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FLCRM: Functional linear cox regression model

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  • Dehan Kong
  • Joseph G. Ibrahim
  • Eunjee Lee
  • Hongtu Zhu

Abstract

Summary We consider a functional linear Cox regression model for characterizing the association between time†to†event data and a set of functional and scalar predictors. The functional linear Cox regression model incorporates a functional principal component analysis for modeling the functional predictors and a high†dimensional Cox regression model to characterize the joint effects of both functional and scalar predictors on the time†to†event data. We develop an algorithm to calculate the maximum approximate partial likelihood estimates of unknown finite and infinite dimensional parameters. We also systematically investigate the rate of convergence of the maximum approximate partial likelihood estimates and a score test statistic for testing the nullity of the slope function associated with the functional predictors. We demonstrate our estimation and testing procedures by using simulations and the analysis of the Alzheimer's Disease Neuroimaging Initiative (ADNI) data. Our real data analyses show that high†dimensional hippocampus surface data may be an important marker for predicting time to conversion to Alzheimer's disease. Data used in the preparation of this article were obtained from the ADNI database (adni.loni.usc.edu).

Suggested Citation

  • Dehan Kong & Joseph G. Ibrahim & Eunjee Lee & Hongtu Zhu, 2018. "FLCRM: Functional linear cox regression model," Biometrics, The International Biometric Society, vol. 74(1), pages 109-117, March.
    • Handle: RePEc:bla:biomet:v:74:y:2018:i:1:p:109-117
    DOI: 10.1111/biom.12748
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    References listed on IDEAS

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    Cited by:

    1. Cai Li & Luo Xiao & Sheng Luo, 2022. "Joint model for survival and multivariate sparse functional data with application to a study of Alzheimer's Disease," Biometrics, The International Biometric Society, vol. 78(2), pages 435-447, June.
    2. Wu Wang & Ying Sun & Huixia Judy Wang, 2023. "Latent group detection in functional partially linear regression models," Biometrics, The International Biometric Society, vol. 79(1), pages 280-291, March.
    3. Xifen Huang & Jinfeng Xu & Yunpeng Zhou, 2022. "Profile and Non-Profile MM Modeling of Cluster Failure Time and Analysis of ADNI Data," Mathematics, MDPI, vol. 10(4), pages 1-21, February.
    4. Tao Sun & Ying Ding, 2023. "Neural network on interval‐censored data with application to the prediction of Alzheimer's disease," Biometrics, The International Biometric Society, vol. 79(3), pages 2677-2690, September.
    5. Shu Jiang & Yijun Xie & Graham A. Colditz, 2021. "Functional ensemble survival tree: Dynamic prediction of Alzheimer’s disease progression accommodating multiple time‐varying covariates," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 70(1), pages 66-79, January.
    6. Marta Spreafico & Francesca Ieva & Marta Fiocco, 2023. "Modelling time-varying covariates effect on survival via functional data analysis: application to the MRC BO06 trial in osteosarcoma," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(1), pages 271-298, March.
    7. Sudaraka Tholkage & Qi Zheng & Karunarathna B. Kulasekera, 2022. "Conditional Kaplan–Meier Estimator with Functional Covariates for Time-to-Event Data," Stats, MDPI, vol. 5(4), pages 1-17, November.
    8. Yue Wang & Joseph G. Ibrahim & Hongtu Zhu, 2020. "Partial least squares for functional joint models with applications to the Alzheimer's disease neuroimaging initiative study," Biometrics, The International Biometric Society, vol. 76(4), pages 1109-1119, December.
    9. Ruiyuan Cao & Jiang Du & Jianjun Zhou & Tianfa Xie, 2020. "FPCA-based estimation for generalized functional partially linear models," Statistical Papers, Springer, vol. 61(6), pages 2715-2735, December.

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