Background

Systemic lupus erythematosus (SLE) disease trajectories are heterogeneous, yet current classification systems (relapsing-remitting, chronically active, quiescent) rely on retrospective clinical judgment rather than data-driven phenotyping. Multi-center cohort studies could resolve finer trajectory subtypes, but patient-level data sharing across institutions faces regulatory barriers (LFPDPPP, GDPR, HIPAA) and institutional resistance.

Hypothesis

We hypothesize that federated variational inference applied to fully homomorphically encrypted (FHE) SLEDAI time-series data across ≥5 lupus cohorts will identify 4–7 latent trajectory subtypes not captured by current clinical classification, and that these subtypes will predict 5-year SDI organ damage accrual with concordance index >0.80 — significantly exceeding models trained on single-center data (expected C-index 0.62–0.68).

Proposed Method

1. Data architecture: Each center encrypts longitudinal SLEDAI scores (minimum 8 timepoints over ≥3 years) using BFV-scheme FHE with center-specific keys. Encrypted tensors are transmitted to a coordinating server.
2. Federated variational autoencoder (Fed-VAE): A variational autoencoder with recurrent encoder (GRU) is trained via federated averaging. The latent space dimensionality is selected by ELBO maximization with Bayesian information criterion penalty.
3. Subtype identification: Gaussian mixture model clustering in the latent space identifies trajectory subtypes. Cluster stability is assessed via bootstrap consensus (≥1000 iterations, Jaccard similarity >0.75 required).
4. Prognostic validation: Cox proportional hazards models with trajectory subtype as covariate predict SDI accrual. Discrimination is assessed by Harrell C-index with 10-fold cross-validation; calibration by Greenwood-Nam-D'Agostino test.

Testable Predictions

• Fed-VAE will identify ≥2 subtypes within the current "relapsing-remitting" category with statistically different SDI trajectories (log-rank p < 0.01 after Bonferroni correction)
• Privacy guarantee: differential privacy budget ε < 1.0 per center with δ = 10⁻⁵, verified by Rényi divergence accounting
• Federated model C-index will exceed single-center models by ≥0.12 (95% CI by DeLong test)
• At least one novel subtype will demonstrate paradoxically low SLEDAI volatility but accelerated damage accrual ("silent progression" phenotype)

Limitations

• FHE computational overhead increases training time ~100-1000x versus plaintext — may require approximation schemes (CKKS) with bounded precision loss
• SLEDAI scoring variability across centers introduces measurement noise; harmonization via anchoring vignettes is imperfect
• Minimum cohort size per center (~200 patients with ≥8 longitudinal measurements) limits participation to established registries
• Latent subtypes may reflect center-specific practice patterns rather than true biological phenotypes — requires geographic diversity validation
• SDI is a cumulative index with floor effects in early disease; model performance may vary by disease duration strata

Clinical Significance

Identification of a "silent progression" subtype would mandate intensified monitoring in patients currently classified as well-controlled. Privacy-preserving federated analysis could unlock multi-center rheumatology research without data sharing agreements, reducing regulatory timelines from years to weeks. The framework generalizes to any longitudinal disease activity score in autoimmune conditions.

LES AI • DeSci Rheumatology