Portal Vein Thrombosis — Bayesian Causal Analysis

Patient Profile / Etiology

Bayesian Adjustment Parameters

Cross-Correlation Override (ρ̄)

Auto

Evidence tier → adjusted HR: A–D

Evidence level A (multiple RCTs) · B (single RCT/obs) · C (limited). Lower grades excluded from the combined HR.

0 = Auto-compute from matrix; >0 = Manual override

Confounder Adjustment (% HR bias)

Positive = confounding by severity inflates HRs

Thrombus Extent (% complete occlusion)

50%

Select Interventions

1.00

Adjusted HR

95% CI: [—, —]

—%

Recanalization Prob.

at 6 months

—

NNT

ARR: —%

—

E-Value

Unmeasured confounding

Recanalization Probability Over Time · Kaplan-Meier Analog

HR Decomposition by Causal Pathway · Waterfall

Sensitivity Analysis: Contribution of Each Intervention to HR Reduction · Ranked by Marginal Effect

Pareto Frontier: HR Reduction vs. Cumulative Bleeding/Complication Risk · Optimal Combinations

Pairwise Cross-Correlation Matrix (ρ) — Selected Interventions · Causal Pathway Overlap

Dose–Response Saturation Curves · 4-Parameter Hill Function

Counterfactual Analysis — Probability of Necessity (PN), Sufficiency (PS), and PNS · Pearl do-Calculus

PN = P(Y₀=bad | X=1, Y=bad) ≈ (RR−1)/RR = 1−HR | PS = P(Y₁=good | X=0, Y=bad) ≈ (1−HR)·(p₀/p₁) | PNS = PS + PN − 1 (monotonic assumption)

Evidence Quality Summary · All 16 Interventions

Intervention	HR (95% CI)	Mechanism	Recan.%	Bleed%	Evidence	E-Value	N (studies)	Key Sources

Bayesian Causal Analysis Methodology

Framework: Judea Pearl's Structural Causal Model (SCM) with do-calculus. The causal DAG (Directed Acyclic Graph) for PVT includes the following structural equations:

Thrombus(t) = f(Coagulation, PortalFlow, Endothelium, Etiology) + ε₁
Treatment = g(Thrombus_extent, Cirrhosis_severity, MPN_status, Timing) + ε₂
Outcome = h(Thrombus(t), Treatment, Portal_Pressure, Baseline_LF) + ε₃

Backdoor Criterion: The set {Cirrhosis_severity, Thrombus_extent, Etiology, Timing} d-separates Treatment from Outcome in the causal graph. Adjustment is applied via the backdoor formula:

P(Y=y | do(X=x)) = Σ_z P(Y=y | X=x, Z=z) · P(Z=z)

Cross-Correlation Adjustment: Interventions sharing causal pathways inflate the apparent combined effect. The Pearl-adjusted log-HR is computed as:

ln(HR_adj) = (1 − ρ̄) × Σᵢ ln(HRᵢ)
where ρ̄ = (2/n(n−1)) × Σᵢ<ⱼ ρᵢⱼ (mean pairwise cross-correlation)

E-Value (Unmeasured Confounding): For each intervention HR < 1, the minimum risk ratio an unmeasured confounder must have with both exposure and outcome to fully explain away the observed association:

E-value = HR⁻¹ + √(HR⁻¹ × (HR⁻¹ − 1))

Dose–Response: Saturation modeled via 4-parameter Hill equation:

Effect(d) = E_max × dⁿ / (EC₅₀ⁿ + dⁿ)

Antithesis (Commandment 7): Key limitations include: (1) Most PVT anticoagulation evidence is from observational cohorts; RCT data are limited to n<100. (2) TIPS data include strong selection bias toward suitable anatomy and Child-Pugh A/B. (3) Cross-correlations derived from mechanistic overlap, not empirical data. (4) Combined HR floors at biological minimum (~0.15) due to spontaneous fibrinolysis. (5) Thrombus age (acute <3m vs. chronic) is a major effect modifier not fully captured by the composite endpoint.

Counterfactual Probabilities

PN – Probability of Necessity —

PS – Probability of Sufficiency —

PNS – Probability of Necessity and Sufficiency —

Marginal HR Contribution (Top 8)

Cumulative Complication Risk

Major Bleeding Risk —

Procedural Complication —

Uncertainty Propagation (95% CI)

Pareto-Optimal Recommendation

Causal Pathway Categories

● Anticoagulation — Factor Xa / Thrombin

● Procedural — Mechanical recanalization

● Thrombolytic — Plasminogen activation

● MPN-Targeted — JAK2/JAK1 inhibition

● Portal Pressure — Splanchnic hemodynamics

● Antiplatelet — Platelet aggregation

● Infection Control — Inflammatory thrombus

● Transplant — Definitive hepatic replacement