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Comparison of alternative regression models for paired binary data

R J Glynn1, B Rosner

  • 1Department of Medicine, Harvard Medical School, Boston, MA.

Statistics in Medicine
|May 30, 1994
PubMed
Summary
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Standard logistic regression is less effective for paired ophthalmologic data than methods accounting for eye correlation. No single advanced method outperformed others across all tested conditions, highlighting the need for careful selection in paired binary data analysis.

Area of Science:

  • Ophthalmology
  • Biostatistics
  • Statistical Modeling

Background:

  • Paired binary data, common in ophthalmology (e.g., fellow eyes), presents unique analytical challenges due to inherent correlation.
  • Standard logistic regression methods may not adequately account for this correlation, potentially leading to biased results or reduced statistical power.
  • Evaluating alternative statistical approaches is crucial for accurate analysis of correlated ophthalmologic outcomes.

Purpose of the Study:

  • To assess the performance of various logistic regression models for analyzing paired binary ophthalmologic data.
  • To compare standard logistic regression against marginal and conditional logistic regression approaches that account for inter-eye correlation.

Main Methods:

  • Simulated ophthalmologic data, based on real-world examples, was utilized for performance evaluation.

Related Experiment Videos

  • Compared standard logistic regression (ignoring correlation, using most impaired eye, or right eye only) with marginal (Lipsitz, Laird & Harrington; Liang & Zeger) and conditional (Rosner; Connolly & Liang) models.
  • Taylor series approximations were employed to compare parameter estimates between marginal and conditional models.

    • Main Results:

    • Standard logistic regression demonstrated inferior performance regarding Type I and II error rates compared to methods that incorporated inter-eye correlation.
    • Methods accounting for the correlation between fellow eyes outperformed standard approaches.
    • No single advanced method (marginal or conditional) was consistently superior across all simulated conditions evaluated.

    Conclusions:

    • Statistical methods that acknowledge the correlation between fellow eyes are essential for accurate analysis of paired ophthalmologic binary data.
    • Standard logistic regression is suboptimal for such data.
    • The choice of advanced logistic regression model for paired data requires careful consideration of specific study conditions, as no single method is universally best.