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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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The association between different outcome measures and prognostic factors in patients with neck pain: a cohort study
Myhrvold, B. L., Kongsted, A., Irgens, P. M. S., Robinson, H. S., & Vøllestad, N. K. (2022) · BMC Musculoskeletal Disorders · doi:10.1186/s12891-022-05558-5 · Cited by 13
“to calculate for the efficient sample size for multivariable linear regression modeling [44].”
Method
The development of a HAMstring InjuRy (HAMIR) index to mitigate injury risk through innovative imaging, biomechanics, and data analytics: protocol for an observational cohort study
Heiderscheit, B. C., Blemker, S. S., Opar, D. A., Stiffler-Joachim, M. R., Bedi, A., Hart, J. M., Mortensen, B., Kliethermes‌, S., The HAMIR Study Group, Baer, G. S., et al. (2022) · BMC Sports Science Medicine and Rehabilitation · doi:10.1186/s13102-022-00520-3 · Cited by 13
Full Blood Count Trends for Colorectal Cancer Detection in Primary Care: Development and Validation of a Dynamic Prediction Model
Virdee, P. S., Patnick, J., Watkinson, P., Holt, T., & Birks, J. (2022) · Cancers · doi:10.3390/cancers14194779 · Cited by 17
“The required sample size was calculated using the pmsampsize package in Stata software [22].”
Method
Deep learning in acute vertigo diagnosis
Rastall, D. P. W., & Green, K. E. (2022) · Journal of the Neurological Sciences · doi:10.1016/j.jns.2022.120454 · Cited by 13
How to Develop and Validate Prediction Models for Orthopedic Outcomes
Zaniletti, I., Larson, D. R., Lewallen, D. G., Berry, D. J., & Kremers, H. M. (2022) · The Journal of Arthroplasty · doi:10.1016/j.arth.2022.12.032 · Cited by 13
Built environment factors predictive of early rapid lung function decline in cystic fibrosis
Gecili, E., Brokamp, C., Rasnick, E., Afonso, P. M., Andrinopoulou, E., Dexheimer, J. W., Clancy, J. P., Keogh, R. H., Ni, Y., Palipana, A., et al. (2023) · Pediatric Pulmonology · doi:10.1002/ppul.26352 · Cited by 13
Exploring the EVolution in PrognOstic CapabiLity of MUltisequence Cardiac MagneTIc ResOnance in PatieNts Affected by Takotsubo Cardiomyopathy Based on Machine Learning Analysis
Cau, R., Muscogiuri, G., Pisu, F., Gatti, M., Velthuis, B. K., Loewe, C., Cademartiri, F., Pontone, G., Montisci, R., Guglielmo, M., et al. (2023) · Journal of Thoracic Imaging · doi:10.1097/rti.0000000000000709 · Cited by 14
Prediction of acute kidney injury in patients with liver cirrhosis using machine learning models: evidence from the MIMIC-III and MIMIC-IV
Tian, J., Cui, R., Song, H., Zhao, Y., & Zhou, T. (2023) · International Urology and Nephrology · doi:10.1007/s11255-023-03646-6 · Cited by 13
“It is recommended to use all data for model development to avoid data splitting (e.g., into model derivation and validation samples), and to apply resampling methods (e.g., bootstrapping) for internal validation [50].”
Predictors of Mortality in Patients with Infections Due to Carbapenem-Resistant Gram-Negative Bacteria
Rivera-Villegas, H., Martínez-Guerra, B. A., Garcia-Couturier, R., Xancal-Salvador, L. F., Esteban-‬Kenel, V., Jaimes-Aquino, R. A., Mendoza-Rojas, M., Sánchez, A. C., Méndez-Ramos, S., Alonso-Montoya, J. E., et al. (2023) · Antibiotics · doi:10.3390/antibiotics12071130 · Cited by 13
“Considering a primary outcome probability of 50% [2,3], a mean absolute percentage error of 10%, and the identification of up to 10 potential predictors, we calculated a sample size of at least 165 patients [14].”
