Widespread adoption of AI for medical decision making is still hindered due to ethical and safety-related concerns. For AI-based decision support systems in healthcare settings it is paramount to be reliable and trustworthy. Common deep learning approaches, however, have the tendency towards overconfidence under data shift. Such inappropriate extrapolation beyond evidence-based scenarios may have dire consequences. This highlights the importance of reliable estimation of local uncertainty and its communication to the end user. While stochastic neural networks have been heralded as a potential solution to these issues, this study investigates their actual reliability in clinical applications. We centered our analysis on the exemplary use case of mortality prediction for ICU hospitalizations using EHR from MIMIC3 study. For predictions on the EHR time series, Encoder-Only Transformer models were employed. Stochasticity of model functions was achieved by incorporating common methods such as Bayesian neural network layers and model ensembles. Our models achieve state of the art performance in terms of discrimination performance (AUC ROC: 0.868+-0.011, AUC PR: 0.554+-0.034) and calibration on the mortality prediction benchmark. However, epistemic uncertainty is critically underestimated by the selected stochastic deep learning methods. A heuristic proof for the responsible collapse of the posterior distribution is provided. Our findings reveal the inadequacy of commonly used stochastic deep learning approaches to reliably recognize OoD samples. In both methods, unsubstantiated model confidence is not prevented due to strongly biased functional posteriors, rendering them inappropriate for reliable clinical decision support. This highlights the need for approaches with more strictly enforced or inherent distance-awareness to known data points, e.g., using kernel-based techniques.
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