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Consistent estimation of a joint model for multivariate longitudinal and survival data with latent variables

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  • Kang, Kai
  • Song, Xinyuan

Abstract

The investigation of the relationship between a time-to-event outcome and time-dependent risk factors is often of great interest in longitudinal studies. However, the time-dependent risk factors may not be directly observed or simply measured by a single variable. Instead, they are latent and should be characterized by several observed variables from different aspects. In this article, we consider a novel joint modeling framework to examine the effects of latent time-dependent risk factors on the hazard of interest. A factor analysis model is used to depict the dependence between time-dependent latent variables and multivariate longitudinal observed variables, and a proportional hazard model is adopted for linking latent time-dependent factors to the hazard of interest. We develop a hybrid procedure that combines an asymptotically distribution-free generalized least square approach and a conditional score method. Theoretical results are provided on the consistency and asymptotic normality of parameter estimators. The method is evaluated through simulation studies and applied to a dataset about Alzheimer’s disease.

Suggested Citation

  • Kang, Kai & Song, Xinyuan, 2022. "Consistent estimation of a joint model for multivariate longitudinal and survival data with latent variables," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:jmvana:v:187:y:2022:i:c:s0047259x21001056
    DOI: 10.1016/j.jmva.2021.104827
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    References listed on IDEAS

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    1. Deng Pan & Haijin He & Xinyuan Song & Liuquan Sun, 2015. "Regression Analysis of Additive Hazards Model With Latent Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1148-1159, September.
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    6. Molei Liu & Jiehuan Sun & Jose D. Herazo-Maya & Naftali Kaminski & Hongyu Zhao, 2019. "Joint Models for Time-to-Event Data and Longitudinal Biomarkers of High Dimension," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 11(3), pages 614-629, December.
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