Sample size for binary logistic prediction models: Beyond events per variable criteria

TLDR

Binary logistic regression is widely used for clinical prediction models, and developers often rely on an Events Per Variable (EPV) criterion of at least 10 to determine minimal sample size and the maximum number of candidate predictors. This study investigates how EPV, events fraction, predictor count, predictor correlations and distributions, AUC, and effect sizes influence out‑of‑sample predictive performance, and proposes new sample‑size criteria based on the number of predictors, total sample size, and events fraction. The authors performed extensive simulations varying EPV, events fraction, predictor count, correlations, distributions, AUC, and effect sizes, then assessed calibration, discrimination, and prediction error of models before and after shrinkage and variable selection. EPV is not strongly related to predictive performance and is an inappropriate criterion, whereas predictive performance is better approximated by the number of predictors, total sample size, and events fraction.

Abstract

Binary logistic regression is one of the most frequently applied statistical approaches for developing clinical prediction models. Developers of such models often rely on an Events Per Variable criterion (EPV), notably EPV ≥10, to determine the minimal sample size required and the maximum number of candidate predictors that can be examined. We present an extensive simulation study in which we studied the influence of EPV, events fraction, number of candidate predictors, the correlations and distributions of candidate predictor variables, area under the ROC curve, and predictor effects on out-of-sample predictive performance of prediction models. The out-of-sample performance (calibration, discrimination and probability prediction error) of developed prediction models was studied before and after regression shrinkage and variable selection. The results indicate that EPV does not have a strong relation with metrics of predictive performance, and is not an appropriate criterion for (binary) prediction model development studies. We show that out-of-sample predictive performance can better be approximated by considering the number of predictors, the total sample size and the events fraction. We propose that the development of new sample size criteria for prediction models should be based on these three parameters, and provide suggestions for improving sample size determination.