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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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Method
Machine Learning for Prediction of Immunotherapy Efficacy in Non-Small Cell Lung Cancer from Simple Clinical and Biological Data
Benzekry, S., Grangeon, M., Karlsen, M., Alexa, M., Bicalho-Frazeto, I., Chaléat, S., Tomasini, P., Barbolosi, D., Barlesi, F., & Greillier, L. (2021) · medRxiv · doi:10.3390/cancers13246210 · Cited by 36
“In addition, the main limitation of such studies is the small sample size, despite being a critical determinant to ensure the robustness and generalizability of the results [27].”
Background
Penalized Regression Methods With Modified Cross‐Validation and Bootstrap Tuning Produce Better Prediction Models
Pavlou, M., Omar, R., & Ambler, G. (2024) · Biometrical Journal · doi:10.1002/bimj.202300245 · Cited by 17
“Despite this, we suggest as a conservative approach that penalized regression with either modified or bootstrap tuning methods alwaysbeusedinconjunctionwiththerecommendedsamplesize requirements according to the criterion of limiting overfitting and other criteria (Riley et al. 2020).”
Refining clinically relevant cut-offs of prostate specific antigen density for risk stratification in patients with PI-RADS 3 lesions
Mjaess, G., Haddad, L., Jabbour, T., Baudewyns, A., Bourgeno, H.-A., Lefebvre, Y., Ferriero, M. C., Simone, G., Fourcade, A., Fournier, G., et al. (2024) · Prostate Cancer and Prostatic Diseases · doi:10.1038/s41391-024-00872-6 · Cited by 17
“…minimum sample size for the multivariable logistic regression analysis was determined using two methods: (1) the ﬁ rst method, a classical approach, required a number of events equal to 10 subjects per included variable, and (2) the second method followed the criteria proposed by Riley et al. [13].”
Screening tools for subjective cognitive decline and mild cognitive impairment based on task-state prefrontal functional connectivity: a functional near-infrared spectroscopy study
Pu, Z., Huang, H., Li, M., Li, H., Shen, X., Du, L., Wu, Q., Fang, X., Meng, X., Ni, Q., et al. (2025) · NeuroImage · doi:10.1016/j.neuroimage.2025.121130 · Cited by 17
“Another important flaw is that most of these studies only extracted features for which P > 0.05 or > 0.01, which ignored general trends and could lead to overfitting, resulting in an artificial inflated ACC (Ding et al., 2022; Riley et al., 2020).”
Influential
Individual participant data meta‐analysis for external validation, recalibration, and updating of a flexible parametric prognostic model
Ensor, J., Snell, K. I. E., Debray, T. P. A., Lambert, P. C., Look, M. P., Mamas, M. A., Moons, K. G. M., & Riley, R. D. (2021) · Statistics in Medicine · doi:10.1002/sim.8959 · Cited by 17
Molecular Screening and Analysis Reveal Novel Oral Site-Specific Locations for the Cariogenic Pathogen Scardovia wiggsiae
McDaniel, S., McDaniel, J., Howard, K. M., & Kingsley, K. (2021) · Dentistry Journal · doi:10.3390/dj9060073 · Cited by 17
“In addition, there are limitations associated with the inferences that can be made from this study due to the limitations of this pilot study sample size, a common feature among many clinical and epidemiologic studies that attempt to produce relevant clinical data without significant external funding sources [51,52].”
Background
Development of prognostic model for preterm birth using machine learning in a population-based cohort of Western Australia births between 1980 and 2015
Wong, K., Tessema, G. A., Chai, K. E. K., & Pereira, G. F. (2022) · Scientific Reports · doi:10.1038/s41598-022-23782-w · Cited by 17
Prediction of all-cause mortality for chronic kidney disease patients using four models of machine learning
Tran, N. T. D., Balezeaux, M., Granal, M., Fouque, D. P., Ducher, M., & Fauvel, J. (2022) · Nephrology Dialysis Transplantation · doi:10.1093/ndt/gfac316 · Cited by 18
Establishment and validation of a predictive nomogram for gestational diabetes mellitus during early pregnancy term: A retrospective study
Li, L., Zhu, Q., Wang, Z., Yun, T., Liu, H., Tang, F., Liu, S., & Zhang, Y. (2023) · Frontiers in Endocrinology · doi:10.3389/fendo.2023.1087994 · Cited by 18
“Based on the 10EPP rule (19), the sample size of our predictor model should be at least 170; our study sample consists of 824 women in the training dataset and 392 women in the validation dataset, and based on the sample size of our study, the power (1 − b) calculation is equal to 1.”
Method
Effects of television viewing on brain structures and risk of dementia in the elderly: Longitudinal analyses
Takeuchi, H., & Kawashima, R. (2023) · Frontiers in Neuroscience · doi:10.3389/fnins.2023.984919 · Cited by 15
“Although, we included a wide range of variables in this study, this study has a rich sample size, which mitigates the problem of overfitting (Riley et al., 2020).”