Method
Prognostic models predicting transition to psychotic disorder using blood-based biomarkers: a systematic review and critical appraisal
Byrne, J. F., Mongan, D., Murphy, J., Healy, C., Föcking, M., Cannon, M. D., & Cotter, D. (2023) · Translational Psychiatry · doi:10.1038/s41398-023-02623-y · Cited by 14
“This systematic review was prospectively registered with PROS-PERO, CRD42022302047.”
Method
Nomogram for predicting difficult total laparoscopic hysterectomy: a multi-institutional, retrospective model development and validation study
Yin, C., jiang, J., He, M., Zhong, K., Tang, S., Deng, L., & Wang, Y. (2024) · International Journal of Surgery · doi:10.1097/js9.0000000000001406 · Cited by 13
Online interpretable dynamic prediction models for clinically significant posthepatectomy liver failure based on machine learning algorithms: a retrospective cohort study
Jin, Y., Li, W., Wu, Y., Wang, Q., Xiang, Z., Long, Z., Liang, H., Zou, J., Zhu, Z., & Dai, X. (2024) · International Journal of Surgery · doi:10.1097/js9.0000000000001764 · Cited by 13
“In this research, the sample size of the binary outcome prediction model was calculated according to the following formula [31] : ).”
Quantifying the Enhancement of Sarcopenic Skeletal Muscle Preservation Through a Hybrid Exercise Program: Randomized Controlled Trial
Guo, H., Cao, J., He, S., Wei, M., Meng, D., Yu, I., Wang, Z., Chang, X., Yang, G., & Wang, Z. (2024) · JMIR Aging · doi:10.2196/58175 · Cited by 19
“This study’s sample size offers valuable insights, yet further validation in larger cohorts is recommended in alignment with the sample size guidelines proposed [82] for clinical prediction models prior to clinical implementation.”
Predicting preterm birth using electronic medical records from multiple prenatal visits
Huang, C., Long, X., van der Ven, M., Kaptein, M. C., Oei, S. G., & van den Heuvel, E. R. (2024) · BMC Pregnancy and Childbirth · doi:10.1186/s12884-024-07049-y · Cited by 15
The role of umbilical vein blood flow assessment in the prediction of fetal growth velocity and adverse outcome: a prospective observational cohort study
Farsetti, D., Barbieri, M., Magni, E., Zamagni, G., Monasta, L., Maso, G., Vasapollo, B., Pometti, F., Ferrazzi, E. M., Lees, C. C., et al. (2025) · American Journal of Obstetrics and Gynecology · doi:10.1016/j.ajog.2025.01.001 · Cited by 13
AI ‐Based Platelet‐Independent Noninvasive Test for Liver Fibrosis in MASLD Patients
Wakabayashi, S., Kimura, T., Tamaki, N., Iwadare, T., Okumura, T., Kobayashi, H., Yamashita, Y., Tanaka, N., Kurosaki, M., & Umemura, T. (2025) · JGH Open · doi:10.1002/jgh3.70150 · Cited by 13
AutoCOPD–A novel and practical machine learning model for COPD detection using whole-lung inspiratory quantitative CT measurements: a retrospective, multicenter study
Lin, F., Zhang, Z., Wang, J., Liang, C., Xu, J., Zeng, X., Zeng, Q., Chen, H., Zhuang, J., Ma, Y., et al. (2025) · EClinicalMedicine · doi:10.1016/j.eclinm.2025.103166 · Cited by 13
“The sample size was calculated beforehand using the online software (https:// mvansmeden.shinyapps.io/BeyondEPV/) by Riley RD et al. 30 (Parameter: number of candidate predictors = 10; events fraction = 0 ⋅ 34; criterion value rMPSE = 0 ⋅ 05), resulting in at least 870 participants and 29 ⋅ 7…”
Ninety-Day Mortality: Redefining the Perioperative Period After Lung Resection
Taylor, M., Grant, S. W., West, D., Shackcloth, M. J., Woolley, S. M., Naidu, B. V., & Shah, R. D. (2020) · Clinical Lung Cancer · doi:10.1016/j.cllc.2020.12.011 · Cited by 13
