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

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.

Keywords: EPV; Logistic regression; prediction models; predictive performance; sample size; simulations.

Figure 1.

Marginal out-of-sample predictive performance.

Figure 2.

Boxplot distribution of out-of-sample predictive performance outcomes (restricted to conditions with events fraction = 1/2).

Figure 3.

Average relative out-of-sample performances of modeling strategies per simulation factor level.

Figure 4.

Relation required sample size and events fraction. Calculations based on metamodels with criterion values that were kept constant. For illustration purposes, the criterion values were chosen such that they would intersect at events fraction = 1/2.