Cited by 2,917Statistical Methods in EpidemiologyMeta-analysis and systematic reviewsStatistical Methods in Clinical Trials

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Calculating the sample size required for developing a clinical prediction model

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Riley, Richard D, Ensor, Joie, Snell, Kym I E, Harrell, Frank E, Martin, Glen P, Reitsma, Johannes B, Moons, Karel G M, Collins, Gary, van Smeden, Maarten·2020·BMJ

DOI 10.1136/bmj.m441

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Abstract

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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Background
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“Moreover, we estimated sample size by using pmsampsize package of R software (R2cs = 0.28, parameters = 10, prevalence = 0.15), and then at least 294 cases were required for model development [34].”
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“Statistical analysis According to the literature [24], the required sample size for a binary outcome is calculated as the following”
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“…in the present study ( R 2adj = .82; M and SD of TotDisTea = 78.3 and 6.3 km, respectively) and the four-step pro - cedure proposed by Riley et al. [33, 34], future football studies will be able to more adequately calculate the minimum sample size re - quired to build a linear regression model to…”
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“Although literature published after our sample size estimation has suggested that more events per predictor may be required, 34,35 our analysis still allows for a multivariable analysis.”
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“The sample size of this study was 336 patients (290 with CAS and 46 without CAS), which was determined using a validated sample size calculator for clinical prediction models [35].”
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“34 As the study population was far greater, there was less concern about model overﬁtting and, thus, a validation cohort was not employed.”
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“Although data from two centres were used, the sample size from the second centre was insufficient for validation [48].”
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“A widely accepted guideline recommends at least 10 events per variable (EPV) 13 .”
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“…required a minimum sample size of 7954 participants (125 outcomes) based on a maximum of 20 parameters, Cox-Snell R 2 of 0.02235 (15% of the maximum permitted value, 0.149), estimated outcome rate of 0.0053 per person year, and a 3 year time horizon, and a mean follow-up period of 2.96 years [36].”
Influential
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“Based on a 23% carcinoma prevalence from the KSThR2016 study, 20 and the C indexes from existing prediction models, we planned to include approximately 720 nodules, as Riley et al. 21 indicated.”

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: Riley, Richard D
Ensor, Joie
Snell, Kym I E
Harrell, Frank E
Martin, Glen P
Reitsma, Johannes B
Moons, Karel G M
Collins, Gary
Venue: BMJ
Publisher: BMJ
Published: 2020-03-18
Volume: 368
Pages: m441
ISSN: 1756-1833 (ISSN-L)
DOI: 10.1136/bmj.m441
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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Calculating the sample size required for developing a clinical prediction model

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