Predicting Survived Events in Nontraumatic Out-of-Hospital Cardiac Arrest: A Comparison Study on Machine Learning and Regression Models
Lo, Y. H., & Siu, A. Y. C. (2021) · Journal of Emergency Medicine · doi:10.1016/j.jemermed.2021.07.058 · Cited by 11
Facilitating Safe Discharge Through Predicting Disease Progression in Moderate Coronavirus Disease 2019 (COVID-19): A Prospective Cohort Study to Develop and Validate a Clinical Prediction Model in Resource-Limited Settings
Chandna, A., Mahajan, R., Gautam, P., Mwandigha, L., Gunasekaran, K., Bhusan, D., Cheung, A. T. L., Day, N., Dittrich, S., Dondorp, A. M., et al. (2022) · Clinical Infectious Diseases · doi:10.1093/cid/ciac224 · Cited by 15
Predicting the risk of active pulmonary tuberculosis in people living with HIV: development and validation of a nomogram
Chen, J., Li, L., Chen, T., Yang, X., Ru, H., Li, X., Yang, X., Xie, Q., & Xu, L. (2022) · BMC Infectious Diseases · doi:10.1186/s12879-022-07368-5 · Cited by 13
“Sample size calculation The calculation of study sample size followed the method of developing a clinical prediction model [27, 28].”
Method
Including modifiable and non-modifiable factors improves injury risk assessment in professional baseball pitchers.
Shanley, E., Thigpen, C., Collins, G., Arden, N., Noonan, T., Wyland, D. J., Kissenberth, M., & Bullock, G. (2022) · Journal of Orthopaedic and Sports Physical Therapy · doi:10.2519/jospt.2022.11072 · Cited by 12
External validation and extension of the Early Prediction of Functional Outcome after Stroke (EPOS) prediction model for upper limb outcome 3 months after stroke
Veerbeek, J. M., Pohl, J., Luft, A. R., & Held, J. P. O. (2022) · PLoS ONE · doi:10.1371/journal.pone.0272777 · Cited by 13
Development and external validation of a prediction model for the transition from mild to moderate or severe form of COVID-19
Zysman, M., Asselineau, J., Saut, O., Frison, É., Oranger, M., Maurac, A., Charriot, J., Achkir, R., Regueme, S. C., Klein, É., et al. (2023) · European Radiology · doi:10.1007/s00330-023-09759-x · Cited by 13
“A sample size of the development cohort was calculated using Riley and colleagues’ approach [29].”
Systematic review finds risk of bias and applicability concerns for models predicting central line-associated bloodstream infection
Gao, S., Albu, E., Tuand, K., Cossey, V., Rademakers, F. E., CALSTER, B. V., & Wynants, L. (2023) · Journal of Clinical Epidemiology · doi:10.1016/j.jclinepi.2023.07.019 · Cited by 14
Unveiling neural activity changes in mild cognitive impairment using microstate analysis and machine learning
Wu, X., Liu, Y., Che, J., Cheng, N., Dong, W., Liu, H., & Dong, X. (2025) · Journal of Alzheimer s Disease · doi:10.1177/13872877241305961 · Cited by 13
“To determine the optimal number of features, we adopted the method proposed by Riley et al., 45 using the pmsampsize package in R to estimate sample size and feature quantity.”
Development of a machine learning prediction model for loss to follow-up in HIV care using routine electronic medical records in a low-resource setting
Endebu, T., Taye, G., & Deressa, W. A. (2025) · BMC Medical Informatics and Decision Making · doi:10.1186/s12911-025-03030-7 · Cited by 12
“Key among these are estimating the overall outcome proportion with adequate precision, targeting a small mean absolute prediction error, and establishing a shrinkage factor to minimize optimism in the apparent R² Nagelkerke [35].”
