A closed testing procedure to select an appropriate method for updating prediction models

Abstract

Prediction models fitted with logistic regression often show poor performance when applied in populations other than the development population. Model updating may improve predictions. Previously suggested methods vary in their extensiveness of updating the model. We aim to define a strategy in selecting an appropriate update method that considers the balance between the amount of evidence for updating in the new patient sample and the danger of overfitting. We consider recalibration in the large (re-estimation of model intercept); recalibration (re-estimation of intercept and slope) and model revision (re-estimation of all coefficients) as update methods. We propose a closed testing procedure that allows the extensiveness of the updating to increase progressively from a minimum (the original model) to a maximum (a completely revised model). The procedure involves multiple testing with maintaining approximately the chosen type I error rate. We illustrate this approach with three clinical examples: patients with prostate cancer, traumatic brain injury and children presenting with fever. The need for updating the prostate cancer model was completely driven by a different model intercept in the update sample (adjustment: 2.58). Separate testing of model revision against the original model showed statistically significant results, but led to overfitting (calibration slope at internal validation = 0.86). The closed testing procedure selected recalibration in the large as update method, without overfitting. The advantage of the closed testing procedure was confirmed by the other two examples. We conclude that the proposed closed testing procedure may be useful in selecting appropriate update methods for previously developed prediction models.