信息右删失数据下比例风险模型的估计问题

Proportional Hazard Model Analysis for Informative Right-Censored Data

  • 摘要: 在生存分析中, 对右删失数据问题的研究常假设删失时间与失效时间相互独立. 然而研究者经常要面对非独立删失的问题, 即删失时间与失效时间可能相互关联并彼此影响, 尤其表现在临床试验中. 如果不考虑这种相关性, 便无法得到生存函数的有效估计. 针对这种相依结构已有很多处理方法, 其中连接函数因结构简单而尤为受到关注. 本文主要对信息右删失数据下比例风险模型的相关估计问题进行了研究. 利用阿基米德连接函数对删失时间和失效时间的联合分布函数进行假定, 在连接函数参数的可识别条件下, 得到了连接函数的参数、比例风险模型参数以及基准累积风险函数的极大似然估计, 并通过模拟计算的方法验证了估计方法的可行性以及估计量的有效性.

     

    Abstract: In survival analysis, most existing approaches for analysing right-censored failure time data assume that the censoring time is independent of the failure time. However, investigators often face problems involving dependent censoring, i.e., failure time and censoring time are possibly dependent and they may be censored one another, especially in clinical trials. Without accounting for such dependence, survival distributions cannot be estimated consistently. Numerous attempts to model this dependence have been made. Among them, copula models are of particular interest because of their simple structure. Proportional hazard model analysis for informative right-censored data has been discussed in this paper. An Archimedean copula is assumed for the joint distribution function of failure time and censoring time variables. Under the conditions of identifiability of the parameter of the Archimedean copula, the maximum likelihood estimators of the parameter of Archimedean copula, the parameters and the cumulative hazard function of PH model are worked out. Extensive simulation studies show that the feasibility of the proposed method and the consistency of the estimators.

     

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