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Polynomials with asymptotes for longitudinal data

R H Jones1

  • 1Department of Preventive Medicine and Biometrics, School of Medicine, University of Colorado Health Sciences Center, Denver 80262, USA.

Statistics in Medicine
|January 15, 1996
PubMed
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Laguerre polynomials model asymptotic growth curves, particularly for non-monotonic surgical recovery data. This longitudinal mixed-effects model accounts for subject variability and time-dependent factors.

Area of Science:

  • Biostatistics
  • Longitudinal Data Analysis
  • Mathematical Modeling

Background:

  • Growth and time-response curves often exhibit asymptotic behavior.
  • Modeling non-monotonic recovery data, such as post-surgical variables, presents challenges due to unknown functional forms.
  • Longitudinal studies require methods that account for repeated measures and individual differences.

Purpose of the Study:

  • To introduce Laguerre polynomials as a flexible tool for modeling asymptotic growth and time-response curves.
  • To demonstrate the application of these polynomials within a longitudinal data mixed-effects model framework.
  • To analyze complex, non-monotonic recovery patterns observed in surgical patients.

Main Methods:

  • Utilized Laguerre polynomials to define the functional form of the curves.

Related Experiment Videos

  • Employed a longitudinal data mixed-effects model to incorporate random subject effects.
  • Accounted for within-subject serial correlation and included fixed or time-varying covariates.

    • Main Results:

    • Laguerre polynomials effectively modeled the asymptotic nature of the growth curves.
    • The mixed-effects model successfully captured individual variability and temporal dependencies in surgical recovery data.
    • Demonstrated the model's utility with two distinct examples of patient recovery trajectories.

    Conclusions:

    • Laguerre polynomials provide a robust and adaptable method for analyzing time-response data approaching an asymptote.
    • The proposed longitudinal mixed-effects modeling approach is suitable for complex, non-monotonic biological recovery processes.
    • This methodology enhances the understanding of patient recovery dynamics in clinical settings.