偏态纵向数据和生存数据的贝叶斯联合建模

doi:10.16088/j.issn.1001-6600.2024090302

Abstract

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

CLC Number: O212.8

WANG Yundi, DAI Jiajia, MAO Wei. Bayesian Joint Modeling of Skewed-Longitudinal and Survival Data[J].Journal of Guangxi Normal University(Natural Science Edition), 2025, 43(5): 175-184.

References

[1] GE L, TU J X, ZHANG H, et al. Modern methods for longitudinal data analysis, capabilities, caveats and cautions[J]. Shanghai Archives of Psychiatry, 2016, 28(5): 293-300. DOI: 10.11919/j.issn.1002-0829. 216081.
[2] FAUCETT C L, THOMAS D C. Simultaneously modelling censored survival data and repeatedly measured covariates: a Gibbs sampling approach[J]. Statistics in Medicine, 1996, 15(15): 1663-1685.
[3] IBRAHIM J G, CHU H T, CHEN L M. Basic concepts and methods for joint models of longitudinal and survival data[J]. Journal of Clinical Oncology, 2010, 28(16): 2796-2801. DOI: 10.1200/JCO.2009.25.0654.
[4] WULFSOHN M S, TSIATIS A A. A joint model for survival and longitudinal data measured with error[J]. Biometrics, 1997, 53(1): 330-339.
[5] AIRY G B. On the algebraical and numerical theory of errors of observations and the combination of observations[M]. 2nd ed. London: Macmillan,1861.
[6] HANSEN B E. Stochastic equicontinuity for unbounded dependent heterogeneous arrays[J]. Econometric Theory, 1996, 12(2): 347-359. DOI: 10.1017/s0266466600006629.
[7] CHEN G, LUO S. Bayesian hierarchical joint modeling using skew-normal/independent distributions[J]. Communications in Statistics-Simulation and Computation, 2018, 47(5): 1420-1438. DOI: 10.1080/03610918.2017.1315730.
[8] 李世君, 唐国强, 杜诗雪. 基于Skew-t-GJRGARCH(1, 1)模型的5G板块风险度量研究[J]. 广西师范大学学报(自然科学版), 2020, 38(5): 56-63. DOI: 10.16088/j.issn.1001-6600.2020.05.007.
[9] 聂晓璐, 冯国双. 生存分析及其应用中的注意事项[J]. 慢性病学杂志, 2016, 17(10): 1065-1066, 1073. DOI: 10.16440/j.cnki.1674-8166.2016.10.001.
[10] 肖媛媛, 陈莹, 何利平, 等. 不同删失比例下AFT模型与Cox模型表现比较的模拟研究[J]. 中国卫生统计, 2017, 34(4): 676-680.
[11] 刘娟, 蔡婷婷, 胡涛. 左截断右删失数据下OLLGG分布的参数估计[J]. 首都师范大学学报(自然科学版), 2024, 45(1): 29-36. DOI: 10.19789/j.1004-9398.2024.01.004.
[12] BROWN E R, IBRAHIM J G. A Bayesian semiparametric joint hierarchical model for longitudinal and survival data[J]. Biometrics, 2003, 59(2): 221-228. DOI: 10.1111/1541-0420.00028.
[13] MARTINS R, SILVA G L, ANDREOZZI V. Bayesian joint modeling of longitudinal and spatial survival AIDS data[J]. Statistics in Medicine, 2016, 35(19): 3368-3384. DOI: 10.1002/sim.6937.
[14] ZHANG D J, CHEN M H, IBRAHIM J G, et al. Bayesian model assessment in joint modeling of longitudinal and survival data with applications to cancer clinical trials[J]. Journal of Computational and Graphical Statistics, 2017, 26(1): 121-133. DOI: 10.1080/10618600.2015.1117472.
[15] 舒婷, 罗幼喜, 李翰芳. 面板数据贝叶斯双惩罚分位回归方法研究[J]. 广西师范大学学报(自然科学版), 2022, 40(1): 150-165. DOI: 10.16088/j.issn.1001-6600.2021060917.
[16] 孙烨, 蒋京京, 王纯杰. 广义极值回归模型下现状数据的贝叶斯估计[J]. 广西师范大学学报(自然科学版), 2022, 40(1): 82-90. DOI: 10.16088/j.issn.1001-6600.2021060907.
[17] SAHU S K, DEY D K, BRANCO M D. A new class of multivariate skew distributions with applications to Bayesian regression models[J]. Canadian Journal of Statistics, 2003, 31(2): 129-150. DOI: 10.2307/3316064.
[18] LEONARD T, HSU J S J. Bayesian methods: an analysis for statisticians and interdisciplinary researchers[M]. Cambridge: Cambridge University Press, 2001.
[19] BENDER R, AUGUSTIN T, BLETTNER M. Generating survival times to simulate Cox proportional hazards models[J]. Statistics in Medicine, 2005, 24(11): 1713-1723. DOI: 10.1002/sim.2059.
[20] RIZOPOULOS D. The R package JMbayes for fitting joint models for longitudinal and time-to-event data using MCMC[J]. Journal of Statistical Software, 2016, 72(7): 1-46. DOI: 10.18637/jss.v072.i07.
[21] GOLDMAN A I, CARLIN B P, CRANE L R, et al. Response of CD4 lymphocytes and clinical consequences of treatment using ddI or ddC in patients with advanced HIV infection[J]. Journal of Acquired Immune Deficiency Syndromes and Human Retrovirology, 1996, 11(2): 161-169. DOI: 10.1097/00042560-199602010-00007.

