💻 computer science

Machine Learning Approaches for Hourly Emergency Department Patient Arrival Forecasting: A Multi-Horizon Comparison with Operational Benchmarking at a Norwegian Hospital

This study demonstrates that machine learning models, particularly a Direct LSTM+Optuna architecture that avoids the "frozen-feature" problem inherent in recursive autoregressive approaches, significantly outperform Norway's operational calendar-based baseline for hourly emergency department patient arrival forecasting across both short and extended planning horizons.

Original authors: Md Ariful Islam Foysal, Gustav Trygve Siqueland, Vetle Ellingsen Hauge, Rasmus Rimestad, Vimala Nunavath, Bjørn-Jostein Singstad

Published 2026-08-25

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Md Ariful Islam Foysal, Gustav Trygve Siqueland, Vetle Ellingsen Hauge, Rasmus Rimestad, Vimala Nunavath, Bjørn-Jostein Singstad

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Hospitals are places of constant motion, where the flow of people is as critical to manage as the flow of blood or electricity. In an emergency department, the difference between a smooth shift and a chaotic crisis often comes down to timing. If a hospital knows exactly how many patients will arrive in the next hour, it can open the right number of beds, schedule the correct number of nurses, and prepare diagnostic equipment before the first person walks through the door. For decades, hospital administrators have relied on simple historical averages to make these decisions, looking at what happened on a Tuesday at 2 p.m. over the last few months and assuming today will be the same. This method works well enough for broad patterns, but it is blind to the immediate reality: a sudden storm, a spike in flu cases, or an unexpected rush of injuries can render a historical average useless. The challenge for modern medicine is to move from guessing based on the past to predicting the future with the help of computers that can learn from complex, changing data.

A team of researchers at Vestfold Hospital Trust in Norway set out to solve this specific problem by building a machine learning system capable of forecasting patient arrivals hour by hour. They gathered a year's worth of data, tracking over 35,000 patient visits, and combined this with real-time information about the weather, local infection rates, and public holidays. They then trained five different types of computer models to learn the patterns hidden in this data. The goal was not just to see if a computer could predict the future better than a simple calendar lookup, but to understand how far into the future that prediction could remain accurate. The researchers compared their new models against the hospital's current system, which simply looks up the median number of arrivals for a specific day and time.

The results showed that for the immediate future, the computer models were significantly more accurate than the traditional method. When predicting just one hour ahead, the best machine learning model reduced the average error by nearly a full patient per hour compared to the hospital's standard approach. This might sound like a small number, but in a busy emergency room, knowing whether to expect four patients or six can determine whether a doctor is called in early or left waiting. The computer models achieved this by noticing subtle signals that a calendar cannot see, such as how the arrival rate is changing right now or how the current weather might influence people's decisions to seek care.

However, the study uncovered a surprising and critical flaw in how some of these advanced computer models work when asked to look further into the future. When the researchers asked the models to predict twelve or twenty-four hours ahead, the most sophisticated deep learning systems suddenly failed. Their predictions became so inaccurate that they were worse than simply guessing the average. The researchers discovered the cause: a structural issue they called the "frozen-feature problem." These models were designed to look at a window of the past to predict the next step, then use that prediction to guess the step after that. In doing so, they kept the time-of-day information fixed at the starting point of the window. Because the time of day is the single most important factor in predicting patient arrivals, the model effectively forgot that time was passing. It kept predicting the future as if it were still the same hour it started with, leading to a complete breakdown in accuracy as the forecast horizon extended.

To fix this, the team developed a different approach that does not try to predict one hour at a time and feed the result back into the system. Instead, they built a model that calculates all twenty-four hours of the future in a single, simultaneous step. This method, which they named the Direct LSTM model, avoided the trap of forgetting the passage of time. While it was slightly less precise for the very first hour compared to the other models, it remained reliable all the way out to a full day. At the twelve-hour mark, where the other advanced models had collapsed into uselessness, this new approach still provided a meaningful prediction. At the twenty-four-hour mark, it was the only model that could offer a useful forecast, outperforming both the traditional hospital system and the other machine learning attempts.

The study concludes that there is no single "best" model for every situation. For immediate decisions, such as staffing the next hour, the traditional deep learning models work best. But for longer planning, such as preparing for the next day, the new direct approach is essential. The researchers have already turned this solution into a prototype tool that the hospital can use directly, feeding it current data to generate a full twenty-four-hour forecast that fits seamlessly into their existing planning dashboard. This work demonstrates that while artificial intelligence can dramatically improve hospital operations, the way the technology is built matters just as much as the data it learns from. By identifying and fixing a specific structural weakness in how these models handle time, the researchers have provided a practical path forward for hospitals everywhere to manage their most precious resource: time.

