HierSTT: A Hierarchical Spatio-Temporal Transformer for Coherent Emergency Department Forecasting

It introduces a single end-to-end hierarchical Transformer framework that simultaneously predicts ED visits at hospital (81), regional (5), and national levels, using a 42-day input window and a 28-day horizon. Prior studies largely treat ED forecasting as an isolated single-level problem or apply reconciliation only post hoc; this work embeds hierarchical dependence in one model via top-down conditioning, where national TFT outputs condition regional decoding and regional outputs condition hospital decoding. The method is fully formalized (Eqs. 1-6) with described TFT and spatio-temporal Transformer encoder-decoder structures, and experiments on real nationwide data are repeated across six fixed random seeds with mean ± standard deviation reported.

It adds a coherence-aware loss that softly penalizes cross-level inconsistency during training rather than enforcing coherence after the fact. Classical hierarchical approaches (bottom-up, top-down, middle-out, reconciliation) usually impose aggregation constraints after independently generating forecasts; this work places a coherence term directly in the training objective (Eqs. 7-8), penalizing hospital-to-regional, hospital-to-national, and regional-to-national aggregation constraints together. An ablation over α ∈ {0, 0.3, 0.5, 0.7, 0.99, 0.999} reports average WAPE and prediction-side and ground-truth HAgE, with α = 0.3 giving the lowest average WAPE of 7.06 ± 0.20%, alongside an analysis of the structural imbalance between 87 supervised series and 7 aggregation constraints.

It releases a hierarchical dataset of nationwide Portuguese ED activity covering 81 hospitals, 5 regional health administrations, and national indicators, spanning January 1, 2021 to April 20, 2024. The dataset explicitly preserves differences in variable availability across levels (e.g., air quality and temperature only at regional level, mortality only at national level, ED type and access pathways only at hospital level), forming a heterogeneous feature space across the hierarchy. A table itemizes available variables per level, and the text states data come from Portuguese Ministry of Health open sources cross-referenced with external air quality, temperature, and mortality data, with missing values filled by linear interpolation.

It evaluates both accuracy and hierarchical coherence, reporting that HierSTT achieves best or near-best results at most levels and aggregation transitions. Most prior work reports single-level accuracy only; this work uses MAE, RMSE, WAPE, and Hierarchical Aggregation Error (HAgE) on both prediction side and ground-truth side, and notes that a model can perform well at one level while performing poorly at another. Extended result tables give MAE/RMSE/WAPE per level and HAgE for three aggregation transitions; the paper reports a 23% hospital-level WAPE reduction versus N-BEATS (10.8% vs. 14.1%), a 38% regional MAE reduction versus the best non-hierarchical competitor (162.8 vs. 261.6), and national-level performance essentially tied with TFT.

The result targets ED demand forecasting in settings with an explicit administrative aggregation hierarchy, specifically the Portuguese National Health Service: 81 hospitals, 5 regional health administrations, a 42-day input window and a 28-day horizon, with training data from August 2021 onward to avoid COVID-19-related demand shifts. It suits planning situations that need mutually alignable forecasts at hospital, regional, and national levels, such as staffing, bed management, and regional coordination; because the coherence constraint relies on the aggregation definition that lower-level values sum to higher-level ones, it fits systems with clear hierarchy and well-defined aggregation.

A careful reader may still watch: whether the relationship between the coherence weight α and the imbalance in the number of loss terms holds at other hierarchy sizes; how the regional-only granularity of environmental variables, aggregated at RHA level due to limited reliable hospital-specific measurements, affects hospital-level forecasts; that qualitative examples were selected by lowest WAPE at each level and thus show favorable samples; and that the model underestimates some sharp peaks in lower-volume hospitals while predicting near-zero demand on closure days via the open/closed status variable. These are scope and follow-up validation directions rather than defects in the conclusions.