Bayesian logistic regression for online recalibration and revision of risk prediction models with performance guarantees |
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| Authors: | Jean Feng Alexej Gossmann Berkman Sahiner Romain Pirracchio |
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| Affiliation: | Department of Epidemiology and Biostatistics, University of California, San Francisco, San Francisco, California, USA;CDRH-Center for Devices and Radiological Health, Food and Drug Administration, Silver Spring, Maryland, USA;Department of Anesthesia and Perioperative Care, University of California, San Francisco, San Francisco, California, USA |
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| Abstract: | ObjectiveAfter deploying a clinical prediction model, subsequently collected data can be used to fine-tune its predictions and adapt to temporal shifts. Because model updating carries risks of over-updating/fitting, we study online methods with performance guarantees. Materials and MethodsWe introduce 2 procedures for continual recalibration or revision of an underlying prediction model: Bayesian logistic regression (BLR) and a Markov variant that explicitly models distribution shifts (MarBLR). We perform empirical evaluation via simulations and a real-world study predicting Chronic Obstructive Pulmonary Disease (COPD) risk. We derive “Type I and II” regret bounds, which guarantee the procedures are noninferior to a static model and competitive with an oracle logistic reviser in terms of the average loss.ResultsBoth procedures consistently outperformed the static model and other online logistic revision methods. In simulations, the average estimated calibration index (aECI) of the original model was 0.828 (95%CI, 0.818–0.938). Online recalibration using BLR and MarBLR improved the aECI towards the ideal value of zero, attaining 0.265 (95%CI, 0.230–0.300) and 0.241 (95%CI, 0.216–0.266), respectively. When performing more extensive logistic model revisions, BLR and MarBLR increased the average area under the receiver-operating characteristic curve (aAUC) from 0.767 (95%CI, 0.765–0.769) to 0.800 (95%CI, 0.798–0.802) and 0.799 (95%CI, 0.797–0.801), respectively, in stationary settings and protected against substantial model decay. In the COPD study, BLR and MarBLR dynamically combined the original model with a continually refitted gradient boosted tree to achieve aAUCs of 0.924 (95%CI, 0.913–0.935) and 0.925 (95%CI, 0.914–0.935), compared to the static model’s aAUC of 0.904 (95%CI, 0.892–0.916).DiscussionDespite its simplicity, BLR is highly competitive with MarBLR. MarBLR outperforms BLR when its prior better reflects the data.ConclusionsBLR and MarBLR can improve the transportability of clinical prediction models and maintain their performance over time. |
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| Keywords: | model recalibration machine learning clinical prediction models Bayesian model updating |
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