The longitudinal course of bipolar disorder is characterised by recurrent episodes whose frequency tends to increase over time in a subset of patients the kindling hypothesis [5]. Established recurrence risk factors include the number and polarity of prior episodes, the inter-episode interval, residual subsyndromal symptoms, medication adherence and regimen stability, and circadian and social rhythm disruption. These factors are not independent; they interact through the temporal and causal structure of the illness course, which motivates a relational rather than a flat-feature representation.

The social zeitgeber theory holds that life events disrupt social rhythms (regular patterns of daily activity, sleep, and social interaction), which in turn destabilise circadian biological rhythms and precipitate mood episodes in vulnerable individuals. Social rhythm regularity, measured by the Social Rhythm Metric, predicts episode recurrence, and interpersonal and social rhythm therapy which stabilises these rhythms reduces recurrence [6]. This establishes social rhythm disruption as a relation between episodes worth encoding explicitly.

Graph neural networks learn node, edge, and graph-level representations by iterative message passing, in which each node aggregates transformed messages from its neighbours. The graph convolutional network (GCN) [7], GraphSAGE [8], and the graph attention network (GAT) [9] are homogeneous architectures: they assume a single edge type. For graph-level classification here, predicting recurrence from a patient’s episode-history graph a readout function pools node representations into a graph representation.

The relational graph convolutional network (R-GCN) extends the GCN to heterogeneous graphs with multiple relation types by learning a relation-specific weight matrix for each relation, so that messages passed along a temporal edge are transformed differently from messages passed along a pharmacological or social-rhythm edge. This relation-specific message passing is precisely what distinguishes the heterogeneous from the homogeneous approach and is the architectural basis of the present work. Heterogeneous graph transformers [10] further incorporate attention, but on small episode-history graphs the additional parameters do not justify themselves, as our experiments confirm.

Each patient’s observed history was represented as one graph containing 4 - 10 mood-episode nodes. Node features encoded episode polarity (depressive, manic, hypomanic, or mixed), normalised severity, duration, preceding inter-episode interval, chronological position, and episode-level social-rhythm instability. Three directed relation types connected nodes: 1) temporal succession, linking each episode to the next observed episode; 2) pharmacological transition, linking consecutive episodes when the simulated medication class, mood-stabiliser coverage, or regimen state changed; and 3) social-rhythm disruption, linking episode pairs that both exceeded the prespecified social-rhythm-instability threshold. Medication identity and pairwise social-rhythm co-disruption were represented in typed edges rather than duplicated as node features. All nodes and edges belonged to the observed history and preceded the outcome window.

Recurrence was defined as at least one new syndromal depressive, manic, hypomanic, or mixed episode during the 12 months following the final observed episode. The graph-level binary label was assigned at the end of the observed sequence: y = 1 for recurrence within the subsequent 12-month horizon and y = 0 otherwise. The outcome episode itself and all post-index information were excluded from node features and edge construction. Thus, the reported AUC, sensitivity, and specificity refer to discrimination of simulated 12-month recurrence from a patient graph constructed only from pre-horizon episode history.

The cohort comprised 700 independently simulated patients. Patient-level latent variables represented bipolar subtype, baseline episode propensity, medication-response vulnerability, adherence/regimen stability, and social-rhythm vulnerability. Episode counts were sampled between 4 and 10; episode polarity followed subtype-dependent categorical probabilities, while severity, duration, and inter-episode intervals were sampled from bounded continuous distributions calibrated to the ranges described in longitudinal bipolar-disorder literature. Correlated latent vulnerability terms induced clinically plausible dependence among frequent prior episodes, shorter inter-episode intervals, medication changes, and social-rhythm instability. Pharmacological-transition edges were generated whenever the simulated regimen state changed between adjacent episodes. Social-rhythm edges were generated when both episode nodes exceeded the instability threshold, with a small edge-flip probability to represent measurement error. Continuous node variables included random measurement noise, and a small proportion of values were set missing completely at random and median-imputed using training-set statistics. The recurrence probability was generated by a logistic rule combining prior episode burden, shorter recent inter-episode intervals, node-level residual severity, counts of pharmacological-transition edges, counts of social-rhythm-disruption edges, and interaction terms between medication instability and social-rhythm disruption. Bernoulli sampling from this probability produced a 31.4% recurrence prevalence. Consequently, the label-generation rule depended directly on two relation types also supplied as model inputs. This deliberate design tests whether relation-aware models can recover a known heterogeneous signal, but it may structurally favour the proposed architecture and is addressed explicitly as a limitation.

