Background

Differential diagnosis between Rheumatoid Arthritis (RA), Psoriatic Arthritis (PsA), Gout, Reactive Arthritis, and early SLE with articular predominance remains challenging, particularly in seronegative presentations. Current approaches rely on classification criteria applied independently, missing the conditional dependencies between features.

Hypothesis

A Directed Acyclic Graph (DAG) Bayesian Network encoding expert-elicited causal relationships between clinical features achieves AUC >0.90 for 5-way differential diagnosis of inflammatory arthritis, outperforming multinomial logistic regression (expected AUC 0.75-0.82) by explicitly modeling:

1. Conditional dependencies: RF positivity and anti-CCP are not independent given RA diagnosis
2. Causal structure: HLA-B27 → axial involvement → sacroiliitis (directed path)
3. Missing data propagation: Bayesian inference naturally handles incomplete workups via marginalization
4. Prior incorporation: Prevalence priors from Latin American cohorts (GLADAR, BIOBADAMEX)

Network Structure

Proposed DAG nodes (27 variables):

• Serological: RF, anti-CCP, ANA, anti-dsDNA, uric acid, HLA-B27, HLA-DRB1
• Clinical: joint distribution (symmetric/asymmetric), DIP involvement, dactylitis, enthesitis, tophi, skin psoriasis, morning stiffness duration, onset age, sex
• Imaging: erosions, joint space narrowing, periostitis, sacroiliitis
• Acute phase: ESR, CRP
• Diagnosis node: {RA, PsA, Gout, ReA, SLE-articular}

Edge structure derived from ACR/EULAR criteria + CASPAR + Yamaguchi + expert rheumatologist consensus (Dr. Zamora-Tehozol).

Parameter Learning

• Structure: Expert-defined DAG (not learned from data — avoids overfitting)
• Parameters: Maximum likelihood from BIOBADAMEX cohort + Bayesian smoothing (Dirichlet priors α=1)
• Inference: Variable elimination for exact posterior P(Diagnosis | observed features)
• Implementation: pgmpy library (Python), exportable to ONNX for deployment

Testable Predictions

1. Bayesian Network AUC >0.90 vs logistic regression AUC 0.75-0.82 on held-out test set
2. Calibration (Brier score <0.15) superior to random forest and gradient boosting
3. The network correctly identifies seronegative RA (RF−/CCP−) with sensitivity >0.70 by leveraging imaging and clinical pattern nodes
4. Missing data scenarios (incomplete workup) degrade BN performance by <5% AUC vs >15% for complete-case logistic regression

Clinical Impact

Early accurate differential diagnosis reduces time-to-appropriate-DMARD by 3-6 months in ambiguous presentations, directly improving ACR/EULAR treat-to-target outcomes.

References

• Aletaha D, et al. 2010 RA Classification Criteria. Arthritis Rheum. 2010;62:2569-81.
• Taylor W, et al. CASPAR Criteria for PsA. Arthritis Rheum. 2006;54:2665-73.
• Koller D, Friedman N. Probabilistic Graphical Models. MIT Press, 2009.
• Scutari M. Learning Bayesian Networks with the bnlearn R Package. J Stat Softw. 2010.