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Related Experiment Videos

Longitudinal data analysis for linear Gaussian models with random disturbed-highest-derivative-polynomial subject

P D Wilson1

  • 1Department of Epidemiology & Preventive Medicine, School of Medicine, University of Maryland at Baltimore 21201, USA.

Statistics in Medicine
|June 15, 1995
PubMed
Summary

A new disturbed highest derivative polynomial (DHDP) model generalizes random effects models for longitudinal data. This approach accounts for non-linear time trends and serial correlation, offering a robust analysis of population-averaged effects.

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Area of Science:

  • Statistics
  • Biostatistics
  • Longitudinal Data Analysis

Background:

  • Traditional random effects models for longitudinal data assume deterministic polynomial random effects.
  • These models may not fully capture complex within-subject time trends and dependencies.

Purpose of the Study:

  • To propose a novel generalization of random effects models for longitudinal data.
  • To introduce disturbed highest derivative polynomials (DHDPs) to model complex subject-specific time trends and induce serial correlation.

Main Methods:

  • Generalizing random effects models by adding Gaussian disturbances to polynomial coefficients.
  • Analyzing data using a marginal model for a population-averaged interpretation.
  • Selecting the DHDP order using an information criterion.

Related Experiment Videos

  • Exploring the relationship between DHDPs and smoothing polynomial splines.

    • Main Results:

    • The DHDP model allows for non-linear subject-specific time trends and induces serial correlation.
    • The model provides a population-averaged interpretation through marginal analysis.
    • The optimal DHDP order can be selected via an information criterion.
    • The DHDP model can be replaced by a smoothing polynomial spline model.

    Conclusions:

    • The proposed DHDP model offers a flexible extension to traditional random effects models for longitudinal data.
    • This method enhances the modeling of within-subject dependence and population-averaged trends.
    • DHDPs provide a valuable alternative for analyzing complex longitudinal patterns.