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A comparative investigation of methods for logistic regression with separated or nearly separated data
Abstract
In logistic regression analysis of small or sparse data sets, results obtained by classical maximum likelihood methods cannot be generally trusted. In such analyses it may even happen that the likelihood meets the convergence criteria while at least one parameter estimate diverges to ±∞. This situation has been termed ‘separation’, and it typically occurs whenever no events are observed in one of the two groups defined by a dichotomous covariate. More generally, separation is caused by a linear combination of continuous or dichotomous covariates that perfectly separates events from non‐events. Separation implies infinite or zero maximum likelihood estimates of odds ratios, which are usually considered unrealistic. I provide some examples of separation and near‐separation in clinical data sets and discuss some options to analyse such data, including exact logistic regression analysis and a penalized likelihood approach. Both methods supply finite point estimates in case of separation. Profile penalized likelihood confidence intervals for parameters show excellent behaviour in terms of coverage probability and provide higher power than exact confidence intervals. General advantages of the penalized likelihood approach are discussed. Copyright © 2006 John Wiley & Sons, Ltd.
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Cites
Bias reduction of maximum likelihood estimates
FIRTH, D. (1993) · Biometrika · doi:10.1093/biomet/80.1.27 · Cited by 5,035
A solution to the problem of separation in logistic regression
Heinze, G., & Schemper, M. (2002) · Statistics in Medicine · doi:10.1002/sim.1047 · Cited by 2,711
Self-citation(2008) · The Concise Encyclopedia of Statistics · doi:10.1007/978-0-387-32833-1_5 · Cited by 2,670
Collett, D. (1991) · Springer eBooks · doi:10.1007/978-1-4899-4475-7 · Cited by 1,936
On the existence of maximum likelihood estimates in logistic regression models
ALBERT, A., & ANDERSON, J. A. (1984) · Biometrika · doi:10.1093/biomet/71.1.1 · Cited by 1,153
A method for computing profile-likelihood-based confidence intervals
Venzon, D. J., & Moolgavkar, S. H. (1988) · Applied Statistics · doi:10.2307/2347496 · Cited by 565
Exact logistic regression: Theory and examples
Mehta, C. R., & Patel, N. R. (1995) · Statistics in Medicine · doi:10.1002/sim.4780141908 · Cited by 481
Wald's Test as Applied to Hypotheses in Logit Analysis
Hauck, W. W., & Donner, A. (1977) · Journal of the American Statistical Association · doi:10.1080/01621459.1977.10479969 · Cited by 392
Computing Distributions for Exact Logistic Regression
Hirji, K. F., Mehta, C. R., & Patel, N. R. (1987) · Journal of the American Statistical Association · doi:10.1080/01621459.1987.10478547 · Cited by 311
Bias Correction in Generalized Linear Models
Cordeiro, G. M., & McCullagh, P. (1991) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1991.tb01852.x · Cited by 306
Medical conditions increasing the risk of chronic thromboembolic pulmonary hypertension
Bonderman, D., Jakowitsch, J., Adlbrecht, C., Schemper, M., Kyrle, P., Schönauer, V., Exner, M., Klepetko, W., Kneussl, M., Maurer, G., et al. (2005) · Thrombosis and Haemostasis · doi:10.1160/th04-10-0657 · Cited by 296
Wald's Test as Applied to Hypotheses in Logit Analysis
Hauck, W. W., & Donner, A. (1977) · Journal of the American Statistical Association · doi:10.2307/2286473 · Cited by 178
High expression of lipoprotein lipase in poor risk B-cell chronic lymphocytic leukemia
Heintel, D., Kienle, D., Shehata, M. M., Kröber, A., Kroemer, E., Schwarzinger, I., Mitteregger, D., Le, T., Gleiß, A., Mannhalter, C., et al. (2005) · Leukemia · doi:10.1038/sj.leu.2403748 · Cited by 153
Efficient Monte Carlo Methods for Conditional Logistic Regression
Mehta, C. R., Patel, N. R., & Senchaudhuri, P. (2000) · Journal of the American Statistical Association · doi:10.1080/01621459.2000.10473906 · Cited by 107
King, E. N., & Ryan, T. P. (2002) · The American Statistician · doi:10.1198/00031300283 · Cited by 94
Bias correction in maximum likelihood logistic regression
Schaefer, R. L. (1983) · Statistics in Medicine · doi:10.1002/sim.4780020108 · Cited by 94
Median Unbiased Estimation for Binary Data
Hirji, K. F., Tsiatis, A. A., & Mehta, C. R. (1989) · The American Statistician · doi:10.1080/00031305.1989.10475597 · Cited by 93
A permutation test for inference in logistic regression with small‐ and moderate‐sized data sets
Potter, D. M. (2004) · Statistics in Medicine · doi:10.1002/sim.1931 · Cited by 91
Gorak, E. J., Geller, N. L., Srinivasan, R., Espinoza‐Delgado, I., Donohue, T., Barrett, A. J., Suffredini, A. F., & Childs, R. W. (2005) · Transplantation and Cellular Therapy · doi:10.1016/j.bbmt.2005.04.009 · Cited by 71
Gulyaeva, N., Zaslavsky, A., Lechner, P., Chlenov, M. A., McConnell, O. J., Chait, A., Kipnis, V., & Zaslavsky, B. Y. (2003) · European Journal of Medicinal Chemistry · doi:10.1016/s0223-5234(03)00044-8 · Cited by 71
Fixing the nonconvergence bug in logistic regression with SPLUS and SAS
Heinze, G., & Ploner, M. (2003) · Computer Methods and Programs in Biomedicine · doi:10.1016/s0169-2607(02)00088-3 · Cited by 70
Self-citationCAUCHEMEZ, B., Extramiana, F., Cauchemez, S., Cosson, S., ZOUZOU, H., Meddane, M., d’Allonnes, L. R., Lavergne, T., Leenhardt, A., Coumel, P., et al. (2004) · Journal of Cardiovascular Electrophysiology · doi:10.1046/j.1540-8167.2004.03401.x · Cited by 65
Improving on exact tests by approximate conditioning
Pierce, D. A. (1999) · Biometrika · doi:10.1093/biomet/86.2.265 · Cited by 32
JACKKNIFE BIAS REDUCTION FOR POLYCHOTOMOUS LOGISTIC REGRESSION
Bull, S. B., Greenwood, C. M. T., & Hauck, W. W. (1997) · Statistics in Medicine · Cited by 22
On bias reduction in exponential and non-exponential family regression models
Cordeiro, G. M., & Cribari‐Neto, F. (1998) · Communications in Statistics - Simulation and Computation · doi:10.1080/03610919808813491 · Cited by 19
Bias Reduction using Stochastic Approximation
Leung, D. H. Y., & Wang, Y. (1998) · Australian & New Zealand Journal of Statistics · doi:10.1111/1467-842x.00005 · Cited by 17
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Metadata
- Authors
- Heinze, G.
- Venue
- Statistics in Medicine
- Publisher
- Wiley
- Published
- 2006-09-06
- Volume
- 25
- Issue
- 24
- Pages
- 4216-4226
- ISSN
- 0277-6715 (ISSN-L)
- 1097-0258
- OpenAlex
- W1964838085
- Cited by
- 379
- References
- 26
- FWCI
- 4.27
- Type
- journal article
- Language
- en
- Open access
- closed
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