Riley, RD, Snell, KIE, Ensor, J, Burke, DL, Harrell, FE, Moons, KGM and Collins, GS (2019) Minimum sample size for developing a multivariable prediction model: Part I - Continuous outcomes. Statistics in Medicine, 38 (7). 1262 - 1275. ISSN 1097-0258

[thumbnail of Sample size for linear accepted.pdf]
Sample size for linear accepted.pdf - Accepted Version
Available under License Creative Commons Attribution Non-commercial.

Download (688kB) | Preview


In the medical literature, hundreds of prediction models are being developed to predict health outcomes in individuals. For continuous outcomes, typically a linear regression model is developed to predict an individual's outcome value conditional on values of multiple predictors (covariates). To improve model development and reduce the potential for overfitting, a suitable sample size is required in terms of the number of subjects (n) relative to the number of predictor parameters (p) for potential inclusion. We propose that the minimum value of n should meet the following four key criteria: (i) small optimism in predictor effect estimates as defined by a global shrinkage factor of ≥0.9; (ii) small absolute difference of ≤ 0.05 in the apparent and adjusted R2 ; (iii) precise estimation (a margin of error ≤ 10% of the true value) of the model's residual standard deviation; and similarly, (iv) precise estimation of the mean predicted outcome value (model intercept). The criteria require prespecification of the user's chosen p and the model's anticipated R2 as informed by previous studies. The value of n that meets all four criteria provides the minimum sample size required for model development. In an applied example, a new model to predict lung function in African-American women using 25 predictor parameters requires at least 918 subjects to meet all criteria, corresponding to at least 36.7 subjects per predictor parameter. Even larger sample sizes may be needed to additionally ensure precise estimates of key predictor effects, especially when important categorical predictors have low prevalence in certain categories.

Item Type: Article
Additional Information: The final accepted manuscript can be found at;
Uncontrolled Keywords: multivariable prediction model.
Subjects: H Social Sciences > H Social Sciences (General)
Q Science > Q Science (General)
R Medicine > R Medicine (General)
Divisions: Faculty of Medicine and Health Sciences > School of Primary, Community and Social Care
Related URLs:
Depositing User: Symplectic
Date Deposited: 24 Jan 2020 16:19
Last Modified: 24 Jan 2020 16:19

Actions (login required)

View Item
View Item