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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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Equipping mathematical models for hospital dynamics using information theory.

Jeremy A Balch1,2,3, Jackson G Brandberg4,5, Robert T Andris4,5

  • 1Department of Surgery, University of Florida, Gainesville, FL, USA. jeremy.balch@surgery.ufl.edu.

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Summary

Information theory metrics reveal hospital unit dynamics are ergodic, but entire hospitals are not. These measures can detect systemic changes, inefficiencies, and patient care anomalies.

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Area of Science:

  • Healthcare Operations Research
  • Information Theory
  • Dynamical Systems Analysis

Background:

  • Hospital operations involve complex, dynamic systems.
  • Traditional metrics may not fully capture system-wide behaviors or identify subtle inefficiencies.
  • Information theory offers novel quantitative tools for analyzing complex systems.

Purpose of the Study:

  • To apply information-theoretic concepts like ergodicity, surprisal, and entropy to hospital operational data.
  • To characterize the clinical and operational dynamics within hospital units and across hospitals.
  • To identify the utility of these metrics in detecting systemic shifts, inefficiencies, and anomalies in patient care.

Main Methods:

  • Utilized lab test order data from 15 units across three hospitals (2018-2021).
  • Applied information-theoretic metrics: ergodicity (time- vs. space-averages), surprisal, and entropy.
  • Analyzed data to assess stationarity and identify system dynamics.

Main Results:

  • Hospital units demonstrated ergodicity, suggesting bed-level representativeness.
  • Hospitals as a whole were found to be non-ergodic.
  • External events, such as the COVID-19 pandemic, were shown to significantly perturb hospital dynamics.
  • Information-theoretic metrics successfully indicated systemic shifts and potential inefficiencies.

Conclusions:

  • Ergodicity analysis provides insights into the typicality of components within a larger system.
  • Non-ergodicity at the hospital level highlights the impact of overarching factors on system dynamics.
  • Information-theoretic metrics offer interpretable signals for monitoring hospital performance, detecting data drift, and preventing label leakage in predictive systems.