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Bayesian Joint Modeling Analysis of Longitudinal Proportional and Survival Data

Author

Listed:
  • Wenting Liu

    (Yunnan Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming 650091, China)

  • Huiqiong Li

    (Yunnan Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming 650091, China)

  • Anmin Tang

    (Yunnan Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming 650091, China)

  • Zixin Cui

    (Yunnan Key Laboratory of Statistical Modeling and Data Analysis, Yunnan University, Kunming 650091, China)

Abstract

This paper focuses on a joint model to analyze longitudinal proportional and survival data. We utilize a logit transformation on the longitudinal proportional data and employ a partially linear mixed-effect model. With this model, we estimate the unknown function of time using the B-splines technique. Additionally, we introduce a centered Dirichlet process mixture model (CDPMM) to capture the random effects, allowing for a flexible distribution. The survival data are assumed using a Cox proportional hazard model, and the sharing random effects joint model is developed for the two types of data. We develop a Bayesian Lasso (BLasso) approach that combines the Gibbs sampler and the Metropolis–Hastings algorithm. The proposed method allows for the estimation of unknown parameters and the selection of significant covariates simultaneously. We evaluate the performance of our proposed methods through simulation studies and also provide an illustration of our methodologies using an example from the MA.5 research experiment.

Suggested Citation

  • Wenting Liu & Huiqiong Li & Anmin Tang & Zixin Cui, 2023. "Bayesian Joint Modeling Analysis of Longitudinal Proportional and Survival Data," Mathematics, MDPI, vol. 11(16), pages 1-17, August.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:16:p:3469-:d:1214801
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    References listed on IDEAS

    as
    1. Barndorff-Nielsen, O. E. & Jørgensen, B., 1991. "Some parametric models on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 106-116, October.
    2. Hui Song & Yingwei Peng & Dongsheng Tu, 2017. "Jointly modeling longitudinal proportional data and survival times with an application to the quality of life data in a breast cancer trial," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 23(2), pages 183-206, April.
    3. Yang, Mingan & Dunson, David B. & Baird, Donna, 2010. "Semiparametric Bayes hierarchical models with mean and variance constraints," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2172-2186, September.
    4. Chris Hans, 2009. "Bayesian lasso regression," Biometrika, Biometrika Trust, vol. 96(4), pages 835-845.
    5. Zhenguo Qiu & Peter X.‐K. Song & Ming Tan, 2008. "Simplex Mixed‐Effects Models for Longitudinal Proportional Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 577-596, December.
    6. Peter Xue-Kun Song & Ming Tan, 2000. "Marginal Models for Longitudinal Continuous Proportional Data," Biometrics, The International Biometric Society, vol. 56(2), pages 496-502, June.
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