部分区间删失数据下时间相依威布尔比例风险模型的参数估计  

Parameter estimation using time-dependent Weibull proportional hazards model for survival analysis with partly interval censored data

作　　者：王淑影 刘新宇 李润东 李洋 WANG Shuying;LIU Xinyu;LI Rundong;LI Yang(School of Mathematics and Statistics,Changchun University of Technology,Changchun 130000,China)

机构地区：[1]长春工业大学数学与统计学院,吉林长春130000

出　　处：《南方医科大学学报》2024年第12期2461-2468,共8页Journal of Southern Medical University

基　　金：吉林省自然科学基金优秀青年项目(20230101371JC)。

摘　　要：目的针对临床研究中常见的部分区间删失数据,提出构建时间相依威布尔比例风险模型的参数估计问题,同时探讨不同协变量对生存时间的影响。方法以威布尔分布作为比例风险模型的基准风险函数,同时在模型中引入时变协变量,建立时间相依威布尔比例风险模型。为了估计模型的参数,采用极大似然方法,并通过优化函数得到参数的估计值。结果数值模拟结果表明,在不同样本量及不同参数设置下,精确观测的比例越高,参数估计效果更好,其覆盖率均近似达到理论预期的95%。此外,随着样本量增大,各参数偏差均呈现减小趋势。结论将该方法运用到实例数据中进一步验证模型的有效性,相较于仅有精准观测个体的失效时间数据,具有额外的区间删失数据有助于给出有效的回归参数估计。此外,与含时变协变量的Cox模型进行对比,进一步表明采用时间相依威布尔比例风险模型可给出有效的估计结果。Objective To assess the validity and effectiveness of parameter estimation using a time-dependent Weibull proportional hazards model for survival analysis containing partly interval censored data and explore the impact of different covariates on the results of analysis.Methods We established a time-dependent Weibull proportional hazards model using the Weibull distribution as the baseline hazard function of the model which incorporated time-varying covariates.Maximum likelihood estimation was employed to estimate the model parameters,which were obtained by optimization of the likelihood function.Results and Conclusion Numerical simulation results showed that with higher proportions of precise observations across different sample sizes and parameter settings,the proposed model resulted in improved accuracy of parameter estimation with coverage probabilities approximating the theoretical expectation of 95%.As the sample sizes increased,the parameter biases of the model tended to decrease.Experiments with empirical data further validated the effectiveness of the model.Compared with the failure time data for each precisely observed individual,additional interval-censored data helped to obtain more effective estimates of the regression parameters.Comparison with the Cox model that included time-varying covariates further demonstrated the effectiveness of the time-dependent Weibull proportional hazards model for parameter estimation in survival analysis with partly interval censored data.

关 键 词：部分区间删失数据 时间相依协变量 威布尔比例风险模型 似然函数 极大似然估计 

分 类 号：O212.1[理学—概率论与数理统计]