The proposed model was a two-layer relational graph convolutional network. Each layer computed a relation-specific message for every node, h_i’ = sigma(W_0 h_i + sum_r sum_{j in N_r(i)} (1/c_ir) W_r h_j), where W_r is the learned transformation for relation r and W_0 is the self-connection. Both layers used hidden dimension 64, ReLU activation, dropout 0.20, and L2 weight decay. A masked mean readout pooled node representations into a graph representation, followed by a two-layer classifier. The three-model ensemble size was fixed before evaluation. Three independently initialised R-GCNs using seeds 42, 43, and 44 were trained under the same protocol, and their predicted probabilities were averaged; models were not selected post hoc according to test performance.

Five comparators isolated the value of typed relations. The MLP operated on mean-pooled node features and ignored all edges. GCN, GraphSAGE, GAT, and the homogeneous graph transformer received the same nodes and the union of all edges, but without relation labels. To limit capacity and optimisation confounding, all neural comparators used two message-passing or hidden layers, hidden dimension 64, dropout 0.20, AdamW optimisation, the same maximum epoch budget, the same validation-based early-stopping rule, and comparable L2 regularisation. A common, prespecified validation grid was used for learning rate {0.0005, 0.001}, dropout {0.10, 0.20, 0.30}, and weight decay {0, 0.0001, 0.001}; architecture-specific parameters such as attention heads and GraphSAGE aggregator were selected only on the validation set. The MLP classifier was width-matched to the graph-level classifier as closely as possible. This design does not make the architectures identical, but it provides matched tuning effort and an approximately matched representation capacity for testing whether typed edges add information beyond general model capacity.

Patients were split once at the graph level using stratified sampling into training (70%, n = 490), validation (15%, n = 105), and test (15%, n = 105) sets with master seed 42; no patient contributed nodes to more than one split. Continuous preprocessing parameters were estimated from the training set only. Models were trained with AdamW and class-weighted binary cross-entropy for up to 200 epochs, with early stopping after 20 epochs without validation-AUC improvement. Hyperparameters and the ensemble specification were finalised using only the validation set. The operating threshold of 0.61 was selected on the validation set by maximising F1 and was then locked before the single test evaluation. No repeated train/validation/test splits were used; uncertainty therefore reflects 1000 patient-level bootstrap resamples of the locked test set rather than variation across data partitions. Outcomes included AUC, F1, sensitivity, specificity, Brier score, calibration, decision curve analysis, and Bayesian model comparison. Relation-type ablation retrained the complete pipeline after removing one edge type at a time. Per-relation message norms were calculated from the fitted heterogeneous model. The absence of repeated split experiments is reported as a reproducibility limitation.

Figure 1Figure 1 presents calibration curves and Figure 2Figure 2 the decision curve analysis. The Heterogeneous R-GCN achieved the lowest Brier score (0.180) of all models, indicating the best-calibrated recurrence probabilities, and the highest net clinical benefit across the range of plausible decision thresholds. The homogeneous models, limited by their inability to exploit relation types, showed both poorer calibration and lower net benefit.

Table 1 presents comparative performance on the locked simulated test set (n = 105). The Heterogeneous R-GCN achieved AUC = 0.822 (95% CI: 0.723 - 0.902), F1 = 0.644, sensitivity = 0.664, and specificity = 0.820. Homogeneous and no-graph comparators achieved AUC values from 0.695 to 0.742. Within this simulation, the approximately 0.08 AUC separation is consistent with an advantage from retaining relation labels under matched tuning. Because the recurrence generator itself used pharmacological-transition and social-rhythm edge statistics, the difference must not be interpreted as evidence of clinical superiority or as proof that the same margin will occur in observational data.

Figure 1. Calibration curves for all models. The Heterogeneous R-GCN (dark) achieves the lowest Brier score (0.180). Homogeneous baselines show poorer calibration. Perfect calibration = dashed diagonal.

Figure 2. Decision curve analysis. The Heterogeneous R-GCN (dark bold) achieves the highest net benefit across decision thresholds, dominating homogeneous GNNs and the no-graph MLP.

Table 1. Comparative model performance test set (n = 105).

95% bootstrap CI (proposed): AUC [0.723 - 0.902], F1 [0.490 - 0.772], Sens [0.500 - 0.826], Spec [0.734 - 0.900]. Threshold = 0.61, selected by maximising F1 on the validation set and locked before test evaluation. Homogeneous baselines (rows 1 - 5) merge or ignore relation types; the proposed model preserves them.

A single patient’s episode history as a typed graph: episode nodes connected by three relation types of temporal succession (blue), pharmacological transition (red dashed), and social rhythm disruption (green dotted). Medication and social-rhythm structure is encoded in the typed edges, not the node features (See Figure 3Figure 3).

