摘要
在实际应用数据中,我们所收集到的纵向数据可能受到测量上下限的影响,出现双侧删失的情形.此外,纵向数据的观测时间可能会携带响应变量部分的信息量.因此,在统计分析中,结合观测时间信息来分析双删失纵向数据十分必要.本文采用半参数回归模型来分析此类观测时间带信息的双删失纵向数据,通过构造鞅差估计方程来估计模型中的回归系数.同时,也指出参数估计量的渐近分布含有未知冗余参数.为进一步研究所得估计量的统计推断,本文应用随机加权方法计算估计量的渐近分布,并说明在给定样本下,随机加权估计的条件渐近分布与参数估计的渐近分布相同.为了计算参数的估计值,受交替乘子算法思想的启迪,本文建立一种新的参数计算算法,并通过数据模拟验证所提随机加权方法的可行性.最后,利用该模型分析临床试验中晚期大肠癌患者的生活质量数据,指出观测次数和治疗方法对患者生活质量有显著的影响.
In many statistical applications,longitudinal data may be doubly truncated by both the upper and the lower limits due to data collection methods,and the observation times may be informative to the responses.It is important to take into account this double truncating and observation times in the statistical analysis.In this paper,semiparametric regression models are introduced for the analysis of doubly truncated longitudinal data with informative observation times.A statistical procedure based on an estimation equation is proposed for the estimation of the parameters in the models,and a random weighting method is developed for the estimation of the variances of these parameter estimates while it avoids estimating complicated nuisance parameters.An algorithm based on the alternating direction method of multipliers is presented to compute these estimates in practical applications.The asymptotic properties of the proposed procedures are investigated and the simulation studies are performed to evaluate their finite sample performances.The proposed models and procedures are also applied to analyze a dataset from a clinical trial in patients with advanced colorectal cancer and the results show that the observation times and the treatment have significant effects on the patients’QoL(quality of life).
作者
王占锋
柳海娇
丁浩
涂冬生
吴耀华
Zhanfeng Wang;Haijiao Liu;Hao Ding;Dongsheng Tu;Yaohua Wu
出处
《中国科学：数学》
CSCD
北大核心
2023年第9期1253-1268,共16页
Scientia Sinica：Mathematica
基金
国家自然科学基金(批准号:11971457和12201601)
安徽省自然科学基金(批准号:1908085MA06和2208085QA06)
中央高等学校基本业务费(批准号:WK2040000035)
加拿大自然科学和工程研究委员会资助项目。
关键词
双删失数据
观测时间信息
纵向数据
随机加权
TOBIT模型
doubly censored data
informative observation times
longitudinal data
random weighting
Tobit model
