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Using Cholesky Decomposition to Explore Individual Differences in Longitudinal Relations between Reading Skills
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Individual prediction regions for multivariate longitudinal data with small samples.

D Concordet1, R Servien1

  • 1INRA-ENVT, UMR1331 Toxalim Research Centre in Food Toxicology, Université de Toulouse, F-31027 Toulouse, France.

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Summary

This study introduces a new method for jointly monitoring multiple correlated health variables over time, improving upon traditional single-variable approaches for personalized health assessments.

Keywords:
Corrected coverage rateLongitudinal follow‐upMultivariate mixed Gaussian modelPlug‐in estimatorPrediction regionReference intervals

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Area of Science:

  • Biostatistics
  • Longitudinal Data Analysis
  • Veterinary Medicine

Background:

  • Individualized follow-up in medicine and doping control uses reference intervals for single variables.
  • Current methods do not account for correlations between multiple health variables over time.
  • Personalized health monitoring requires methods that consider inter-variable relationships.

Purpose of the Study:

  • To develop a general method for jointly following up several correlated variables over time.
  • To provide a robust methodology for individualized health monitoring using multivariate data.
  • To address limitations of variable-by-variable follow-up in longitudinal health assessments.

Main Methods:

  • Utilized a multivariate linear mixed-effects model for joint follow-up of correlated variables.
  • Developed a method for estimating model parameters.
  • Derived asymptotic and small-sample individualized prediction regions for robust monitoring.

Main Results:

  • The proposed method allows for the joint follow-up of multiple correlated variables.
  • Asymptotic prediction regions are derived for large sample sizes.
  • Three alternative prediction regions are proposed and compared for improved performance with small sample sizes.

Conclusions:

  • The new methodology offers a significant advancement in personalized health monitoring by analyzing multiple correlated variables simultaneously.
  • The approach is applicable to various fields, including medical and doping controls.
  • The study demonstrates the method's utility through an illustration of kidney insufficiency follow-up in cats.