  After 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. We introduce two 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 COPD risk. We derive "Type I and II" regret bounds,
which guarantee the procedures are non-inferior to a static model and
competitive with an oracle logistic reviser in terms of the average loss. Both
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, 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 AUC
(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). Despite its simplicity,
BLR is highly competitive with MarBLR. MarBLR outperforms BLR when its prior
better reflects the data. BLR and MarBLR can improve the transportability of
clinical prediction models and maintain their performance over time.