Influential
Statistical Models in Clinical Studies
Matsui, S., Le‐Rademacher, J. G., & Mandrekar, S. J. (2021) · Journal of Thoracic Oncology · doi:10.1016/j.jtho.2021.02.021 · Cited by 12
Patients With Femoral Neck Fractures Are at Risk for Conversion to Arthroplasty After Internal Fixation: A Machine‐learning Algorithm
van de Kuit, A., Oosterhoff, J. H. F., Dijkstra, H., Sprague, S., Bzovsky, S., Bhandari, M., Swiontkowski, M. F., Schemitsch, E. H., IJpma, F. F. A., Poolman, R. W., et al. (2022) · Clinical Orthopaedics and Related Research · doi:10.1097/corr.0000000000002283 · Cited by 12
Predicting type 2 diabetes prevalence for people with severe mental illness in a multi-ethnic East London population
Shamsutdinova, D. D., Das‐Munshi, J., Ashworth, M. J., Roberts, A., & Stahl, D. R. (2023) · International Journal of Medical Informatics · doi:10.1016/j.ijmedinf.2023.105019 · Cited by 13
Prediction of Acute Myocardial Injury in Noncardiac Surgery in Patients at Risk for Major Adverse Cardiovascular and Cerebrovascular Events: A Multivariable Risk Model
Mases, A., de Heredia, S. B., Gallart, L., Román, L., Bosch, L., Núñez, M., Rueda, M., Recasens, L., & Sabaté, S. (2023) · Anesthesia & Analgesia · doi:10.1213/ane.0000000000006469 · Cited by 12
Clinical utility of WHO-recommended screening tools and development and validation of novel clinical prediction models for pulmonary tuberculosis screening among outpatients living with HIV: an individual participant data meta-analysis
Dhana, A. V., Gupta, R. K., Hamada, Y., Kengne, A. P., Kerkhoff, A. D., Yoon, C., Cattamanchi, A., Reeve, B. W. P., Theron, G., Ndlangalavu, G., et al. (2023) · European Respiratory Review · doi:10.1183/16000617.0021-2023 · Cited by 12
“The derived population was considered sufficient [26] and sample size calculations are provided in the appendix.”
Background
Multiclass risk models for ovarian malignancy: an illustration of prediction uncertainty due to the choice of algorithm
Ledger, A., Ceusters, J., Valentin, L., Testa, A. C., Holsbeke, C. V., Franchi, D., Bourne, T., Froyman, W., Timmerman, D., & CALSTER, B. V. (2023) · BMC Medical Research Methodology · doi:10.1186/s12874-023-02103-3 · Cited by 12
“The recently established guidance for minimum sample size to develop a regression-based prediction model is a crucial step forward [55, 56].”
Background
Automated machine learning-based model for the prediction of pedicle screw loosening after degenerative lumbar fusion surgery
Jiang, F., Li, X., Liu, L., Xie, Z., Wu, X., & Wang, Y. (2024) · BioScience Trends · doi:10.5582/bst.2023.01327 · Cited by 12
Risk-stratified monitoring for sulfasalazine toxicity: prognostic model development and validation
Abhishek, A., Grainge, M. J., Card, T. R., Williams, H. C., Taal, M. W., Aithal, G. P., Fox, C. P., Mallen, C. D., Stevenson, M. D., Nakafero, G., et al. (2024) · RMD Open · doi:10.1136/rmdopen-2023-003980 · Cited by 12
“The data analysis was undertaken using the Stata command ‘mi estimate’ in a combined dataset that included all imputations.”