Figure 3. Heterogeneous episode-graph schema.

Figure 4Figure 4 presents ROC curves with bootstrap CI bands. The Heterogeneous R-GCN (dark bold) dominates the homogeneous models across the operating range. The clustering of all homogeneous curves well below the heterogeneous curve provides a visual confirmation of the central result: the relation-type information, available only to the heterogeneous model, is what separates the two performance tiers.

Figure 4. ROC curves with 95% bootstrap CI bands (400 resamples). Heterogeneous R-GCN (dark bold) AUC = 0.822, separated from the homogeneous baseline tier (AUC 0.70 - 0.74).

Figure 5Figure 5 presents the relation-type ablation, the study’s central mechanistic result. Removing each relation type and retraining quantifies its contribution. Removing the pharmacological-transition relation caused the largest AUC drop (from 0.822 to 0.719, 0.103), identifying it as the most predictive relation. The social rhythm disruption relation was second (drop to 0.774), and temporal succession contributed least (drop to 0.787). That the temporal relation the only relation a naive sequential model would use is the least important, while the pharmacological and social-rhythm relations dominate, is the key argument for the heterogeneous formulation: the predictive structure lies precisely in the relation types that homogeneous and sequential models discard.

Figure 6Figure 6 presents the per-relation message-norm importance learned by the heterogeneous model, for all patients and for recurrence patients specifically. The

Figure 5. Relation-type ablation. AUC when each relation type is removed and the model retrained. Pharmacological transition is most critical (drop 0.103), social rhythm disruption second (0.048), temporal succession least (0.035). Red labels: AUC change from full model.

Figure 6. Per-relation message-norm importance in the Heterogeneous R-GCN, all patients (solid) versus recurrence patients (hatched). Pharmacological and social-rhythm relations contribute the largest message magnitude, consistent with the ablation.

message-norm analysis complements the ablation: it measures how much each relation contributes to node representations during message passing. The three relations carry substantial and comparable message magnitude (temporal 0.31, pharmacological 0.34, social rhythm 0.35), with the pharmacological and social-rhythm relations contributing the most consistent with the ablation result. The stability of relation importance between all patients and recurrence patients indicates that the model relies on the same relational structure across the population, rather than exploiting a subgroup-specific artefact.

Table2 and Figure 7Figure 7 present the Bayesian comparison. The Heterogeneous R-GCN achieved the lowest BIC (302.8), computed with an equal effective parameter

Table 2. Bayesian model comparison: BIC, WAIC, and Bayes Factors.

k_eff: equal effective parameter count across the comparable GNN models. log₁₀(BF): Bayes Factor in favour of the Heterogeneous R-GCN. Decisive: log₁₀(BF) > 2.

Figure 7. Bayesian model comparison. Left: BIC (Heterogeneous R-GCN = 302.8, lowest). Right: log₁₀ Bayes Factor evidence; all homogeneous baselines exceed the decisive threshold.

count across the architecturally comparable GNN models, with decisive Bayes Factor evidence (log₁₀ BF > 2) over every homogeneous baseline. Because the models share comparable complexity, the BIC difference reflects the heterogeneous model’s superior fit to the held-out data, providing formal model-selection evidence that relation-type information improves the model beyond what its parameter cost would justify [11].

Table3 presents subgroup performance. The model-maintained discrimination across clinical subgroups, with the highest performance in patients with frequent medication changes (AUC = 0.875) and frequent episodes (AUC = 0.853), the subgroups whose episode graphs are richest in pharmacological-transition and temporal edges, where the heterogeneous structure carries the most information. Performance in the no-adequate-mood-stabiliser subgroup (AUC = 0.842) confirms reliable prediction in a high-clinical-risk group [12][13].

Figure 8Figure 8 visualises the episode graphs of a representative recurrence patient and a representative stable patient. The recurrence patient’s graph exhibits denser pharmacological-transition and social-rhythm-disruption connectivity the relation

Table 3. Subgroup analysis—Heterogeneous R-GCN.

All subgroup n ≥ 12. Highest performance in subgroups with the richest relational structure (frequent medication changes, frequent episodes).

Figure 8. Representative patient episode graphs. Left: a recurrence patient, with dense pharmacological (red dashed) and social-rhythm (green dotted) connectivity. Right: a stable patient, dominated by temporal succession (blue). Node labels: episode type. Predicted recurrence probabilities shown per patient.

types the ablation identified as most predictive while the stable patient’s graph is dominated by simple temporal succession with sparse pharmacological and social-rhythm edges. This visualisation makes concrete the mechanism behind the model’s predictions: recurrence risk is encoded in the density and type of relational connections in the episode history, not in any single episode’s attributes.