Background
Prognostic Models in Nephrology: Where Do We Stand and Where Do We Go from Here? Mapping Out the Evidence in a Scoping Review
Milders, J., Ramspek, C. L., Janse, R. J., Bos, W. J. W., Rotmans, J. I., Dekker, F. W., & van Diepen, M. (2023) · Journal of the American Society of Nephrology · doi:10.1681/asn.0000000000000285 · Cited by 20
Development of an MRI-Based Prediction Model for Anti-TNF Treatment Failure in Perianal Crohn’s Disease: A Multicenter Study
McCurdy, J. D., Munir, J., Parlow, S., Reid, J., Yanofsky, R., Alenezi, T. A., Meserve, J. D., Becker, B., Lahijanian, Z., Eddin, A. H., et al. (2023) · Clinical Gastroenterology and Hepatology · doi:10.1016/j.cgh.2023.12.006 · Cited by 17
Concurrent Endometrial Cancer in Women with Atypical Endometrial Hyperplasia: What Is the Predictive Value of Patient Characteristics?
Giannella, L., Piva, F., Carpini, G. D., Giuseppe, J. D., Grelloni, C., Giulietti, M., Sopracordevole, F., Giorda, G., Fabro, A. D., Clemente, N., et al. (2023) · Cancers · doi:10.3390/cancers16010172 · Cited by 17
“Based on previous data for prediction models, we considered a minimum of 10 events (EC) for each predictor variable [16].”
Method
Effective sample size: A measure of individual uncertainty in predictions
Thomassen, D., le Cessie, S., van Houwelingen, H. V., & Steyerberg, E. (2023) · Statistics in Medicine · doi:10.1002/sim.10018 · Cited by 22
“21 This would require specification of a minimal n eff for the prediction to be of added value in clinical practice.”
Background
Design of ANCHOR-RA: a multi-national cross-sectional study on screening for interstitial lung disease in patients with rheumatoid arthritis
Sparks, J. A., Dieudé, P., Hoffmann‐Vold, A., Burmester, G. R., Walsh, S. L. F., Kreuter, M., Stock, C., Sambevski, S., Alves, M., & Emery, P. (2024) · BMC Rheumatology · doi:10.1186/s41927-024-00389-4 · Cited by 20
“…based on an assumed number of model parameters of 22 to 24, an assumed prevalence of RA-ILD in the study population (which is enriched for patients with RA-ILD) of 30%, an assumed c-statistic for the model of 0.75, and an assumed shrink-age factor associated with the predictors of 0.9 [52].”
BackgroundInfluential
Development of a Prediction Model and Corresponding Scoring Table for Postherpetic Neuralgia Using Six Machine Learning Algorithms: A Retrospective Study
Lin, Z., Yu, L.-Y., Pan, S., Cao, Y., & Lin, P. (2024) · Pain and Therapy · doi:10.1007/s40122-024-00612-7 · Cited by 17
“…the pmsampsize package in R, which implements the specification of the prediction model sam‑ ple size calculation method previously pub‑ lished [34], with the following parameters (type = "b", cstatistic = 0.90, parameters = 8, prevalence = 0.4), where the cstatistic param‑ eter was obtained…”
MethodInfluential
Clinical nurses’ work procrastination and smartphone addiction: a potential profile study
Xue, H., Jing, S., Song, X., Zhang, F., Liu, X., & Si, X. (2024) · Frontiers in Psychology · doi:10.3389/fpsyg.2024.1387288 · Cited by 24
“The sample size calculation was based on the 10 events per variable (10 EPV) principle and a general generalized multivariate analysis design, i.e., the sample size was 5–10 times the total number of questionnaire items (Riley et al., 2020).”
Method
Challenges in predictive modelling of chronic kidney disease: A narrative review
Khandpur, S., Mishra, P., Mishra, S., & Tiwari, S. (2024) · World Journal of Nephrology · doi:10.5527/wjn.v13.i3.97214 · Cited by 17
Development and external validation of an admission risk prediction model after treatment from early intervention in psychosis services
Puntis, S., Whiting, D., Pappa, S., & Lennox, B. (2021) · Translational Psychiatry · doi:10.1038/s41398-020-01172-y · Cited by 17
Statistical model building: Background “knowledge” based on inappropriate preselection causes misspecification
Hafermann, L., Becher, H., Herrmann, C., Klein, N., Heinze, G., & Rauch, G. (2021) · BMC Medical Research Methodology · doi:10.1186/s12874-021-01373-z · Cited by 20
“Recent development even goes one step further, Riley et al. (2020) state that the calculation of the sample size should also incorporate other factors like the expected predictive performance of the model [22].”
