The elephant in the machine: Proposing a new metric of data reliability and its application to a medical case to assess classification reliability

In this paper, we present and discuss a novel reliability metric to quantify the extent a ground truth, generated in multi-rater settings, as a reliable basis for the training and validation of machine learning predictive models. To define this metric, three dimensions are taken into account: agreement (that is, how much a group of raters mutually agree on a single case); confidence (that is, how much a rater is certain of each rating expressed); and competence (that is, how accurate a rater is). Therefore, this metric produces a reliability score weighted for the raters' confidence and competence, but it only requires the former information to be actually collected, as the latter can be obtained by the ratings themselves, if no further information is available. We found that our proposal was both more conservative and robust to known paradoxes than other existing agreement measures, by virtue of a more articulated notion of the agreement due to chance, which was based on an empirical estimation of the reliability of the single raters involved. We discuss the above metric within a realistic annotation task that involved 13 expert radiologists in labeling the MRNet dataset. We also provide a nomogram by which to assess the actual accuracy of a classification model, given the reliability of its ground truth. In this respect, we also make the point that theoretical estimates of model performance are consistently overestimated if ground truth reliability is not properly taken into account.