The DOI matches its Crossref record; 78 of the 80 references it cites were found in a registry or an index.
Calculating the sample size required for developing a clinical prediction model
Open accessAbstract
Clinical prediction models aim to predict outcomes in individuals, to inform diagnosis or prognosis in healthcare. Hundreds of prediction models are published in the medical literature each year, yet many are developed using a dataset that is too small for the total number of participants or outcome events. This leads to inaccurate predictions and consequently incorrect healthcare decisions for some individuals. In this article, the authors provide guidance on how to calculate the sample size required to develop a clinical prediction model.
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“In step three, the sample size needed to reduce model overfitting is calculated, assuming an expected shrinkage rate of 10%, with an expected number of variables P to be included in the final predictive model of 30: S is the expected shrinkage factor, and the noise ratio evaluation index R2cs is 0.3; the calculated sample size is 740 cases.”
From Machine learning-driven prediction model for successful weaning of patients from mechanical ventilation in ICU (2026) · cites this paper as Riley [13]
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In the citing paper
“Genomic and molecular data support integration of tumour biology and genetic risk into decision-making, particularly in precision medicine applications [42].”
From Artificial Intelligence in Clinical Decision-Making: A Comprehensive Review of Diagnostic, Prognostic, and Therapeutic Applications, Validation Gaps, Bias, and Deployment Challenges (2026) · cites this paper as [42]
Experimental — accuracy not yet measuredIn the citing paper
“The sample size calculated this way is the minimum for a standard statistical model.”
From Developing clinical prediction models: a step-by-step guide (2024) · cites this paper as [50]
In the citing paper
“Sample size calculations50 indicated a minimum sample of 2082 patients, which is larger than the available sample, raising concerns about possible overfitting issues (step 6).”
From Developing clinical prediction models: a step-by-step guide (2024) · cites this paper as [50]
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Citations
Cites
Regression shrinkage and selection via the lasso
Tibshirani, R. (1996) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1996.tb02080.x · Cited by 51,482
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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
Harrell (2015) · Springer Series in Statistics · doi:10.1007/978-3-319-19425-7 · Cited by 6,878
A note on a general definition of the coefficient of determination
NAGELKERKE, N. J. D. (1991) · Biometrika · doi:10.1093/biomet/78.3.691 · Cited by 5,927
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
Clinical Prediction Models: A Practical Approach to Development, Validation, and Updating
Steyerberg, E. W. (2019) · Statistics for Biology and Health · doi:10.1007/978-3-030-16399-0 · Cited by 3,281
PROBAST: A Tool to Assess the Risk of Bias and Applicability of Prediction Model Studies
Wolff, R. F., Moons, K. G. M., Riley, R. D., Whiting, P. F., Westwood, M., Collins, G. S., Reitsma, J. B., Kleijnen, J., Mallett, S., & for the PROBAST Group† (2019) · Annals of Internal Medicine · doi:10.7326/m18-1376 · Cited by 2,984
Self-citation
Research works printed but not linked: 2
- 10.1177/962280218784726 · DOI
- McFadden, 1974, Frontiers in Econometrics New York., 104
Cited by
Sorted by citations
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
Wynants, L., Van Calster, B., Bonten, M. M., Collins, G. S., Debray, T. P., De Vos, M., Haller, M. C., Heinze, G., Moons, K. G., Riley, R. D., et al. (2020) · doi:10.1101/2020.03.24.20041020 · Cited by 3,070
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
Self-citationKnight, S. R., Ho, A. Y. W., Pius, R., Buchan, I. E., Carson, G., Drake, T. M., Dunning, J. W., Fairfield, C. J., Gamble, C. L., Green, C., et al. (2020) · BMJ · doi:10.1136/bmj.m3339 · Cited by 1,039
Evaluation of clinical prediction models (part 1): from development to external validation
Collins, G. S., Dhiman, P., Ma, J., Schlussel, M. M., Archer, L., Van Calster, B., Harrell, F. E., Martin, G. P., Moons, K. G. M., van Smeden, M., et al. (2024) · BMJ · doi:10.1136/bmj-2023-074819 · Cited by 798
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Metadata
- Authors
- 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.
- Affiliations
- Keele University (GB)
- Vanderbilt University (US)
- Manchester Academic Health Science Centre (GB)
- University Medical Center Utrecht (NL)
- Corresponding author
- Riley, Richard D
- ORCID
- Venue
- BMJ
- Publisher
- BMJ
- Published
- 2020-03-18
- Volume
- 368
- Pages
- m441
- ISSN
- 1756-1833 (ISSN-L)
- OpenAlex
- W3012413426
- Cited by
- 2,917
- References
- 80
- Citations by year
- 2026: 863 · 2025: 606 · 2024: 531 · 2023: 402 · 2022: 275 · 2021: 174 · 2020: 58
- FWCI
- 160.59
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- www.bmj.com/company/legal-information/terms-conditions/legal-information/tdm-licencepolicy (tdm)
- Locations
- BMJ (publishedVersion)
- PubMed (publishedVersion)
- Research Explorer (The University of Manchester) (publishedVersion, other-oa)
- Keele Research Repository (Keele University) (submittedVersion, cc-by)
- Utrecht University Repository (Utrecht University) (submittedVersion, other-oa)
- HighWire Press Open Archive (submittedVersion)
- University of Birmingham Research Portal (University of Birmingham) (submittedVersion)
- Funders
- Georgia Clinical and Translational Science Alliance (UL1TR002243)
- Cancer Research UK (27294)
- National Institute for Health and Care Research (SPCR-142)
- Department of Health and Social Care
- Nederlandse Organisatie voor Wetenschappelijk Onderzoek (91208004, 918.10.615, project 9120.8004)
- National Institutes of Health (UL1TR002243)
- NIHR School for Primary Care Research
- National Center for Advancing Translational Sciences (TR002243)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Clinical Trials
- Keywords
- sample size determination, clinical prediction model, model development, prediction accuracy, prognostic model, diagnostic model, small sample size
- MeSH terms
- Clinical Decision-Making, Forecasting, Humans, Models, Theoretical, Sample Size
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