Background
A Model Predicting Mortality of Hospitalized Covid-19 Patients Four Days After Admission: Development, Internal and Temporal-External Validation
Heber, S., Pereyra, D., Schrottmaier, W. C., Kammerer, K., Santol, J., Rumpf, B., Pawelka, E., Hanna, M., Scholz, A., Liu, M., et al. (2022) · Frontiers in Cellular and Infection Microbiology · doi:10.3389/fcimb.2021.795026 · Cited by 17
Automated whole-slide images assessment of immune infiltration in resected non-small-cell lung cancer: towards better risk-stratification
Lin, H., Pan, X., Feng, Z., Yan, L., Hua, J., Liang, Y., Han, C., Xu, Z., Wang, Y., Wu, L., et al. (2022) · Journal of Translational Medicine · doi:10.1186/s12967-022-03458-9 · Cited by 17
“Hence, the maximum number of candidate risk factors was determined as 7 based on the number of events in the discovery cohort, to ensure that there were at least 10 events per candidate predictor (10 EPP rule [26]).”
Background
Cohort profile:Stop the Spread Ottawa (SSO)—a community-based prospective cohort study on antibody responses, antibody neutralisation efficiency and cellular immunity to SARS-CoV-2 infection and vaccination
Collins, E., Galipeau, Y., Arnold, C. R., Bosveld, C. J., Heiskanen, A., Keeshan, A., Nakka, K. K., Shir-Mohammadi, K., Bissonnette, F. S.-D., Tamblyn, L., et al. (2022) · BMJ Open · doi:10.1136/bmjopen-2022-062187 · Cited by 16
COVID-19 prediction models should adhere to methodological and reporting standards
Collins, P. G. S., van Smeden, M., & Riley, R. D. (2020) · European Respiratory Journal · doi:10.1183/13993003.02643-2020 · Cited by 17
Multicentre validation of a machine learning model for predicting respiratory failure after noncardiac surgery
Yoon, H., Kim, H. J., Kim, Y., Lee, H., Kim, B. R., Oh, H., Park, H., & Lee, H. (2024) · British Journal of Anaesthesia · doi:10.1016/j.bja.2024.01.030 · Cited by 17
A Machine Learning Prediction Model of Adult Obstructive Sleep Apnea Based on Systematically Evaluated Common Clinical Biochemical Indicators
Huang, J., Zhuang, J., Zheng, H., Yao, L., Chen, Q., Wang, J., & Fan, C. (2024) · Nature and Science of Sleep · doi:10.2147/nss.s453794 · Cited by 16
Development and validation of predictive models of early immune effector cell–associated hematotoxicity
Liang, E. C., Huang, J. J., Portuguese, A. J., Ortiz‐Maldonado, V., Albittar, A. A., Wuliji, N., Basom, R., Jeon, Y., Wu, Q. V., Torkelson, A., et al. (2024) · Blood Advances · doi:10.1182/bloodadvances.2024014455 · Cited by 17
“20 Model speci ﬁ cation and variable selection were based on recommendations by Riley et al. 21 Brie ﬂ y, based on a prevalence of severe eICAHT of 16%, shrinkage factor of 0.9, Cox-Snell R squared statistic of 0.1, and multiplicative margin of error of 1.1, the minimum sample size required for new multivariable devel…”
Influential
Development and validation of risk-predicting model for oral frailty in older adults patients with stroke
Ma, R., Fan, X., Tao, X., Zhang, W., & Li, Z. (2025) · BMC Oral Health · doi:10.1186/s12903-025-05428-1 · Cited by 16
“According to related studies [24], the sample size for a risk prediction model should be at least five to ten times the number of independent variables.”
OnRAMP for Regulating Artificial Intelligence in Medical Products
Higgins, D. C. (2021) · Advanced Intelligent Systems · doi:10.1002/aisy.202100042 · Cited by 19
Decision tree‐based rules outperform risk scores for childhood asthma prognosis
Owora, A. H., Tepper, R. S., Ramsey, C. D., & Becker, A. B. (2021) · Pediatric Allergy and Immunology · doi:10.1111/pai.13530 · Cited by 16
Development and External Validation of a Model to Predict Overall Survival in Patients With Resected Gallbladder Cancer
Lohman, E. A. J. D. S., de Bitter, T. J. J., Hannink, G., Wietsma, M. F. T., Vink‐Börger, E. M., Nagtegaal, I. D., Hugh, T. J., Gill, A. J., Bhimani, N., Ahadi, M. S., et al. (2021) · Annals of Surgery · doi:10.1097/sla.0000000000005154 · Cited by 16
Development and validation of early prediction for neurological outcome at 90 days after return of spontaneous circulation in out-of-hospital cardiac arrest
Nishioka, N., Kobayashi, D., Kiguchi, T., Irisawa, T., Yamada, T., Yoshiya, K., Park, C., Nishimura, T., Ishibe, T., Yagi, Y., et al. (2021) · Resuscitation · doi:10.1016/j.resuscitation.2021.09.027 · Cited by 16
Development and validation of a predictive nomogram for preoperative deep vein thrombosis (DVT) in isolated calcaneal fracture
Cheng, X., Lei, X., Wu, H., Luo, H., Fu, X., Gao, Y., Wang, X., Zhu, Y., & Yan, J. (2022) · Scientific Reports · doi:10.1038/s41598-022-10002-8 · Cited by 16
Dynamic Risk Prediction via a Joint Frailty-Copula Model and IPD Meta-Analysis: Building Web Applications
Emura, T., Michimae, H., & Matsui, S. (2022) · Entropy · doi:10.3390/e24050589 · Cited by 16
“For this reason, the CI is provided only to show the variability of the prediction results, not as a tool to determine the sample size [46].”