Technical Summary: Machine Learning Approaches for Hourly Emergency Department Patient Arrival Forecasting

Problem Statement
Emergency Department (ED) overcrowding is a global crisis linked to increased mortality and reduced patient satisfaction. Effective management requires accurate forecasting of patient arrival volumes to enable proactive staffing and resource allocation. While forecasting literature has evolved from statistical methods (e.g., ARIMA) to machine learning (ML), significant gaps remain:

Most studies operate at daily resolution rather than the operational hourly resolution required for shift planning.
Multi-step forecasting performance often degrades severely at longer horizons, with the structural causes of this degradation not fully isolated.
Few approaches benchmark against the actual operational systems hospitals use (e.g., calendar-based median lookups), limiting practical relevance.

This study addresses these gaps by developing and evaluating ML frameworks for hourly ED arrival forecasting at Vestfold Hospital Trust (SiV) in Norway, explicitly comparing multiple model families against the hospital's existing operational baseline across 1 to 24-hour horizons.

Methodology
The study utilized 12 months of ED visit data (35,674 patients, October 2023–October 2024) combined with external covariates to create a 46-variable feature set. Data sources included:

Temporal features: Cyclical encodings (sine/cosine) for time, lag features, and exponential moving averages (EMA).
External covariates: Hourly weather data, monthly infection statistics (influenza, COVID-19), and public holiday indicators.

The dataset was split chronologically (80/10/10) to prevent information leakage. Five models were trained and evaluated:

Median Baseline: The hospital's operational system, a 7×24 lookup table of median arrivals based on the preceding four months.
LightGBM: A gradient boosting model with explicit recomputation of temporal features at every prediction step.
LSTM / BiLSTM: Standard and Bidirectional Long Short-Term Memory networks using recursive autoregressive rollout.
LSTM+Optuna: An LSTM architecture optimized via Bayesian hyperparameter search (Optuna).
Direct LSTM+Optuna: A multi-output model predicting all 24 future hours simultaneously in a single forward pass, eliminating recursive rollout.

Performance was assessed using RMSE, MAE, $R^2$ , and MAPE at 1, 2, 6, 12, and 24-hour horizons.

Key Contributions and Findings

1. Short-Horizon Performance (1–6 Hours)
At the 1-hour horizon, all autoregressive ML models outperformed the operational Median Baseline in RMSE.

LSTM+Optuna achieved the lowest RMSE (1.75 patients/hour) compared to the baseline's 2.43.
LightGBM achieved the highest coefficient of determination ( $R^2 = 0.46$ ), indicating superior capture of arrival variance compared to the LSTM family ( $R^2 \approx 0.36–0.39$ ).
Feature importance analysis revealed that while temporal features (specifically hour cos) dominated, LightGBM leveraged real-time signals (EMA trends, infection rates, pressure) to improve variance explanation, capabilities the calendar-only baseline lacks.

2. The "Frozen-Feature Problem" in Long-Horizon Forecasting
A critical finding was the catastrophic failure of autoregressive LSTM models at the 12-hour horizon.

Observation: All three autoregressive LSTM variants (LSTM, BiLSTM, LSTM+Optuna) yielded negative $R^2$ values at 12 hours (ranging from -0.08 to -0.45), performing worse than a simple global mean.
Mechanism: The study identifies the "frozen-feature problem" as the cause. In recursive rollout, temporal features within the scaled lookback window (specifically hour cos) remain fixed at their starting values rather than updating to reflect the target forecast hour. Since hour cos is the most important feature (gain importance 119,021), this structural flaw systematically misdirects predictions.
Contrast: LightGBM avoided this collapse because it explicitly recomputes temporal features at every rollout step, maintaining a positive $R^2$ (0.14) at 12 hours.

3. Direct Multi-Output as a Solution
The Direct LSTM+Optuna model, which predicts the full 24-hour trajectory in a single forward pass, successfully eliminated both error compounding and the frozen-feature problem.

It maintained positive $R^2$ across all horizons, declining smoothly from 0.29 (1h) to 0.26 (12h) and 0.18 (24h).
At 12 and 24 hours, it significantly outperformed the autoregressive LSTM variants, achieving the highest $R^2$ of any model at the 24-hour horizon.

Significance and Claims
The paper claims that while ML models offer meaningful improvements over operational baselines for short-term planning, model architecture is critical for longer horizons.

Strategic Recommendation: The authors propose a per-horizon model selection strategy: use LSTM+Optuna or BiLSTM for 1–6 hour windows (minimizing RMSE), and switch to Direct LSTM+Optuna for 12–24 hour planning windows to avoid structural degradation.
Generalizability: The "frozen-feature problem" is identified as a general structural cause of long-horizon degradation in any LSTM-based recursive forecaster that incorporates cyclical temporal encodings. The direct multi-output architecture is presented as a general remedy.
Operational Integration: The Direct LSTM+Optuna model has been deployed as a prototype inference API on Hugging Face, designed to align directly with SiV's existing 24-hour planning dashboard without requiring bespoke preprocessing pipelines.

The study concludes that machine learning can enhance ED operations, but only when specific architectural choices are made to address the unique challenges of recursive time-series forecasting in healthcare settings.

Technical Summary: Machine Learning Approaches for Hourly Emergency Department Patient Arrival Forecasting

More like this