Interpretable statistical modeling of patient flow in emergency departments

This paper aims to develop a data-driven simulation framework for modeling patient flow in a hospital Emergency Department using interpretable methods throughout the entire process in the absence of system resource data. The goal is to improve understanding of system dynamics and support decision-making processes through transparent simulations, even when resource data are unavailable.

We developed a simulation framework using anonymized medical records from a Spanish hospital's Emergency Department. The model captures patient flow considering triage levels by identifying routes and measuring the transition times between each stage in them. We estimated these transitions using both parametric (theoretical) distributions and non-parametric Kernel Density Estimation (KDE). Patient admissions times are modeled by using probability distributions. We enhanced realism through an iterative refinement process guided by tolerance thresholds and quantitative metrics. This process refined the synthetic data to match the original distributions.

Our approach produces highly realistic patient flow simulations with low tolerance values in the iterative method. The process gradually converges toward the original data. Distance and divergence metrics, together with statistical test results, indicate a high degree of similarity between the simulations and the real data, passing the Mann-Whitney U and Kolmogorov-Smirnov tests simultaneously in 100% of the generated samples when the tolerance threshold is low.

The experimental results demonstrate that our simulation method effectively reproduces patient flow dynamics with a high level of realism and flexibility, even in the absence of information related to service resources. Its interpretable design and adjustable parameters enable safe data analysis and the exploration of alternative management strategies (e.g., modifying potential patient routes or restricting some transitions). These features position the methodology as a valuable tool for supporting informed decision-making and suggest its potential for use in other hospitals with suitable data, pending validation on external datasets.