Cited by 2,711Statistical Methods in EpidemiologyStatistical Methods and Bayesian InferenceStatistical Methods and Inference

A solution to the problem of separation in logistic regression

Heinze, Georg, Schemper, Michael·2002·Statistics in Medicine

Abstract

The phenomenon of separation or monotone likelihood is observed in the fitting process of a logistic model if the likelihood converges while at least one parameter estimate diverges to ± infinity. Separation primarily occurs in small samples with several unbalanced and highly predictive risk factors. A procedure by Firth originally developed to reduce the bias of maximum likelihood estimates is shown to provide an ideal solution to separation. It produces finite parameter estimates by means of penalized maximum likelihood estimation. Corresponding Wald tests and confidence intervals are available but it is shown that penalized likelihood ratio tests and profile penalized likelihood confidence intervals are often preferable. The clear advantage of the procedure over previous options of analysis is impressively demonstrated by the statistical analysis of two cancer studies. Copyright © 2002 John Wiley & Sons, Ltd.

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Crossref · 10.1002/sim.1047

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Authors
Heinze, G., & Schemper, M.
Affiliations
University of Vienna (AT)
Corresponding author
Heinze, Georg
Venue
Statistics in Medicine
Publisher
Wiley
Published
2002-07-26
Volume
21
Issue
16
Pages
2409-2419
ISSN
  • 0277-6715 (ISSN-L)
  • 1097-0258
OpenAlex
W2013416277
Cited by
2,711
References
36
Citations by year
2026: 770 · 2025: 160 · 2024: 159 · 2023: 147 · 2022: 142 · 2021: 193 · 2020: 151 · 2019: 142 · 2018: 129 · 2017: 104 · 2016: 112 · 2015: 100 · 2014: 82 · 2013: 73 · 2012: 49
FWCI
7.98
Type
journal article
Language
en
Open access
closed
Locations
  • Statistics in Medicine (publishedVersion)
  • PubMed (publishedVersion)
Topics
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
  • Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Inference
Keywords
penalized likelihood, Wald test, likelihood ratio test, small sample bias
MeSH terms
Breast Neoplasms, Computer Simulation, Female, Humans, Lung Neoplasms, Monte Carlo Method, Neovascularization, Pathologic, Radiotherapy, Smoking, Likelihood Functions, Logistic Models, Case-Control Studies, Endometrial Neoplasms

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