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Fitting marginal models in small samples: A simulation study of marginalized multilevel models and generalized

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Summary

For analyzing correlated data, generalized estimating equations (GEE) and marginalized multilevel models (MMMs) offer distinct approaches. In small samples, MMMs show sensitivity to correlation misspecification, while GEE with corrections provides more reliable inference.

Keywords:
cluster correlated datacluster randomized trialsgeneralized estimating equationsmarginalized multilevel modelssmall sample bias

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Area of Science:

  • Statistics
  • Biostatistics
  • Econometrics

Background:

  • Analysts often choose between conditional and marginal models for correlated data.
  • Generalized Estimating Equations (GEE) and Marginalized Multilevel Models (MMMs) are two frameworks for estimating population-averaged parameters.
  • Theoretical comparisons exist, but small-sample performance is less understood.

Purpose of the Study:

  • To compare the small-sample performance of GEE and MMMs.
  • To guide analysts in choosing appropriate models for correlated data in practice.
  • To evaluate bias and standard error estimation in small sample sizes.

Main Methods:

  • Comprehensive simulation studies were conducted.
  • GEE and MMMs were fitted under various correlation structure specifications.
  • Small-sample bias and standard error estimation were analyzed.

Main Results:

  • Both GEE and MMMs showed similar small-sample bias when the correlation structure was correctly specified or moderately misspecified.
  • MMMs were sensitive to correlation structure misspecification.
  • In small clusters, MMMs underestimated standard errors for between-cluster associations.
  • GEE severely underestimated standard errors, but the Mancl and DeRouen correction improved inference.

Conclusions:

  • MMMs may be unreliable with misspecified correlation structures in small samples.
  • GEE with the Mancl and DeRouen correction offers more robust inference for small-sample correlated data.
  • Model choice should consider potential correlation misspecification and sample size.