Method
Machine Learning–Based Prediction of Large-for-Gestational-Age Infants in Mothers With Gestational Diabetes Mellitus
Kang, M., Zhu, C., Lai, M., Weng, J., Zhuang, Y., He, H., Qiu, Y., Wu, Y., Qi, Z., Zhang, W., et al. (2024) · The Journal of Clinical Endocrinology & Metabolism · doi:10.1210/clinem/dgae475 · Cited by 12
Prediction models for the risk of ventilator-associated pneumonia in patients on mechanical ventilation: A systematic review and meta-analysis
Li, J., Li, G., Liu, Z., Yang, X., & Yang, Q. (2024) · American Journal of Infection Control · doi:10.1016/j.ajic.2024.07.006 · Cited by 13
Development and Validation of a Risk Prediction Model for Cognitive Frailty in Elderly Patients With Type 2 Diabetes Mellitus
Yu, Q., & Yu, H. (2025) · Journal of Clinical Nursing · doi:10.1111/jocn.17508 · Cited by 12
Development and international validation of a novel multivariate prognostic tool: posterior urethral valve risk of chronic kidney disease (PURK) score
Kim, J. K., Yadav, P., Bitcon, C., Keefe, D. T., Comella, A., Taghavi, K., Kattini, R., Davis-Dao, C. A., Khoury, A. E., Khondker, A., et al. (2025) · Pediatric Nephrology · doi:10.1007/s00467-025-06701-9 · Cited by 12
“…(accounting for the fact that few ‘strong’ predictors were found in the past such as nadir creatinine), a sample size of 116 would be required to satisfy the criteria outlined by Riley et al., and this would provide sufficient power to determine statistical significance of the prognostic tool [10].”
Development, Validation, and Clinical Utility of a Nomogram for Urological Tumors: How to Build the Best Predictive Model
Utsumi, T., Ishitsuka, N., Noro, T., Suzuki, Y., Iijima, S., Sugizaki, Y., Somoto, T., Oka, R., Endo, T., Kamiya, N., et al. (2025) · International Journal of Urology · doi:10.1111/iju.70075 · Cited by 12
“Even with a fixed dataset, sample size calculations can determine whether the available sample size is sufficient and how many predictors can be included before overfitting becomes a concern [44].”
Artificial neural network model effectively estimates muscle and fat mass using simple demographic and anthropometric measures
Pathak, P., Panday, S. B., & Ahn, J. (2021) · Clinical Nutrition · doi:10.1016/j.clnu.2021.11.027 · Cited by 12
Using the Revised Cardiac Risk Index to Predict Major Postoperative Events for People With Kidney Failure: An External Validation and Update
Harrison, T. G., Hemmelgarn, B. R., James, M. T., Sawhney, S., Lam, N. N., Ruzycki, S. M., Wilson, T., & Ronksley, P. E. (2022) · CJC Open · doi:10.1016/j.cjco.2022.07.008 · Cited by 12
Clinical prediction models for methotrexate treatment outcomes in patients with rheumatoid arthritis: A systematic review and meta-analysis
Gehringer, C. K., Martin, G. P., Hyrich, K. L., Verstappen, S. M. M., & Sergeant, J. C. (2022) · Seminars in Arthritis and Rheumatism · doi:10.1016/j.semarthrit.2022.152076 · Cited by 13
Intraoperative hypotension in non-emergency decompression surgery for cervical spondylosis: The role of chronic arterial hypertension
Chiang, T.-Y., Wang, Y.-K., Huang, W., Huang, S., & Chu, Y. (2022) · Frontiers in Medicine · doi:10.3389/fmed.2022.943596 · Cited by 12
“Additionally, to avoid overfitting the multivariable regression model, we included only a limited number of independent variables that we thought were clinically meaningful (32).”
Method
BLOod Test Trend for cancEr Detection (BLOTTED): protocol for an observational and prediction model development study using English primary care electronic health record data
Virdee, P. S., Bankhead, C. R., Koshiaris, C., Wright, C., Oke, J. L., Withrow, D. R., Swain, S., Collins, K. K., Chammas, L., Tamm, A., et al. (2023) · Diagnostic and Prognostic Research · doi:10.1186/s41512-022-00138-6 · Cited by 12
Development and validation of a nomogram model for medication non-adherence in patients with chronic kidney disease
Wu, X., Tang, F., Li, H., Chen, C., Zhang, H., Liu, X., Lai, H., Li, Q., Deng, L., & Ye, Z. (2023) · Journal of Psychosomatic Research · doi:10.1016/j.jpsychores.2023.111385 · Cited by 12

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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