Equipping mathematical models for hospital dynamics using information theory

We propose metrics from information theory to characterize the clinical and operational dynamics of hospitals. Ergodicity, the equality of time- and space-averages within a dynamical system, ensures its stationarity. Surprisal, the log-inverse of probability, and entropy, the average surprisal, provide mathematical insights into the nature of dynamical systems. We applied these metrics to lab test order times from 15 units in three hospitals from 2018 to 2021. We found hospital units were ergodic in the sense that each bed is typical of the unit, while hospitals were not, and that external forces like the COVID-19 pandemic can perturb hospital dynamics. These information-theoretic metrics can indicate systemic shifts, inefficiencies, and anomalies in patient care, providing granular and interpretable signals of change. Monitoring these metrics can expose data drift, where evolving inputs and outputs hinder generalizability, and label leakage, where clinician actions inadvertently corrupt predictive monitoring systems.