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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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    1. Johnstone, Iain M. & Lu, Arthur Yu, 2009. "On Consistency and Sparsity for Principal Components Analysis in High Dimensions," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 682-693.
    2. Li, Yehua & Wang, Naisyin & Carroll, Raymond J., 2010. "Generalized Functional Linear Models With Semiparametric Single-Index Interactions," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 621-633.
    3. Patrick J. Heagerty & Yingye Zheng, 2005. "Survival Model Predictive Accuracy and ROC Curves," Biometrics, The International Biometric Society, vol. 61(1), pages 92-105, March.
    4. Philip T. Reiss & R. Todd Ogden, 2010. "Functional Generalized Linear Models with Images as Predictors," Biometrics, The International Biometric Society, vol. 66(1), pages 61-69, March.
    5. Hervé Cardot & Frédéric Ferraty & André Mas & Pascal Sarda, 2003. "Testing Hypotheses in the Functional Linear Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 241-255, March.
    6. Reiss, Philip T. & Ogden, R. Todd, 2007. "Functional Principal Component Regression and Functional Partial Least Squares," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 984-996, September.
    7. Peter Hall & Mohammad Hosseini‐Nasab, 2006. "On properties of functional principal components analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 109-126, February.
    8. Tianxi Cai & Giulia Tonini & Xihong Lin, 2011. "Kernel Machine Approach to Testing the Significance of Multiple Genetic Markers for Risk Prediction," Biometrics, The International Biometric Society, vol. 67(3), pages 975-986, September.
    9. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    10. Dehan Kong & Ana-Maria Staicu & Arnab Maity, 2016. "Classical testing in functional linear models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(4), pages 813-838, October.
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.

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