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Functional linear regression model with randomly censored data: Predicting conversion time to Alzheimer ’s disease

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  • Yang, Seong J.
  • Shin, Hyejin
  • Lee, Sang Han
  • Lee, Seokho

Abstract

Predicting the onset time of Alzheimer’s disease is of great importance in preventive medicine. Structural changes in brain regions have been actively investigated in the association study of Alzheimer’s disease diagnosis and prognosis. In this study, we propose a functional linear regression model to predict the conversion time to Alzheimer’s disease among mild cognitive impairment patients. Midsagittal thickness change in corpus callosum is measured from magnetic resonance imaging scan and put into the model as a functional covariate. A synthetic response approach is taken to deal with the censored data. The simulation studies demonstrate that the proposed model successfully predicts the unobserved true survival time but indicate that high censoring rate may cause poor prediction in time. Through ADNI data application, we find that the atrophy in the rear area of corpus callosum is a possible neuroimaging marker on Alzheimer’s disease prognosis.

Suggested Citation

  • Yang, Seong J. & Shin, Hyejin & Lee, Sang Han & Lee, Seokho, 2020. "Functional linear regression model with randomly censored data: Predicting conversion time to Alzheimer ’s disease," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:csdana:v:150:y:2020:i:c:s0167947320301006
    DOI: 10.1016/j.csda.2020.107009
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    References listed on IDEAS

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    1. Yang, Seong Jun & El Ghouch, Anouar & Van Keilegom, Ingrid, 2014. "Varying coefficient models having different smoothing variables with randomly censored data," LIDAM Reprints ISBA 2014008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Ping Yu & Zhongzhan Zhang & Jiang Du, 2016. "A test of linearity in partial functional linear regression," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(8), pages 953-969, November.
    3. Francesco Bravo, 2014. "Varying coefficients partially linear models with randomly censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(2), pages 383-412, April.
    4. 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.
    5. Seokho Lee & Hyejin Shin & Sang Han Lee, 2016. "Label‐noise resistant logistic regression for functional data classification with an application to Alzheimer's disease study," Biometrics, The International Biometric Society, vol. 72(4), pages 1325-1335, December.
    6. Dehan Kong & Kaijie Xue & Fang Yao & Hao H. Zhang, 2016. "Partially functional linear regression in high dimensions," Biometrika, Biometrika Trust, vol. 103(1), pages 147-159.
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