运用Cox模型时打结数据的处理方法探讨

Discussion on Methods for Tied Survival Times in Cox Model

Cox回归模型是目前生存分析中最为广泛使用的方法之一,模型的假设之一是失效时间不存在打结情况,即个体之间有着不同的失效时间。在实际应用当中,生存时间数据存在打结是很常见的。目前有四种常见的处理方法:Exact法,discrete model法,Efron法以及Breslow法。本文研究目的是比较这四种处理方法的优劣。本文采用模拟进行比较,设置了不同的样本量和打结程度,比较四种方法在拟合统计量,计算时间,参数估计精确性等方面的表现,发现Exact法和discrete model拟合统计量结果最好,但计算耗时最久;Efron法以及Breslow法运算较快但是在参数估计方面存在偏差。另外,样本量和打结程度也影响处理的结果,总的来说,当结点数较小时,四种方法之间差别不大。当数据量较大或打结比例较高时,除exact以外的三种近似方法的偏差增加,但运算时间无明显变化,而exact法的运算时间迅速增加。此时如果估计的精确性没有估计时间那么重要,Efron法以及Breslow法是不错的选择,其中,Efron法更为精确而Breslow方法倾向于低估正确的β值。如果时间上没有限制,可以选择Exact法和discrete model,将得到更为精确的结果。

Cox regression model is one of the most widely used methods in the survival analysis. One assumption of this model is that there is no tie in the failure times, that is, individual has different failure times. In practical applications,the existence of ties in time data is very common. In this paper, four common methods of dealing with ties in Cox model,including Exact method, discrete model method, Efron method and Breslow method, were compared with simulation. The results showed that Exact method and discrete model were the best, but they took the longest time. Efron method and Breslow method were faster but there was a greater deviation in parameter estimation. Moreover, the sample amount and ties degree also affect the results. In general, when there are a few ties, the difference between four methods was small;and in the case of large datasets or a large number of ties, the bias of three approximation methods increased except Exact method. However, there was no significant change on computational time. While the computational time of the Exact method increased rapidly. Therefore, if the estimation precision is not as important as the estimation time, Efron method and Breslow method will be good choices. Efron method is more preferably as it is more precise. And Breslow methodtends to underestimate the true β. If there is no limit in time, Exact method and discrete model can be chosen to achievemore accurate results.