Method
Functional Improvement Trajectories After Surgery (FIT After Surgery) study: protocol for a multicentre prospective cohort study to evaluate significant new disability after major surgery in older adults
Wijeysundera, D. N., Alibhai, S. M. H., Ladha, K. S., Puts, M. T. E., Chesney, T. R., Daza, J. F., Ehtesham, S., Hladkowicz, E., Lebovic, G., Mazer, C. D., et al. (2022) · BMJ Open · doi:10.1136/bmjopen-2022-062524 · Cited by 18
“Recent research on sample sizes to develop robust prediction models, 49 which was published after initiation of the FIT After Surgery study, suggests that this sample size estimate is likely conservative.”
Developing and validating a prediction model of adolescent major depressive disorder in the offspring of depressed parents
Stephens, A., Allardyce, J., Weavers, B., Lennon, J., Jones, R. B., Powell, V. E., Eyre, O., Potter, R., Escott‐Price, V., Osborn, D., et al. (2022) · Journal of Child Psychology and Psychiatry · doi:10.1111/jcpp.13704 · Cited by 16
Predicting mortality in patients with anastomotic leak after esophagectomy: development of a prediction model using data from the TENTACLE—Esophagus study
Ubels, S., Klarenbeek, B. R., Verstegen, M. H. P., Bouwense, S. A. W., Griffiths, E. A., van Workum, F., Rosman, C., Hannink, G., & the TENTACLE—Esophagus Collaborative Group (2022) · Diseases of the Esophagus · doi:10.1093/dote/doac081 · Cited by 15
Peripheral blood lymphocytes differentiation patterns in responses / outcomes to immune checkpoint blockade therapies in non-small cell lung cancer: a retrospective study
Du, X., Wen, S., Shi, R., Xia, J., Wang, R., Zhang, Y., Pan, B., Wu, X., Zhu, W., Feng, J., et al. (2023) · BMC Cancer · doi:10.1186/s12885-023-10502-4 · Cited by 17
“We calculated the sample size of the multivariable Cox regression model for patients’ overall survival using the previously reported method [25].”
Method
Prediction models for cardiovascular disease risk among people living with HIV: A systematic review and meta-analysis
Yu, J., Liu, X., Zhu, Z., Yang, Z., He, J., Zhang, L., & Lu, H. (2023) · Frontiers in Cardiovascular Medicine · doi:10.3389/fcvm.2023.1138234 · Cited by 16
“A small sample size may result in model overfitting and inaccurate predictions (45, 46).”
Background
Prediction of Radiation-Induced Parotid Gland-Related Xerostomia in Patients With Head and Neck Cancer: Regeneration-Weighted Dose
van Rijn–Dekker, M. I., van Luijk, P., Schuit, E., van der Schaaf, A., Langendijk, J. A., & Steenbakkers, R. J. H. M. (2023) · International Journal of Radiation Oncology*Biology*Physics · doi:10.1016/j.ijrobp.2023.04.034 · Cited by 16
Predicting Outcomes Following Endovascular Abdominal Aortic Aneurysm Repair Using Machine Learning
Li, B., Verma, R., Beaton, D., Tamim, H., Hussain, M. A., Hoballah, J. J., Lee, D. S., Wijeysundera, D. N., de Mestral, C., Mamdani, M., et al. (2023) · Annals of Surgery · doi:10.1097/sla.0000000000005978 · Cited by 16
“25 Our cohort of 16,282 patients with 390 primary events meets this sample size requirement.”
Background
Predicting outcomes following open revascularization for aortoiliac occlusive disease using machine learning
Li, B., Verma, R., Beaton, D., Tamim, H., Hussain, M. A., Hoballah, J. J., Lee, D. S., Wijeysundera, D. N., de Mestral, C., Mamdani, M., et al. (2023) · Journal of Vascular Surgery · doi:10.1016/j.jvs.2023.07.006 · Cited by 18

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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