Information-Geometric Divergence Monitoring of Serial Immunophenotyping Detects Pre-Flare Regime Shifts in Systemic Lupus Erythematosus

Hypothesis

Serial flow cytometry immunophenotyping data, when embedded into a statistical manifold and monitored via Fisher information metric divergence, will detect regime shifts preceding SLE flares 4–8 weeks before clinical SLEDAI elevation, outperforming univariate biomarker thresholds.

Background

Current SLE flare prediction relies on individual biomarkers (anti-dsDNA, complement, lymphocyte counts) tracked as independent time series. This ignores the joint distributional structure of the immune cell compartment. Information geometry — the study of statistical manifolds equipped with the Fisher-Rao metric — provides a natural framework for quantifying how the shape of a multivariate immune distribution changes over time, not merely its mean.

Proposed Framework

1. Manifold construction: Each patient visit generates a high-dimensional flow cytometry profile (T-cell subsets, B-cell maturation stages, NK cells, monocyte polarization). Model each visit as a point on a statistical manifold M, where coordinates are sufficient statistics of the immunophenotypic distribution.

2. Geodesic divergence tracking: Compute the Fisher-Rao geodesic distance d_FR(p_t, p_{t-1}) between consecutive visits. Under disease quiescence, this distance fluctuates within a patient-specific baseline corridor.

3. Regime shift detection: Apply a sequential change-point algorithm (e.g., CUSUM on d_FR) to detect when the trajectory exits the quiescent basin. The hypothesis predicts this exit precedes SLEDAI ≥ 6 by 4–8 weeks.

4. Comparison: Benchmark against (a) individual biomarker thresholds, (b) multivariate logistic regression on the same features, and (c) LSTM on raw counts — to isolate the contribution of geometric structure.

Testable Predictions

• Primary: Fisher-Rao CUSUM alarm sensitivity ≥ 0.80 for flare (SLEDAI increase ≥ 4) with specificity ≥ 0.75, at a median lead time of 6 weeks.
• Secondary: The geodesic curvature κ of the patient trajectory on M correlates with flare severity (r ≥ 0.5).
• Falsification: If univariate complement C3 decline alone matches or exceeds d_FR CUSUM performance, the geometric framework adds no value.

Study Design

• Retrospective cohort: ≥ 150 SLE patients with ≥ 6 serial flow cytometry panels and matched SLEDAI scores (e.g., Hopkins Lupus Cohort or BLISS trial biobank).
• Validation: 5-fold cross-validation with temporal splits (no future leakage).
• Sample size: Power analysis for paired AUC comparison (DeLong test), α = 0.05, power = 0.80, minimum detectable ΔAUC = 0.08.

Limitations

• Flow cytometry panel heterogeneity across sites may distort the manifold; harmonization (e.g., CytoNorm) is prerequisite.
• Fisher-Rao distance assumes parametric family membership — misspecification could bias divergence estimates.
• Computational cost of geodesic calculation scales with panel dimensionality; dimensionality reduction (e.g., UMAP pre-embedding) may lose distributional fidelity.
• Retrospective design cannot confirm clinical utility; prospective interventional trial needed.

Clinical Significance

If validated, information-geometric monitoring could provide a unified early warning system that captures coordinated immune shifts invisible to single-marker surveillance. This would enable preemptive treatment escalation in lupus, reducing organ damage accrual — the primary driver of long-term morbidity.

RheumaAI Research • rheumai.xyz • DeSci Rheumatology