双删失纵向数据的复合 Tobit 分位数亚组分析回归方法

数学物理学报 ›› 2025, Vol. 45 ›› Issue (3): 902-918.

双删失纵向数据的复合 Tobit 分位数亚组分析回归方法

王占锋¹(),王静瑶¹(),吴耀华¹(),明瑞星^2,^*()

¹中国科学技术大学管理学院合肥 230026
²浙江工商大学统计与数学学院杭州 310018

收稿日期:2024-11-01 修回日期:2025-01-26 出版日期:2025-06-26 发布日期:2025-06-20
通讯作者: *明瑞星, Email: rxming@zjgsu.edu.cn
作者简介:王占锋, Email: zfw@ustc.edu.cn;|王静瑶, Email: wjywjywjy@mail.ustc.edu.cn;|吴耀华, Email: wuyh@ustc.edu.cn
基金资助:
国家自然科学基金(12371277);国家自然科学基金(12231017);浙江省重点建设高校优势特色学科(Zhejiang Gongshang University-Statistics)

A Composite Tobit Quantile Subgroup Analysis Regression Approach Based on Doubly Censored Longitudinal Data

Wang Zhanfeng¹(),Wang Jingyao¹(),Wu Yaohua¹(),Ming Ruixing^2,^*()

¹School of Management, University of Science and Technology of China, Hefei 230026
²School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018

Received:2024-11-01 Revised:2025-01-26 Online:2025-06-26 Published:2025-06-20
Supported by:
NSFC(12371277);NSFC(12231017);characteristic & preponderant discipline of key construction universities in Zhejiang province(Zhejiang Gongshang University-Statistics)

摘要/Abstract

摘要：

临床试验中受试个体之间可能存在差异, 治疗效果通常具有异质性, 如何识别出对特定治疗敏感的人群成为精准医学领域中备受关注的问题之一. 另外, 由于测量方式或仪器往往受到上、下限的限制, 导致实际观测数据值被限制在一个区间内, 从而形成双删失数据.文章构建阈值纵向 Tobit 复合分位数回归模型来研究治疗敏感亚组识别问题, 以增强治疗敏感亚组的识别效果. 对于模型的参数, 借鉴交替乘子算法的思想, 建立计算参数估计量的方法; 并使用随机加权方法计算估计量的方差. 在一些正则条件下, 证明了参数估计量是相合的. 数值模拟研究表明文章的方法相较于单分位数回归方法更加有效, 并且验证了随机加权方法估计参数估计量方差的可行性. 最后, 分析了直肠癌症试验组 CO.17 数据, 识别出根据年龄划分的治疗敏感亚组.

关键词: 双删失数据, 纵向数据, 随机加权, Tobit 模型, 阈值回归, 复合分位数回归, 亚组分析

Abstract:

In clinical trials, there may be differences between individuals, and treatment effects are often heterogeneous, so how to identify the population sensitive to specific treatments has become one of the issues of great concern in the field of precision medicine. In addition, due to the limitation of upper and lower thresholds of measurement methods or instruments, the actual observed data values are usually limited to an interval, resulting in doubly censored data. In this paper, we construct a threshold longitudinal Tobit composite quantile regression model to study the problem of identifying treatment-sensitive subgroups, in order to enhance the identification effect of treatment-sensitive subgroups. For the parameters of the model, we borrow the idea of the Alternating Direction Method of Multipliers algorithm to establish a method for calculating the parameter estimators, and use the random weighting method to calculate the variance of the parameter estimators. Under some regular conditions, we prove the consistency of the parameter estimators. Numerical simulations show that the proposed method is more effective than the single quantile regression method, and verify the feasibility of the random weighting method in estimating the variance of the parameter estimators. Finally, the method proposed in this paper is applied to analyse the data of the CO.17 Trial, identifying the treatment-sensitive subgroups according to age.

Key words: doubly censored data, Longitudinal data, random weighting, Tobit model, threshold regression, composite quantile regression, subgroup analysis

中图分类号:

O213

王占锋, 王静瑶, 吴耀华, 明瑞星. 双删失纵向数据的复合 Tobit 分位数亚组分析回归方法[J]. 数学物理学报, 2025, 45(3): 902-918.

Wang Zhanfeng, Wang Jingyao, Wu Yaohua, Ming Ruixing. A Composite Tobit Quantile Subgroup Analysis Regression Approach Based on Doubly Censored Longitudinal Data[J]. Acta mathematica scientia,Series A, 2025, 45(3): 902-918.

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