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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2026, Vol. 43 ›› Issue (2): 373-382.doi: 10.3969/j.issn.1005-3085.2026.02.012cstr: 32411.14.cjem.CN61-1269/O1.2026.02.012

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区间删失型数据下相依AFT模型的参数估计

赵  煜1,2,  候苗苗1   

  1. 1. 兰州财经大学统计与数据科学学院，兰州  730020
    2. 甘肃经济发展数量分析研究中心，兰州 730020
  • 收稿日期:2024-12-27 接受日期:2025-11-09 出版日期:2026-04-15 发布日期:2026-06-15
  • 基金资助:
    国家社会科学基金西部项目 (21XTJ004).

Parameter Estimation of Dependent AFT Model with Interval Censored Data

ZHAO Yu1,2,  HOU Miaomiao1   

  1. 1. School of Statistics and Data Science, Lanzhou University of Finance and Economics, Lanzhou 730020
    2. Center for Quantitative Analysis of Gansu Economic Development, Lanzhou 730020
  • Received:2024-12-27 Accepted:2025-11-09 Online:2026-04-15 Published:2026-06-15
  • Supported by:
    The National Social Science Foundation Western Project (21XTJ004).

摘要：

在生存分析领域，区间删失数据是常见的数据类型。基于K型区间删失响应变量和区间删失型协变量，构建相依加速失效时间模型来研究失效时间与删失时间存在的相依关系。在该模型中，采用多项式核函数表述失效时间和删失时间的未知关系，并采用Pólya Tree分布对区间删失型协向量进行逼近，运用极大似然估计方法估计参数。模拟实验结果显示，该方法在不同情况下均取得较好效果，且当协向量彼此具有较强相关性时，非线性模型能够较好地拟合失效时间与删失时间的关系。最后，将所提出的方法和模型应用于临床试验数据进一步验证了其有效性。

关键词: 加速失效时间模型, K型区间删失, 相依关系, 删失时间, 多项式核函数

Abstract:

In the field of survival analysis, interval censored data is a common data type. Based on the K-type interval censored response variable and the interval censored covarites, the dependent accelerated failure time model is constructed. The dependence relationship between the failure time and the censored time is studied. In this model, the polynomial kernel function is used to express the unknown relationship between the failure time and the censoring time. The Pólya Tree distribution is used to approximate the interval censored covarites. Moreover, the maximum likelihood estimation method is adopted to estimate the parameters. The simulation results show that the method achieves good results in different cases, and the nonlinear model can better fit the relationship between failure time and censoring time when the covarites have strong correlation with each other. Finally, the proposed method and model are applied to clinical trial data to further verify its effectiveness.

Key words: accelerated failure time model, K-type interval censored, interdependent relationship, censored time, polynomial kernel function

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