之前，去除某些原因时的失效率估计问题并未得到妥善解决。遵循这样的规范，有时人们能够从现有数据合理推断到涉及原因去除的情况。白血病骨髓移植的临床项目为讨论和说明这些观点提供了背景。生存研究中因删失导致的失效引发了进一步的讨论。
