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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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When the whole is greater than the sum of its parts: why machine learning and conventional statistics are complementary for predicting future health outcomes
Janse, R. J., Abu–Hanna, A., Vagliano, I., Stel, V. S., Jager, K. J., Tripepi, G. L., Zoccali, C., Dekker, F. W., & van Diepen, M. (2025) · Clinical Kidney Journal · doi:10.1093/ckj/sfaf059 · Cited by 12
“The number of candidate predictors may be limited by the size of the available data, for which sample size calculations for certain techniques are available [15 , 16 , 17 ].”
External validation of a machine learning prediction model for massive blood loss during surgery for spinal metastases: a multi-institutional study using 880 patients
de Reus, D. C., Kuijten, R. H., Saha, P., Lastoria, D. A. A., Warr-Esser, A., Taylor, C. F. C., Groot, O. Q., Lui, D. F., Verlaan, J., & Tobert, D. G. (2025) · The Spine Journal · doi:10.1016/j.spinee.2025.03.018 · Cited by 11
C-reactive protein-to-albumin ratio predicts outcome of neoadjuvant chemotherapy for colorectal liver metastases: A multicenter prediction model
Zheng, T., Yuanyuan, Z., Zhou, Z., Ye, R., Jia, H., Chen, W., Zheng, M., & Chen, Y. (2025) · Surgery · doi:10.1016/j.surg.2025.109334 · Cited by 10
An interactive dynamic online nomogram for predicting the frailty trajectories among older people with chronic heart failure
Gou, D., Wu, H., Min, C., Peng, X., Jiang, M., Zhang, L., Luo, X., & Tao, M. (2025) · Journal of Affective Disorders · doi:10.1016/j.jad.2025.04.033 · Cited by 10
A machine learning–based framework for predicting postpartum chronic pain: a retrospective study
Liu, F., Li, T., Zhou, D., Shi, S., & Gong, X. (2025) · BMC Medical Informatics and Decision Making · doi:10.1186/s12911-025-03004-9 · Cited by 10
“The sample size selected for the clinical prediction model establishment met the standard of 10 events per variable [31].”
A Retrospective Study of Ultramassive Transfusion in Trauma Patients: Is There a Value After Which Additional Transfusions Are Futile?
Major, F. R., Pickering, T. A., Stefanescu, K., Singh, M., Clark, D. H., Inaba, K., Nahmias, J. T., Tay-Lasso, E., Alvarez, C., Chen, J. L., et al. (2025) · Anesthesia & Analgesia · doi:10.1213/ane.0000000000007569 · Cited by 10
Bridging Traditional-Statistics and Machine-Learning Approaches in Psychology: Navigating Small Samples, Measurement Error, Nonindependent Observations, and Missing Data
Lavelle-Hill, R. E., Smith, G., & Murayama, K. (2025) · Advances in Methods and Practices in Psychological Science · doi:10.1177/25152459251345696 · Cited by 11
“Several studies have provided formulas to evaluate the adequacy of sample size in certain applied-machine-learning fields (e.g., in medicine; Riley et al., 2019a, 2019b, 2020; van Smeden et al., 2019), but the extent to which these methods can be extended to different classes of machine-learning…”
A study protocol for a predictive algorithm to assess population-based premature mortality risk: Premature Mortality Population Risk Tool (PreMPoRT)
Rosella, L. C., O’Neill, M., Fisher, S., Hurst, M., Diemert, L. M., Kornas, K., Hong, A., & Manuel, D. G. (2020) · Diagnostic and Prognostic Research · doi:10.1186/s41512-020-00086-z · Cited by 10
“90) and the expected model performance in terms of overall model fit (R(2)) [38, 39].”
Background
A Prospective, observational cohort study to identify neonates and children at risk of postdischarge mortality in Dar es Salaam, Tanzania and Monrovia, Liberia: the PPDM study protocol
Rees, C. A., Kisenge, R. R., Ideh, R. C., Kamara, J., Samma, A., Godfrey, E. K., Manji, H. K., Sudfeld, C. R., Westbrook, A. L., Niescierenko, M. L., et al. (2022) · BMJ Paediatrics Open · doi:10.1136/bmjpo-2021-001379 · Cited by 10
Optimising telephone triage of patients calling for acute shortness of breath during out-of-hours primary care: protocol of a multiple methods study (Opticall)
Spek, M., Venekamp, R. P., GROOT, E. D., Geersing, G., Erkelens, D. C. A., van Smeden, M., Rutten, F. H., & Zwart, D. L. M. (2022) · BMJ Open · doi:10.1136/bmjopen-2021-059549 · Cited by 10
Characteristics and Quality of Diagnostic and Risk Prediction Models for Frailty in Older Adults: A Systematic Review
Gao, Y., Chen, Y., Hu, M., Gan, T., Sun, X., Zhang, Z., He, W., & Wu, X. (2022) · Journal of Applied Gerontology · doi:10.1177/07334648221097084 · Cited by 11
“%) of included models were developed or validated based on insufficient sample size, which would introduce model overfitting, cause inaccurate predictions, and subsequently limit the generalizability outside the original data set (Riley et al., 2020).”
