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Hélène Jacqmin-Gadda1, Cécile Proust-Lima, Hélène Amiéva

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This study introduces a novel semi-parametric threshold model for analyzing longitudinal ordinal and discrete data. The model effectively captures cognitive changes over time in Alzheimer

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Area of Science:

  • Biostatistics
  • Neuroscience
  • Longitudinal Data Analysis

Background:

  • Ordinal and quantitative discrete data are common in biomedical and neuropsychological research.
  • Analyzing changes in such data over time in longitudinal studies presents statistical challenges.
  • Existing models may not adequately capture the complex dynamics of cognitive decline.

Purpose of the Study:

  • To propose a novel semi-parametric threshold model for analyzing longitudinal ordinal and discrete data.
  • To model the time-course of cognitive scores in individuals at risk for Alzheimer's disease.
  • To flexibly account for correlations in repeated measures within a longitudinal study design.

Main Methods:

  • A threshold model is defined, linking observed outcomes to an underlying Gaussian latent process.
  • The latent process is modeled using a Gaussian linear mixed model with a non-parametric function of time (f(t)).
  • Penalized likelihood estimation with cubic-spline approximation is used for parameter and f(t) estimation; an approximate cross-validation criterion estimates the smoothing parameter.

Main Results:

  • The proposed model was applied to the Paquid cohort data, analyzing cognitive scores over 14 years.
  • The time-course of cognitive changes was compared between future Alzheimer's patients and a matched healthy group.
  • Confidence bands were computed for estimated curves of the latent process and the outcome.

Conclusions:

  • The semi-parametric threshold model provides a flexible framework for analyzing longitudinal discrete data.
  • The method allows for detailed comparison of cognitive trajectories in disease progression studies.
  • The approach is applicable to understanding long-term changes in cognitive function in at-risk populations.