Penalization and shrinkage methods produced unreliable clinical prediction models especially when sample size was small

OBJECTIVES: When developing a clinical prediction model, penalization techniques are recommended to address overfitting, as they shrink predictor effect estimates toward the null and reduce mean-square prediction error in new individuals. However, shrinkage and penalty terms ('tuning parameters') are estimated with uncertainty from the development data set. We examined the magnitude of this uncertainty and the subsequent impact on prediction model performance.

STUDY DESIGN AND SETTING: This study comprises applied examples and a simulation study of the following methods: uniform shrinkage (estimated via a closed-form solution or bootstrapping), ridge regression, the lasso, and elastic net.

RESULTS: In a particular model development data set, penalization methods can be unreliable because tuning parameters are estimated with large uncertainty. This is of most concern when development data sets have a small effective sample size and the model's Cox-Snell R² is low. The problem can lead to considerable miscalibration of model predictions in new individuals.

CONCLUSION: Penalization methods are not a 'carte blanche'; they do not guarantee a reliable prediction model is developed. They are more unreliable when needed most (i.e., when overfitting may be large). We recommend they are best applied with large effective sample sizes, as identified from recent sample size calculations that aim to minimize the potential for model overfitting and precisely estimate key parameters.