Background
Evaluating future risk of NAFLD in adolescents: a prediction and decision curve analysis
Abeysekera, K. W. M., Orr, J. G., Gordon, F. H., Howe, L. D., Hamilton-Shield, J. P., Heron, J., & Hickman, M. (2022) · BMC Gastroenterology · doi:10.1186/s12876-022-02401-y · Cited by 12
Development and validation of a nomogram to predict postoperative delirium in type B aortic dissection patients underwent thoracic endovascular aortic repair
Huang, W., Wu, Q., Zhang, Y., Tian, C., Huang, H., Wang, H., & Mao, J. (2022) · Frontiers in Surgery · doi:10.3389/fsurg.2022.986185 · Cited by 10
“(21), at least 10 outcome events are needed per variable (EPV≥ 10).”
Background
Geometric morphometrics and machine learning from three-dimensional facial scans for difficult mask ventilation prediction
Pei, B., Jin, C., Cao, S., Ji, N., Xia, M., & Jiang, H. (2023) · Frontiers in Medicine · doi:10.3389/fmed.2023.1203023 · Cited by 10
Integration of clinical demographics and routine laboratory analysis parameters for early prediction of gestational diabetes mellitus in the Chinese population
Zhang, H., Dai, J., Zhang, W., Sun, X., Sun, Y., Wang, L., Li, H., & Zhang, J. (2023) · Frontiers in Endocrinology · doi:10.3389/fendo.2023.1216832 · Cited by 10
DNA Logical Computing on a Transistor for Cancer Molecular Diagnosis
Kong, D., Zhang, S., Ma, X., Yang, Y., Dai, C., Geng, L., Liu, Y., & Wei, D. (2024) · Angewandte Chemie · doi:10.1002/ange.202407039 · Cited by 10
Elevated Serum Uric Acid is Associated with Rapid Decline in Kidney Function: A 10-Year Follow-Up Study
Kritmetapak, K., Charoensri, S., Thaopanya, R., & Pongchaiyakul, C. (2020) · International Journal of General Medicine · doi:10.2147/ijgm.s277957 · Cited by 10
Development and validation of a predictive model for urinary incontinence postpartum: a prospective longitudinal study
Wang, X., Jin, Y., Xu, X., Wang, H., & Feng, S. (2022) · International Urogynecology Journal · doi:10.1007/s00192-022-05105-9 · Cited by 10
A Model to Detect Significant Prostate Cancer Integrating Urinary Peptide and Extracellular Vesicle RNA Data
Connell, S. P., Frantzi, M., Latosińska, A., Webb, M., Mullen, W., Pejchinοvski, M., Salji, M. J., Mischak, H., Cooper, C. S., Clark, J., et al. (2022) · Cancers · doi:10.3390/cancers14081995 · Cited by 10
Pre‐Surgery Hip‐Knee‐Ankle Angle and Weightbearing Line Percentage Are Nearly Perfectly Correlated to the Miniaci Angle When Planning Open Wedge High Tibial Osteotomies
Jiang, X., Zhang, D., Li, B., Yan, M., Hu, X., Wang, L., & Gao, L. (2022) · Arthroscopy The Journal of Arthroscopic and Related Surgery · doi:10.1016/j.arthro.2022.11.007 · Cited by 10
Machine Learning in Clinical Journals
Singh, K., Beam, A. L., & Nallamothu, B. K. (2020) · Circulation Cardiovascular Quality and Outcomes · doi:10.1161/circoutcomes.120.007491 · Cited by 10
“For instance, while there is helpful statistical guidance on the determination of appropriate sample sizes for prediction models, 27 it is unclear how this guidance could be applied to models utilizing radiology images consisting of millions of pixels.”
Background
Predicting the Risk of Unplanned Readmission at 30 Days After PCI: Development and Validation of a New Predictive Nomogram
Xu, W., Tu, H., Xiong, X., Peng, Y., & Cheng, T. (2022) · Clinical Interventions in Aging · doi:10.2147/cia.s369885 · Cited by 9
“According to sample size calculation requirements, a minimum of 10 events per variable were necessary for the multivariate analysis.(11,12) A total of 1348 patients were eventually included.”
