Susmann Herbert, Chambaz Antoine, Josse Julie, Aegerter Philippe, Wargon Mathias, Bacry Emmanuel
CEREMADE (UMR 7534), Université Paris-Dauphine PSL, Place du Maréchal de Lattre de Tassigny, Paris, 75016, France.
Université Paris Cité, CNRS, MAP5, F-75006 Paris, France; Fédération Parisienne de Modélisation Mathématique, CNRS FR 2036, France.
Int J Med Inform. 2025 Mar;195:105728. doi: 10.1016/j.ijmedinf.2024.105728. Epub 2024 Dec 4.
Forecasts of future demand is foundational for effective resource allocation in emergency departments (EDs). As ED demand is inherently variable, it is important for forecasts to characterize the range of possible future demand. However, extant research focuses primarily on producing point forecasts using a wide variety of prediction algorithms. In this study, our objective is to generate point and interval predictions that accurately characterize the variability in ED demand using ensemble methods that combine predictions from multiple base algorithms based on their empirical performance.
Data consisted in daily arrivals and subsequent hospitalizations at 72 emergency departments in Île-de-France from 2014-2018. Additional explanatory variables were collected including public and school holidays, meteorological variables, and public health trends. One-day ahead point and 80% interval predictions of arrivals and hospitalizations were produced by predicting the 10%, 50%, and 90% quantiles of the forecast distribution. Quantile prediction algorithms included methods such as ARIMAX, variations of random forests, and generalized additive models. Ensemble predictions were then formed using Exponentially Weighted Averaging, Bernstein Online Aggregation, and Super Learning. Prediction intervals were post-processed using Adaptive Conformal Inference techniques. Point predictions were evaluated by their Mean Absolute Error (MAE) and Mean Absolute Percentage Error (MAPE), and 80% interval predictions by their empirical coverage and mean interval width.
For point forecasts, ensemble methods achieved lower average MAE and MAPE than any of the base algorithms. All of the base algorithms and ensemble methods yielded prediction intervals with near optimal empirical coverage after conformalization. For hospitalizations, the shortest mean interval widths were achieved by the ensemble methods.
Ensemble methods yield joint point and prediction intervals that adapt to individual EDs and achieve better performance than individual algorithms. Conformal inference techniques improve the performance of the prediction intervals.
对未来需求进行预测是急诊科有效资源分配的基础。由于急诊科需求具有内在的变异性，因此预测能够描述未来可能需求的范围非常重要。然而，现有研究主要集中在使用各种预测算法来生成点预测。在本研究中，我们的目标是使用集成方法生成能够准确描述急诊科需求变异性的点预测和区间预测，该集成方法基于多个基础算法的实证表现来组合预测结果。
数据包括2014年至2018年法国法兰西岛大区72个急诊科的每日就诊人数及随后的住院人数。还收集了其他解释变量，包括公共和学校假期、气象变量以及公共卫生趋势。通过预测预测分布的第10%、50%和90%分位数，生成提前一天的就诊人数和住院人数的点预测以及80%区间预测。分位数预测算法包括自回归整合移动平均模型（ARIMAX）、随机森林变体和广义相加模型等方法。然后使用指数加权平均、伯恩斯坦在线聚合和超级学习形成集成预测。使用自适应共形推理技术对预测区间进行后处理。通过平均绝对误差（MAE）和平均绝对百分比误差（MAPE）评估点预测，通过实证覆盖率和平均区间宽度评估80%区间预测。
对于点预测，集成方法的平均MAE和MAPE低于任何一种基础算法。所有基础算法和集成方法在共形化后产生的预测区间具有接近最优的实证覆盖率。对于住院人数，集成方法实现了最短的平均区间宽度。
集成方法产生适应各个急诊科的联合点预测和预测区间，并且比单个算法具有更好的性能。共形推理技术提高了预测区间的性能。
