The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
No rationale for 1 variable per 10 events criterion for binary logistic regression analysis
Open accessAbstract
BACKGROUND: Ten events per variable (EPV) is a widely advocated minimal criterion for sample size considerations in logistic regression analysis. Of three previous simulation studies that examined this minimal EPV criterion only one supports the use of a minimum of 10 EPV. In this paper, we examine the reasons for substantial differences between these extensive simulation studies. METHODS: The current study uses Monte Carlo simulations to evaluate small sample bias, coverage of confidence intervals and mean square error of logit coefficients. Logistic regression models fitted by maximum likelihood and a modified estimation procedure, known as Firth's correction, are compared. RESULTS: The results show that besides EPV, the problems associated with low EPV depend on other factors such as the total sample size. It is also demonstrated that simulation results can be dominated by even a few simulated data sets for which the prediction of the outcome by the covariates is perfect ('separation'). We reveal that different approaches for identifying and handling separation leads to substantially different simulation results. We further show that Firth's correction can be used to improve the accuracy of regression coefficients and alleviate the problems associated with separation. CONCLUSIONS: The current evidence supporting EPV rules for binary logistic regression is weak. Given our findings, there is an urgent need for new research to provide guidance for supporting sample size considerations for binary logistic regression analysis.
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Cites
A simulation study of the number of events per variable in logistic regression analysis
Peduzzi, P., Concato, J., Kemper, E., Holford, T. R., & Feinstein, A. R. (1996) · Journal of Clinical Epidemiology · doi:10.1016/s0895-4356(96)00236-3 · Cited by 9,655
Moons, K. G. M., Altman, D. G., Reitsma, J. B., Ioannidis, J. P. A., Macaskill, P., Steyerberg, E. W., Vickers, A. J., Ransohoff, D. F., & Collins, G. S. (2015) · Annals of Internal Medicine · doi:10.7326/m14-0698 · Cited by 5,147
Self-citationRelaxing the Rule of Ten Events per Variable in Logistic and Cox Regression
Vittinghoff, E., & McCulloch, C. E. (2007) · American Journal of Epidemiology · doi:10.1093/aje/kwk052 · Cited by 4,359
Logistic Regression in Rare Events Data
King, G., & Zeng, L. (2001) · Political Analysis · doi:10.1093/oxfordjournals.pan.a004868 · Cited by 4,316 · cited 1×
“This over-optimism is commonly referred to as finite sample bias [24], and is well described in statistics literature [3, 7].”
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
Moons, K. G. M., de Groot, J. A. H., Bouwmeester, W., Vergouwe, Y., Mallett, S., Altman, D. G., Reitsma, J. B., & Collins, G. S. (2014) · PLoS Medicine · doi:10.1371/journal.pmed.1001744 · Cited by 2,018 · cited 2×
“EPV, which is thought to be a key determinant of the performance of logistic regression models, is frequently used in sample size considerations and as a methodological quality item for critically appraising published studies [9–11].”
Self-citationVergouwe, Y., Steyerberg, E. W., Eijkemans, M. J. C., & Habbema, J. D. F. (2005) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2004.06.017 · Cited by 636
Self-citationBias in odds ratios by logistic regression modelling and sample size
Nemes, S., Jonasson, J. M., Genell, A., & Steineck, G. (2009) · BMC Medical Research Methodology · doi:10.1186/1471-2288-9-56 · Cited by 437
Cited by
Collins, G. S., Moons, K. G. M., Dhiman, P., Riley, R. D., Beam, A. L., Van Calster, B., Ghassemi, M., Liu, X., Reitsma, J. B., van Smeden, M., et al. (2024) · BMJ · doi:10.1136/bmj-2023-078378 · Cited by 4,718
“61 93 Therefore, TRIPOD+AI has embedded items on fairness throughout, including in the background (item 3c), methods (items 5a, 7, 8a, 8b, 9c, 12f, 14), results (items 20b, 23a), and discussion (items 25, 26).”
Self-citationCalculating the sample size required for developing a clinical prediction model
Riley, R. D., Ensor, J., Snell, K. I. E., Harrell, F. E., Martin, G. P., Reitsma, J. B., Moons, K. G. M., Collins, G., & van Smeden, M. (2020) · BMJ · doi:10.1136/bmj.m441 · Cited by 2,917
Moons, K. G. M., Wolff, R. F., Riley, R. D., Whiting, P. F., Westwood, M., Collins, G. S., Reitsma, J. B., Kleijnen, J., & Mallett, S. (2019) · Annals of Internal Medicine · doi:10.7326/m18-1377 · Cited by 1,669
Self-citationRiley, R. D., Snell, K. I., Ensor, J., Burke, D. L., Harrell Jr, F. E., Moons, K. G., & Collins, G. S. (2019) · Statistics in Medicine · doi:10.1002/sim.7992 · Cited by 1,409
Self-citationMoons, K. G. M., Damen, J. A. A., Kaul, T., Hooft, L., Andaur Navarro, C., Dhiman, P., Beam, A. L., Van Calster, B., Celi, L. A., Denaxas, S., et al. (2025) · BMJ · doi:10.1136/bmj-2024-082505 · Cited by 1,069
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Metadata
- Authors
- van Smeden, M., de Groot, J. A. H., Moons, K. G. M., Collins, G. S., Altman, D. G., Eijkemans, M. J. C., & Reitsma, J. B.
- Venue
- BMC Medical Research Methodology
- Published
- 2016-11-24
- Volume
- 16
- Issue
- 1
- Pages
- 163-163
- ISSN
- 1471-2288 (ISSN-L)
- OpenAlex
- W2553734051
- Cited by
- 595
- References
- 8
- FWCI
- 18.50
- Type
- journal article
- Language
- en
- Open access
- gold
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