Background
Comprehensive analysis of multivariable models for predicting severe dengue prognosis: systematic review and meta-analysis
Lee, H., Hyun, S., & Park, S. (2022) · Transactions of the Royal Society of Tropical Medicine and Hygiene · doi:10.1093/trstmh/trac108 · Cited by 9
Nomogram for predicting the risk of postoperative myasthenic crisis in patients with thymectomy
Ruan, Z., Su, Y., Tang, Y., Lin, J., Lü, Q., Zhou, Y., Guo, R., Liu, Y., Li, H., Sun, C., et al. (2023) · Annals of Clinical and Translational Neurology · doi:10.1002/acn3.51752 · Cited by 9
Perioperative parameters-based prediction model for acute kidney injury in Chinese population following valvular surgery
Yan, Y., Gong, H.-R., Hu, J., Wu, D., Zheng, Z., Wang, L., & Lei, C. (2023) · Frontiers in Cardiovascular Medicine · doi:10.3389/fcvm.2023.1094997 · Cited by 9
“The estimation of overall outcome prevalence in the target population, the number of candidate predictors, and the predicted model performance regarding the overall model fit (R(2)) (22) were used to determine the sample size for binary outcome prediction model development.”
Method
Stratified care in hip arthroscopy: can we predict successful and unsuccessful outcomes? Development and external temporal validation of multivariable prediction models
Ishøi, L., Thorborg, K., Kallemose, T., Kemp, J. L., Reiman, M. P., Nielsen, M. F., & Hölmich, P. (2023) · British Journal of Sports Medicine · doi:10.1136/bjsports-2022-105534 · Cited by 9
A deep surgical site infection risk score for patients with open tibial shaft fractures treated with intramedullary nail
Wilkinson, B. G., Bangura, A., Burke, C. E., O’Connor, K., Gupta, J., Demyanovich, H. K., Healey, K. M., O’Hara, N. N., Schneiderman, B. A., Nascone, J. W., et al. (2023) · Injury · doi:10.1016/j.injury.2023.110965 · Cited by 9
Development and validation of a prognosis risk score model for preterm birth among pregnant women who had antenatal care visit, Northwest, Ethiopia, retrospective follow-up study
Fente, B. M., Asaye, M. M., Tesema, G. A., & Gudayu, T. W. (2023) · BMC Pregnancy and Childbirth · doi:10.1186/s12884-023-06018-1 · Cited by 9
“As a general rule, the required sample size in the development of a prediction model is at least 10 events per predictor [36].”
Background
Machine learning prediction of the failure of high-flow nasal oxygen therapy in patients with acute respiratory failure
Wang, Z., Chao, Y., Xu, M. M., Zhao, W., & Hu, X. (2024) · Scientific Reports · doi:10.1038/s41598-024-52061-z · Cited by 9
Comparing the performance of statistical, machine learning, and deep learning algorithms to predict time-to-event: A simulation study for conversion to mild cognitive impairment
Billichová, M., Coan, L. J., Czanner, S., Kováčová, M., Sharifian, F., & Czanner, G. (2024) · PLoS ONE · doi:10.1371/journal.pone.0297190 · Cited by 9
Associations of preoperative anaemia with healthcare resource use and outcomes after colorectal surgery: a population-based cohort study
Park, L. J., Moloo, H., Ramsay, T., Thavorn, K., Presseau, J., Zwiep, T., Martel, G., Devereaux, P. J., Talarico, R., & McIsaac, D. I. (2024) · British Journal of Anaesthesia · doi:10.1016/j.bja.2024.03.018 · Cited by 9
Development of a risk prediction model for subsequent infection after colonization with carbapenem-resistant Enterobacterales: a retrospective cohort study
Zheng, G., Cai, J., Deng, H., Yang, H., Xiong, W., Chen, E., Bai, H., & He, J. (2024) · Antimicrobial Resistance and Infection Control · doi:10.1186/s13756-024-01394-5 · Cited by 9
“The calculation of the required sample was carried out by R (version 4.1.1) software with the pmsampsize package, according to the methods from Riley et al.’s article [17].”
MethodInfluential
Development of a clinical calculator to aid the identification of MODY in pediatric patients at the time of diabetes diagnosis
Shields, B. M., Carlsson, A., Patel, K. A., Knupp, J., Kaur, A., Johnston, D., Colclough, K., Larsson, H. E., Forsander, G., Samuelsson, U., et al. (2024) · Scientific Reports · doi:10.1038/s41598-024-60160-0 · Cited by 9
“We performed sample size calculations using the pmsampsize package in R, in line with the approach described by Riley et al. 20 .”
