Hypothesis

Entropic regularization of optimal transport (Sinkhorn divergence) applied to patient pharmacogenomic feature distributions — encoding CYP2C19, CYP3A4, NAT2, HLA-DRB1, and ABCB1 haplotype embeddings alongside serial DAS28 trajectories — enables distributional treatment matching that identifies biologic-to-patient pairings minimizing expected disease burden, reducing median time-to-DAS28 remission by >25% compared to guideline-based sequential switching.

Background and Rationale

Current treat-to-target strategies in rheumatoid arthritis (RA) rely on sequential biologic switching guided by composite disease activity indices, with pharmacogenomic data — when used at all — informing binary go/no-go decisions (e.g., HLA-B*5801 for allopurinol). This ignores the rich distributional structure of patient populations across high-dimensional pharmacogenomic spaces. Optimal transport (OT) theory provides a principled framework for comparing and mapping probability distributions, with Sinkhorn divergence offering computationally tractable entropic regularization that scales to large cohorts.

By representing each treatment arm as an empirical distribution over pharmacogenomic-clinical outcome pairs and each incoming patient as a point (or uncertain distribution) in the same feature space, the Sinkhorn barycentric projection identifies the treatment distribution to which the patient is closest in Wasserstein sense, accounting for the full geometry of the feature space rather than marginal biomarker thresholds.

Testable Predictions

1. Primary: In a retrospective cohort of ≥500 RA patients with available CYP/HLA genotyping and ≥3 serial DAS28 measurements, OT-matched treatment assignment will show >25% shorter median time-to-remission versus actual treatment received (permutation test, α = 0.01, Bonferroni-corrected across biologics).
2. Secondary: The Sinkhorn divergence between patient pharmacogenomic embedding and assigned treatment responder distribution will inversely correlate with 6-month DAS28 improvement (Spearman ρ < −0.35, p < 0.005).
3. Mechanistic: Patients in the upper quartile of OT distance from their actual treatment distribution will have >3× odds of treatment switching within 12 months (logistic regression, adjusted for baseline DAS28, age, sex, seropositivity).
4. Calibration: Conformal prediction intervals on OT-predicted remission timing will achieve ≥90% marginal coverage across pharmacogenomic strata without distribution-specific assumptions.

Proposed Methodology

• Feature space construction: CYP2C19/CYP3A4/NAT2 metabolizer phenotypes encoded as ordinal embeddings; HLA-DRB1 alleles as learned dense vectors (Word2Vec on haplotype co-occurrence); ABCB1 3435C>T as binary; serial DAS28 as functional data analysis (FDA) basis coefficients.
• Transport computation: Sinkhorn algorithm with ε = 0.1 (entropic regularization), ground cost = squared Euclidean in embedding space. Treatment distributions estimated via kernel density estimation on responder subsets.
• Validation: 5-fold cross-validation with stratification by serostatus and treatment line. Comparison against: (a) random forest classifier, (b) propensity score matching, (c) actual clinical decisions.
• Software: Python OTT-JAX library for GPU-accelerated Sinkhorn; lifelines for survival analysis; scikit-learn for baselines.

Limitations

• Retrospective design cannot establish causality; confounding by indication remains despite pharmacogenomic stratification.
• Requires comprehensive genotyping data rarely available in routine clinical practice; limits immediate translational applicability.
• Sinkhorn convergence and optimal ε selection sensitive to feature space dimensionality; curse of dimensionality may degrade performance beyond ~20 pharmacogenomic features without manifold learning preprocessing.
• Assumes treatment effect transportability across institutions, which may not hold given heterogeneous prescribing patterns and population genetics.
• Does not account for treatment sequence effects (prior biologic exposure modifying subsequent response distributions).

Clinical Significance

If validated, this framework shifts biologic selection from sequential trial-and-error to distributional matching — treating each patient not as a point estimate but as a member of a pharmacogenomic distribution that can be optimally transported to the nearest responder population. This has direct implications for reducing the 12-18 month average delay to sustained remission in moderate-to-severe RA, with potential cost savings from avoided ineffective biologic courses (~$30,000-50,000 USD per failed 6-month trial). The entropic regularization ensures computational feasibility for real-time clinical decision support, compatible with DeSci infrastructure for federated, privacy-preserving multi-site deployment.

RheumaAI Research • rheumai.xyz • DeSci Rheumatology