ED Triage GNNs: Optimizing Emergency Care

• ED triage GNNs are graph neural network models that capture patient encounters, clinical observations, and care pathways in emergency settings.
• They use link prediction on multi-relational knowledge graphs with domain-informed masks to improve the accuracy of care action predictions.
• Patient-similarity graphs with optimized thresholds enable effective node classification, supporting real-time triage decisions and resource management.

Emergency Department (ED) triage Graph Neural Networks (GNNs) refer to the application of GNN architectures to optimize, automate, and analyze the patient triage process within emergency medical settings. These approaches leverage the expressive capability of GNNs to capture heterogeneous, multi-relational, and high-dimensional patterns in clinical data, enabling robust modeling of patient interactions, institutional resource allocation, and care pathways. The two principal streams in the literature are graph-structured link prediction for multi-modal knowledge graphs as formulated by Valls et al. (Valls et al., 2023), and patient-similarity graph classification as exemplified by Defilippo et al. (Defilippo et al., 2024).

1. Formal Mathematical Frameworks

ED triage GNNs instantiate two principal modeling paradigms:

a) Link Prediction on Multi-relational Knowledge Graphs

Let $G_{KG} = (V, E, K)$ denote a directed, multi-relational KG, where nodes represent patients, encounters, conditions, observations, and care actions; every edge $(i,j,r)$ with label $r \in \{1, ..., R\}$ and indicator $y_{ij}^r \in \{0,1\}$. The embeddings matrix $X \in \mathbb{R}^{n \times d}$ encodes node features, with trainable relational weights $W_r \in \mathbb{R}^{d \times d}$.

Crucially, two adjacency matrices are introduced:

• $A^{KG}$ encodes factual KG topology ($A_{ij}^{KG}=1$ if $(i,j) \in E$),
• $A^{GNN}$ is the designer-specified GNN connectivity (communication mask), decoupled from $A^{KG}$ to enforce clinically valid information flow.

A common message passing layer (Relational-GCN) updates node embeddings via:

$$e_i^{(\ell)} = \sigma\left( \sum_{r=1}^R \sum_{j:(i,j,r)\in E} A^{GNN}_{ij}\,(W_r\,e_j^{(\ell-1)}) + W_0\,e_i^{(\ell-1)} \right)$$

Final scores for link prediction are computed as:

$x_{ij}^{(r)} = \sigma(e_i^\top W_r e_j)$

b) Node Classification on Patient-Similarity Graphs

Each ED visit (episode) is a node $i$ with feature vector $x_i \in \mathbb{R}^{16}$, summarizing demographics, vital signs, and select history. Weighted edges $(i, j)$ are defined by patient-patient similarity $S(i,j)$, derived from distance/similarity metrics (cosine, Manhattan, Euclidean, Minkowski), with threshold $\tau$ controlling graph density.

The GNN (GCN, GATv2, GraphSAGE) propagates information through the patient graph via:

$$h_i^{(k+1)} = \sigma \left( W^{(k)}\,\text{AGG}_{j \in N(i)\cup\{i\}} (h_j^{(k)}) + b^{(k)} \right)$$

The inductive variant, GraphSAGE, employs neighborhood pooling and feature concatenation to enable inference on new nodes at triage.

2. Construction of ED Graphs: Nodes, Edges, and Features

Multi-modal Clinical KGs

• Node types: Patient, Encounter, Observation, Condition, CareAction
• Edge types: P→E, E→O, E→C, E→CA, direction encodes medical workflow
• Features: Node embeddings initialized per type, updated via message passing

Patient-similarity Graphs

• Nodes: Each represents a historical ED visit, characterized by a standardized 16-feature vector (e.g., age, blood pressure, smoking status)
• Edges: Weighted undirected; existence and strength determined by similarity $S(i,j)$ (e.g., $S(i,j) = (x_i \cdot x_j)/(\|x_i\|\|x_j\|)$ for cosine)
• Node labels: True triage code (Red, Orange, Yellow, Green)

3. Message Passing, Connectivity, and Information Flow

The definition of GNN connectivity ($A^{GNN}$) is a critical design variable. In the multi-relational context, Valls et al. demonstrate that domain-informed masks (e.g., only allow information flow Condition/Observation→Encounter, Patient→Encounter, Encounter→CareAction) yield higher accuracy (avg. $0.88$) versus using the raw KG ($0.43$) or bidirectional edges introducing test-time leakage ($0.19$).

For patient-similarity graphs, the choice of similarity metric and threshold $\tau$ modulates information propagation, with optimal $\tau$ values maximizing GNN performance before the graph becomes too dense (Defilippo et al., 2024).

GATv2 layers, employing attention coefficients $\alpha_{ij}$, and GraphSAGE—using neighborhood pooling—both enable the model to capture complex patient-patient influences in the node classification paradigm.