Method
Calibration plots for multistate risk prediction models
Pate, A., Sperrin, M., Riley, R. D., Peek, N. B., van Staa, T. P., Sergeant, J. C., Mamas, M. A., Lip, G. Y. H., O’Flaherty, M., Barrowman, M., et al. (2024) · Statistics in Medicine · doi:10.1002/sim.10094 · Cited by 9
“Sample size criteria do not yet exist for multistate models, 68 but would be dependent on the event rates of all the possible transitions.”
Background
Predictive Modeling for Functional Outcomes After All-Inside Arthroscopic Anterior Talofibular Ligament Repair of Chronic Ankle Instability
Chen, Z., Zhao, Y., Xue, X., Gu, X., Li, Y., & Hua, Y. (2024) · Foot & Ankle International · doi:10.1177/10711007241252091 · Cited by 9
Derivation and Internal Validation of a Novel Risk Assessment Tool to Identify Infants and Young Children at Risk for Post-Discharge Mortality in Dar es Salaam, Tanzania and Monrovia, Liberia
Rees, C. A., Kisenge, R. R., Godfrey, E. K., Ideh, R. C., Kamara, J., Coleman-Nekar, Y.-J. G., Samma, A., Manji, H. K., Sudfeld, C. R., Westbrook, A. L., et al. (2024) · The Journal of Pediatrics · doi:10.1016/j.jpeds.2024.114147 · Cited by 9
Prospective multicenter study to validate the gastrointestinal dysfunction score (GIDS) in intensive care patients: Study protocol for Part A of the international GUTPHOS study
Kouw, I. W. K., Melchers, M., Mändul, M., Arabi, Y. M., Casaer, M. P., Cotoia, A., Gunst, J., Malbrain, M. L. N. G., Schaller, S. J., Starkopf, J., et al. (2024) · Clinical Nutrition ESPEN · doi:10.1016/j.clnesp.2024.07.023 · Cited by 9
Prediction models for postoperative pulmonary complications in intensive care unit patients after noncardiac thoracic surgery
He, X., Dong, M., Xiong, H., Zhu, Y., Ping, F., Wang, B., & Kang, Y. (2024) · BMC Pulmonary Medicine · doi:10.1186/s12890-024-03153-z · Cited by 11
“The sample size of this study was calculated following formulas reported [29].”
Method
Development and validation of claims-based algorithms for estimating gestational age of spontaneous abortion and termination
Zhu, Y., Hernández–Dı́az, S., Bateman, B. T., Gray, K. J., Alt, E. M., Straub, L., Taylor, L. G., Ouellet‐Hellstrom, R., Ma, Y., Qiang, Y., et al. (2024) · American Journal of Epidemiology · doi:10.1093/aje/kwae372 · Cited by 9
Risk factors for atypical hyperplasia or endometrial cancer in premenopausal women aged ≤ 45 years with abnormal uterine bleeding
Jang, S., & Hwang, S.-O. (2024) · European Journal of Obstetrics & Gynecology and Reproductive Biology · doi:10.1016/j.ejogrb.2024.09.030 · Cited by 9
Risk factors and predictive model for nosocomial infections by extensively drug-resistant Acinetobacter baumannii
Shi, J., Mao, X., Cheng, J., Shao, L., Shan, X., & Zhu, Y. (2024) · Frontiers in Cellular and Infection Microbiology · doi:10.3389/fcimb.2024.1475428 · Cited by 9
People living with chronic pain in Canada face difficult decisions and decisional conflict concerning their care: data from the national DECIDE-PAIN survey
Naye, F., Légaré, F., Cachinho, C., Gérard, T., Toupin‐April, K., Sasseville, M., Paquette, J., LeBlanc, A., Gaboury, I., Poitras, M.-È., et al. (2024) · BMC Family Practice · doi:10.1186/s12875-024-02667-z · Cited by 9
“…method proposed by Riley et al. [36] using an estimated prevalence of the outcome = 0.10 (i.e., prevalence of clinically significant decisional conflict in primary care) [11], an estimated Nagelkerke’s R 2 = 0.15 [36] and an estimated number of predictors in the initial model = 30 [36].”
Influential
Exploring the application of machine learning to identify the correlations between phthalate esters and disease: enhancing nursing assessments
Wu, H., Liao, C.-C., Peng, C.-F., Lee, T.-Y., & Liao, P. (2024) · Health Information Science and Systems · doi:10.1007/s13755-024-00324-4 · Cited by 9
“Thus, the model receives at least 10 instances of training for each variable [13].”

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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