A Kalman Filter Based Framework for Monitoring the Performance of In-Hospital Mortality Prediction Models Over Time

Unlike in a clinical trial, where researchers get to determine the least number of positive and negative samples required, or in a machine learning study where the size and the class distribution of the validation set is static and known, in a real-world scenario, there is little control over the size and distribution of incoming patients. As a result, when measured during different time periods, evaluation metrics like Area under the Receiver Operating Curve (AUCROC) and Area Under the Precision-Recall Curve(AUCPR) may not be directly comparable. Therefore, in this study, for binary classifiers running in a long time period, we proposed to adjust these performance metrics for sample size and class distribution, so that a fair comparison can be made between two time periods. Note that the number of samples and the class distribution, namely the ratio of positive samples, are two robustness factors which affect the variance of AUCROC. To better estimate the mean of performance metrics and understand the change of performance over time, we propose a Kalman filter based framework with extrapolated variance adjusted for the total number of samples and the number of positive samples during different time periods. The efficacy of this method is demonstrated first on a synthetic dataset and then retrospectively applied to a 2-days ahead in-hospital mortality prediction model for COVID-19 patients during 2021 and 2022. Further, we conclude that our prediction model is not significantly affected by the evolution of the disease, improved treatments and changes in hospital operational plans.