Metrics

Viewed

Full text

Abstract

Cited

Shared

Discussed

Comments

Recommended 10

[1]	ZHONG Qiao, CHEN Shenglong, TANG Congcong. Hydrogel Technology for Microalgae Collection: Status Overview, Challenges and Development Analysis[J]. Journal of Guangxi Normal University(Natural Science Edition), 2024, 42(6): 16 -29 .
[2]	SHI Huilu, MO Yanhua, LUO Haiyu, MA Jiangming. Inhibitory Activity of Ethyl Acetate Extracts of Loropetalum chinense against Pathogens[J]. Journal of Guangxi Normal University(Natural Science Edition), 2025, 43(1): 1 -8 .
[3]	HE Qing, LI Dong, LUO Siyuan, HE Yudong, LI Biao, WANG Qiang. Research Progress in Ultra-wideband Rydberg Atomic Antenna Technology[J]. Journal of Guangxi Normal University(Natural Science Edition), 2025, 43(2): 1 -19 .
[4]	HUANG Renhui, ZHANG Ruifeng, WEN Xiaohao, BI Jinjie, HUANG Shoulin, LI Tinghui. Complex-value Covariance-based Convolutional Neural Network for Decoding Motor Imagery-based EEG Signals[J]. Journal of Guangxi Normal University(Natural Science Edition), 2025, 43(3): 43 -56 .
[5]	TIAN Sheng, XIONG Chenyin, LONG Anyang. Point Cloud Classification Method of Urban Roads Based on Improved PointNet++[J]. Journal of Guangxi Normal University(Natural Science Edition), 2025, 43(4): 1 -14 .
[6]	LI Zongxiao, ZHANG Jian, LUO Xinyue, ZHAO Yifei, LU Fei. Research on Arrival Trajectory Prediction Based on K-means and Adam-LSTM[J]. Journal of Guangxi Normal University(Natural Science Edition), 2025, 43(4): 15 -23 .
[7]	SONG Mingkai, ZHU Chengjie. Research on Fault Location of Distribution Network Based on H-WOA-GWO and Region Correction Strategies[J]. Journal of Guangxi Normal University(Natural Science Edition), 2025, 43(4): 24 -37 .
[8]	HAN Shuo, JIANG Linfeng, YANG Jianbin. Attention-based PINNs Method for Solving Saint-Venant Equations[J]. Journal of Guangxi Normal University(Natural Science Edition), 2025, 43(4): 58 -68 .
[9]	LI Zhixin, KUANG Wenlan. Fine-grained Image Classification Combining Adaptive Spatial Mutual Attention and Feature Pair Integration Discrimination[J]. Journal of Guangxi Normal University(Natural Science Edition), 2025, 43(4): 69 -82 .
[10]	SHI Tianyi, NAN Xinyuan, GUO Xiangyu, ZHAO Pu, CAI Xin. Improved ConvNeXt-based Algorithm for Apple Leaf Disease Classification[J]. Journal of Guangxi Normal University(Natural Science Edition), 2025, 43(4): 83 -96 .

Bayesian Joint Modeling of Skewed-Longitudinal and Survival Data

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 5

Metrics

Comments

Recommended 10

[1]	ZHU Yan, CAI Jing, LONG Fang. Statistical Analysis of Partially Step Stress Accelerated Life Tests for Compound Rayleigh Distribution Competing Failure Model Under Progressive Type-Ι Hybrid Censoring [J]. Journal of Guangxi Normal University(Natural Science Edition), 2024, 42(3): 159-169.
[2]	LONG Fang, CAI Jing, ZHU Yan. Analysis of Reliability in a Multicomponent Stress-Strength Model for Lomax Distribution under Progressive type-Ⅱ Hybrid Censoring [J]. Journal of Guangxi Normal University(Natural Science Edition), 2024, 42(2): 120-130.
[3]	SUN Ye, JIANG Jingjing, WANG Chunjie. Bayesian Estimation of Current Status Data with Generalized Extreme Value Regression Model [J]. Journal of Guangxi Normal University(Natural Science Edition), 2022, 40(1): 82-90.
[4]	LIN Song, YIN Changming. Asymptotic Properties of Estimation of Penalized Generalized Estimating Equations for Two Stage Logit Models [J]. Journal of Guangxi Normal University(Natural Science Edition), 2019, 37(2): 126-130.
[5]	DING Xin-yue, XU Mei-ping. Bayesian Estimation for Scale Parameter of Inverse Gamma Distribution under Mlinex Loss Function [J]. Journal of Guangxi Normal University(Natural Science Edition), 2014, 32(3): 61-64.