基于模型平均的右删失数据下加速失效时间模型的统计推断研究  

Statistical Inference for the Accelerated Failure Time Model with Right-censored Data Based on Model Averaging

作　　者：王淑影 张亚男 程云飞 WANG Shu-ying;ZHANG Ya-nan;CHENG Yun-fei(School of Mathematics and Statistics,Changchun University of Technology,Changchun 130012,China)

机构地区：[1]长春工业大学数学与统计学院,吉林长春130012

出　　处：《统计与信息论坛》2022年第12期3-9,共7页Journal of Statistics and Information

基　　金：国家自然科学基金青年项目“带有相依观测过程的混合型区间删失数据的统计推断研究”(11901054);中国博士后科学基金面上项目“基于时变模型的相依混合区间删失数据的统计推断及应用”(2021M700536);吉林省博士后择优资助项目。

摘　　要：在生物统计研究领域中,经常会由于各种原因出现数据删失的情况。此时研究人员不能精确观测到某个个体的确切失效时间,只能观测到生存时间大于删失时间,即右删失数据。相对于比例风险模型和可加风险模型,由于加速失效时间(AFT)模型更具有解释性,因此考虑采用AFT模型来对右删失数据进行建模。传统的AFT模型都是在协变量给定的情况下进行统计推断研究,这样可能会导致估计结果不准确。克服这种问题的有效途径是使用模型平均方法,通过对候选模型的估计量进行加权,可以减少估计的均方误差,稳健性更强。据此,从避免指定协变量构建模型引起的不准确性入手,针对右删失数据提出一种基于模型平均方法的加速失效时间模型。在极大似然估计方法的框架下,采用基于信息准则的模型平均方法进行参数估计及预测研究。数值模拟结果显示,在右删失数据下基于模型平均方法的AFT模型估计精度高于模型选择方法下的参数估计精度,证实了在右删失数据下使用模型平均方法可以得到更准确更稳健的估计结果。实例部分采用一组肺癌数据进行分析,结果显示基于模型平均方法的加速失效时间模型预测精度更高,进一步说明了模型平均方法的优势。In the research fields of economics, biomedicine, clinical trials and so on, censored data often occurs for various reasons.As the polular alternative model of proportional hazards model, AFT model, which directly models the linear relationship between covariates and log survival time, is considered to model the right-censored data.In the process of traditional AFT model construction, statistical inference research is often carried out under the assumption of given covariates.Then the uncertainty property will be ignored.And to deal with the problem, the model averaging method is introduced.By weighting the estimators of the candidate models, the mean square error of the estimation can be reduced and the robustness is stronger.In the framework of maximum likelihood estimation method, the model averaging method based on information criterion is used for parameter estimation and prediction.The numerical simulation results show that the estimation accuracy of AFT model based on model averaging method is higher than that of parameter estimation under model selection method under right-censored data.In the example part, a group of lung cancer data is used for analysis.The results show that the prediction accuracy of the accelerated failure time model based on the model averaging method is higher, which further explains the advantages of the model averaging method.

关 键 词：模型平均 右删失数据 加速失效时间模型 极大似然估计 

分 类 号：O212[理学—概率论与数理统计]