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No rationale for 1 variable per 10 events criterion for binary logistic regression analysis.

Maarten van Smeden1, Joris A H de Groot2, Karel G M Moons2

  • 1Julius Center for Health Sciences and Primary Care, University Medical Center Utrecht, Heidelberglaan 100, Utrecht, The Netherlands. M.vanSmeden@umcutrecht.nl.

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|November 25, 2016
PubMed
Summary
This summary is machine-generated.

The minimal 10 events per variable (EPV) rule for logistic regression is not well-supported. Simulation studies show sample size and data separation significantly impact results, suggesting a need for new guidance.

Keywords:
BiasEPVLogistic regressionSample sizeSeparationSimulations

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Area of Science:

  • Statistics
  • Biostatistics
  • Epidemiology

Background:

  • The "10 events per variable" (EPV) rule is a common guideline for sample size in logistic regression.
  • Previous simulation studies have yielded conflicting results regarding the validity of the 10 EPV minimum.
  • This study investigates the reasons behind discrepancies in simulation findings concerning EPV criteria.

Purpose of the Study:

  • To evaluate the impact of sample size and data characteristics on logistic regression model performance.
  • To compare maximum likelihood estimation with Firth's correction in scenarios with limited events per variable.
  • To identify factors influencing simulation results and the phenomenon of "separation" in logistic regression.

Main Methods:

  • Monte Carlo simulations were employed to assess bias, confidence interval coverage, and mean square error.
  • Logistic regression models were fitted using both standard maximum likelihood and Firth's bias-corrected method.
  • The influence of "separation" (perfect prediction) on simulation outcomes was specifically examined.

Main Results:

  • Low EPV issues are influenced by factors beyond EPV, including total sample size.
  • Simulation results are sensitive to "separation," where covariates perfectly predict the outcome.
  • Different methods for handling separation yield divergent simulation results.
  • Firth's correction improves coefficient accuracy and mitigates separation-related problems.

Conclusions:

  • The empirical evidence supporting the 10 EPV rule for binary logistic regression is weak.
  • Sample size calculations for logistic regression require considering factors beyond simple EPV ratios.
  • Further research is urgently needed to establish robust guidelines for sample size determination in binary logistic regression.