A solution to the problem of separation in logistic regression

A solution to the problem of separation in logistic regression 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Statistics in Medicine Wiley

A solution to the problem of separation in logistic regression

Statistics in Medicine, Volume 21 (16) – Aug 30, 2002

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Publisher
Wiley
Copyright
Copyright © 2002 John Wiley & Sons, Ltd.
ISSN
0277-6715
eISSN
1097-0258
D.O.I.
10.1002/sim.1047
Publisher site
See Article on Publisher Site

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.

Journal

Statistics in MedicineWiley

Published: Aug 30, 2002

References

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