Heinze G, Schemper M. A solution to the problem of separation in logistic regression. Stat Med 21: 2409-2419

Section of Clinical Biometrics, Department of Medical Computer Sciences, University of Vienna, Spitalgasse 23, A-1090 Vienna, Austria.
Statistics in Medicine (Impact Factor: 1.83). 08/2002; 21(16):2409-19. DOI: 10.1002/sim.1047
Source: PubMed


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.

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Available from: Georg Heinze, Dec 22, 2014
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