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A simulation study of sample size for multilevel logistic regression models.

Rahim Moineddin1, Flora I Matheson, Richard H Glazier

  • 1Department of Public Health Sciences, University of Toronto, Toronto, Canada. rahim.moineddin@utoronto.ca

BMC Medical Research Methodology
|July 20, 2007
PubMed
Summary
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For multilevel logistic regression models, aim for at least 50 groups with 50 individuals each for accurate estimates. Low prevalence events require larger sample sizes, ensuring more than one event per group.

Area of Science:

  • Health and social sciences research
  • Statistical modeling

Background:

  • Many health and social science studies feature hierarchical data structures (e.g., patients within physicians).
  • Binary outcomes (e.g., disease presence/absence) are common in these multilevel studies.
  • Determining adequate sample size for accurate multilevel model estimates is crucial.

Purpose of the Study:

  • To assess how individual and group sample sizes impact the accuracy of multilevel logistic regression models.
  • To examine the influence of outcome prevalence and intra-class correlation coefficient (ICC) on model estimates.

Main Methods:

  • Simulation studies were conducted to evaluate parameter and variance component estimation.
  • Sample sizes at both individual and group levels were systematically varied.

Related Experiment Videos

  • The effect of outcome prevalence and ICC was analyzed.
  • Main Results:

    • Fixed effect parameter estimates are unbiased with ≥100 groups and ≥50 individuals per group.
    • Variance component estimates show slight bias even with 100 groups and 50 individuals per group.
    • Biases are severe with a group size of 5; standard errors for variance components are underestimated.

    Conclusions:

    • A minimum of 50 groups with 50 individuals per group is recommended for valid multilevel logistic regression estimates.
    • For low prevalence events, increase group size to ensure >1 expected event per group.
    • Adjust sample size based on outcome prevalence for reliable results.