4. Role of Negative Edges, Training Objective, and Loss Functions

In real-world KGs such as Synthea, only positive clinical events are recorded. Valls et al. propose systematic negative edge augmentation: for each encounter $u$ with observed care action $c^+$, create explicit negatives $(u, \text{``encounter–careaction''}, c^-)$ for all $c^- \neq c^+$. The logistic loss over positive and negative links:

$$L = -\sum_{(i,r,j) \in E^+ \cup E^-} [ y^r_{ij} \log x^r_{ij} + (1-y^r_{ij}) \log (1-x^r_{ij}) ]$$

enables robust contrastive learning; removing negative edges severely degrades accuracy from $0.88$ to $0.60$ (Valls et al., 2023).

In the node classification setting, class-balancing (with SMOTE+ENN) and categorical cross-entropy loss are applied:

$$L = -\sum_{i \in V_L} \sum_{c=1}^{4} y_{ic} \log \hat{y}_{ic} + \lambda \| W \|_2^2$$

ensuring stability and convergence during model optimization (Defilippo et al., 2024).

5. Model Architectures, Training Protocols, and Empirical Results

Key architectural and training choices include:

• Relational GCN (KG link prediction): 2-layer encoder, embedding dimension $d\in[5,10]$, binary logistic loss, Adam optimizer with learning rate schedule ($0.1 \rightarrow 0.01 \rightarrow 0.001$), weight decay $5 \times 10^{-4}$, training for $1000$ epochs, early stopping against validation metrics (Valls et al., 2023).
• GraphSAGE (patient similarity): 5 layers, dims $$(16 \rightarrow 64) \rightarrow (64 \rightarrow 32) \rightarrow (32 \rightarrow 16) \rightarrow (16 \rightarrow 8) \rightarrow (8 \rightarrow 4)$$, dropout $p=0.2$, Adam optimizer ($lr=0.01$), up to 200 epochs, early stopping, inductive inference capability (Defilippo et al., 2024).
• GCN and GAT baselines: GCN (Kipf-Welling rule, up to 5 layers), GATv2 (Brody et al. 2021), both with architectures calibrated to input and output dimensions tailored for 4-class prediction.

Empirically, GraphSAGE on cosine-similarity graphs ($\tau=0.95$) achieves $89\%$ accuracy, outperforming SVM ($82.4\%$) and KNN ($78.0\%$) on raw features. R-GCN with domain-informed connectivity achieves accuracy $0.88$ on the Synthea-based triage link-prediction task, with performance degrading if the model is made deeper (over-smoothing) or negative edges are omitted (Valls et al., 2023, Defilippo et al., 2024).

Selected Results Table

Model	Task	Test Accuracy	Data Source & Graph Type
R-GCN (L=2, d=5)	Link Prediction	0.88	Synthea KG, C4 connectivity
R-GCN (raw KG only)	Link Prediction	0.43	Synthea KG, C1 connectivity
GraphSAGE	Node Classification	~0.89	Patient-similarity (cosine, τ=0.95)
SVM, Tabular	Node Classification	0.824	16-feature tabular

6. Integration with Clinical Triage Workflows and Deployment

Deployment for ED triage divides into procedural steps:

• Clinical KG: Extract and encode EHR modalities for patients, encounters, observations, conditions, and care actions. Incorporate negative samples by generating all non-observed care actions per encounter as negatives. Define communication mask $A^{GNN}$ to enforce domain-compliant information flow (e.g., allow only O/C→E, P→E, E→CA).
• Patient-similarity graph: On live triage, collect the 16 standardized features for a new arrival, preprocess as per training, insert as node $i_0$ in the similarity graph (edges to historical visits exceeding similarity threshold), and forward-pass through the trained GraphSAGE model to assign a triage code from the output probability distribution.

Advantages of these GNN-based pipelines include reproducibility, independence of individual nurse subjectivity, utilization of embedded clinical knowledge, adaptability to inductive node arrival (for patient classification), and a demonstrated gain (5–10%) in accuracy over rule-based or standard ML pipelines (Valls et al., 2023, Defilippo et al., 2024).

7. Practical Guidelines and Limitations

To maximize ED triage GNN utility:

• Explicitly separate factual graph structure from GNN communication by masking $A^{GNN}$, preventing test-time label leakage and focusing information flow on meaningful clinical relationships.
• Systematically generate negative samples if not recorded, pairing each encounter with all non-assigned downstream actions.
• Use moderate GNN depth ($L=2$) and embedding dimension ($d \in [5,10]$); over-deep GNNs suffer from over-smoothing.
• Tune similarity threshold $\tau$ to balance graph density and predictive signal in patient-similarity approaches.
• Early stopping and batch strategies: monitor for over-smoothing (notably beyond $L=2$ in R-GCNs) and use whole-graph or node-pair minibatches as appropriate.

These constraints and heuristics are validated in repeated-split experiments using both synthetic (Synthea) and real-world ED datasets, providing a robust foundation for scalable, interpretable, and clinically compatible ED triage automation (Valls et al., 2023, Defilippo et al., 2024).