Multi-Rater Calibration Error Estimation

Calibration, the property of producing predicted probabilities that reflect true likelihoods of outcomes, is a relevant attribute of medical image computing models and a key requirement in clinical decision-making. However, empirical Calibration Error (CE) estimates suffer from instability in data-scarce scenarios. Here, for any existing CE we propose a Multi-Rater version of it (MR-CE), a wrapper over conventional calibration metrics, which provides a new strategy for estimating a CE that effectively addresses this limitation in situations where there are multiple annotations per sample. MR-CEs offer more consistent estimates of calibration errors by leveraging the consensus and disagreement among multiple annotators to generate virtually extended test datasets, more robust to typical binning artifacts. We evaluate a MR version of the popular Expected Calibration Error (ECE), and also of the more recent Kernel Density Estimation-ECE (kdeECE), in a comprehensive set of classification and segmentation problems, demonstrating improved stability compared to their single-rater CE counterparts. Specifically, we show that MR-CEs achieve a reduced variability as the test set size decreases across all analysed datasets. Our findings emphasize the critical role of modelling inter-rater variability not only for training but also for evaluating medical image analysis models, in particular when studying the calibration of modern neural networks.