广西师范大学学报（自然科学版） ›› 2025, Vol. 43 ›› Issue (5): 175-184.doi: 10.16088/j.issn.1001-6600.2024090302

• 数学与统计学 • 上一篇    下一篇

偏态纵向数据和生存数据的贝叶斯联合建模

汪韫頔, 戴家佳*, 毛围   

  1. 贵州大学 数学与统计学院,贵州 贵阳 550000
  • 收稿日期:2024-09-03 修回日期:2024-12-24 出版日期:2025-09-05 发布日期:2025-08-05
  • 通讯作者: 戴家佳(1976—),女,贵州黔西人,贵州大学教授,博士。E-mail:jjdai@gzu.edu.cn
  • 基金资助:
    国家自然科学基金(12361057)

Bayesian Joint Modeling of Skewed-Longitudinal and Survival Data

WANG Yundi, DAI Jiajia*, MAO Wei   

  1. School of Mathematics and Statistics, Guizhou University, Guizhou Guiyang 550000, China
  • Received:2024-09-03 Revised:2024-12-24 Online:2025-09-05 Published:2025-08-05

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摘要： 在纵向数据分析中,模型误差的正态性是一种常规假设,但这一假设可能违背真实数据特征。此外,忽略纵向数据与生存数据之间的相关性可能会造成分析结果的偏差。为解决这些问题,本文首先提出一种贝叶斯联合模型,纵向过程使用误差项服从Skew-t分布的线性混合效应模型进行建模,生存过程使用Cox比例风险模型;然后,通过Metropolis-Hastings(MH)算法和Gibbs抽样对联合模型中的未知参数进行贝叶斯估计,数值模拟结果表明:与传统估计方法相比,Skew-t方法在数据拟合方面表现出更优的性能;最后,将该方法应用于AIDS数据分析,经验证,该方法能够达到良好的拟合效果和准确的参数估计。

关键词: 纵向数据, 生存数据, Skew-t分布, 贝叶斯估计, AIDS数据

Abstract: In longitudinal data analysis, the normality of model errors is a common assumption; however, this assumption may contradict the true characteristics of the data. Additionally, overlooking the correlation between longitudinal data and survival data can lead to biased analytical results. To address these issues, this paper proposes a Bayesian joint model: the longitudinal process is modeled using a linear mixed-effects model with error terms following a Skew-t distribution, while the survival process employs a Cox proportional hazards model. Bayesian estimation of the unknown parameters in the joint model is conducted using the Metropolis-Hastings (MH) algorithm and Gibbs sampling. Numerical simulation results indicate that the Skew-t method demonstrates superior performance in data fitting compared with the traditional estimation methods. Finally, this methodology is applied to the analysis of AIDS data, and validation confirms that it provides good fitting results and accurate parameter estimates.

Key words: longitudinal data, survival data, Skew-t distribution, Bayesian estimation, AIDS data

中图分类号:  O212.8

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