The Annals of Applied Statistics

Early diagnosis of neurological disease using peak degeneration ages of multiple biomarkers

Fei Gao, Yuanjia Wang, and Donglin Zeng

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Neurological diseases are due to the loss of structure or function of neurons that eventually leads to cognitive deficit, neuropsychiatric symptoms, and impaired activities of daily living. Identifying sensitive and specific biological and clinical markers for early diagnosis allows recruiting patients into a clinical trial to test therapeutic intervention. However, many biomarker studies considered a single biomarker at one time that fails to provide precise prediction for disease age at onset. In this paper, we use longitudinally collected measurements from multiple biomarkers and measurement error-corrected clinical diagnosis ages to identify which biomarkers and what features of biomarker trajectories are useful for early diagnosis. Specifically, we assume that the subject-specific biomarker trajectories depend on unobserved states of underlying latent variables with the conditional mean follows a nonlinear sigmoid shape. We show that peak degeneration age of the biomarker trajectory is useful for early diagnosis. We propose an Expectation-Maximization (EM) algorithm to obtain the maximum likelihood estimates of all parameters and conduct extensive simulation studies to examine the performance of the proposed methods. Finally, we apply our methods to studies of Alzheimer’s disease and Huntington’s disease and identify a few important biomarkers that can be used for early diagnosis.

Article information

Ann. Appl. Stat., Volume 13, Number 2 (2019), 1295-1318.

Received: May 2018
Revised: December 2018
First available in Project Euclid: 17 June 2019

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Alzheimer’s disease Huntington’s disease inflection point measurement error nonlinear mixed effects model sigmoid function


Gao, Fei; Wang, Yuanjia; Zeng, Donglin. Early diagnosis of neurological disease using peak degeneration ages of multiple biomarkers. Ann. Appl. Stat. 13 (2019), no. 2, 1295--1318. doi:10.1214/18-AOAS1236.

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Supplemental materials

  • Supplement A: Supplement to “Early diagnosis of neurological disease using peak degeneration ages of multiple biomarkers”. This supplement provides additional information on the theorem and proof on model identifiability, protocol for simulation studies, details on estimating the magnitude of measurement error, and residual plots of the examples.
  • Supplement B: R codes. Codes for the EM algorithm and simulation illustrating the proposed methods.