Renal-BCN

Pearl SCM v2.3 Bayesian Causal Network · Kidney Disease Intervention Modeling
Network: active Interventions on: 0 Adjusted HR: 1.000 Build: 2026.05
Baseline Risk
—%
prior to intervention
Residual Risk
—%
after adjusted HR
Combined HR (do-adjusted)
1.000
95% CI [—, —]
NNT (5-yr)
—
number needed to treat
Overview
Forest / Interventions
Causal DAG
Pareto Set
Sensitivity
Dose–Response
Method
Antithesis
Refs

Pearl-Adjusted Causal Effect

E[Y | do(X1=1, …, Xk=1)] · backdoor-adjusted, ρ̄-decorrelated
GRADE: pending
Combined HR
1.000
95% CI [—, —]
Absolute Risk Reduction
0.0%
vs baseline
E-value (composite)
—
unmeasured confounder threshold

Causal Effect Summary

Hazard ratios are combined via log-additive Pearl back-door adjustment after subtracting the cross-correlation-attributable shared effect. Coverage assumes ITT-equivalent adherence (slider-controlled).
PAF (selected set)
—
population attributable fraction
PNS
—
probability of necessity & sufficiency
PN
—
probability of necessity
PS
—
probability of sufficiency
Independence loss
—
ΔHR from ρ̄-correction
Dose saturation
—
Hill model fractional saturation

Adjusted HR vs Components — Waterfall

Stepwise contribution of each intervention to the final adjusted HR, in mechanism-rank order.

Forest Plot — Individual Intervention HRs

Each bar = hazard ratio (square) with 95% CI (horizontal line). Greyed bars = currently disabled. Sorted by mechanism class. Vertical line at HR = 1.0 marks the null.
active off HR > 1

Intervention Detail Table

InterventionClassBase HR95% CIE-valuePrimary SourceGRADE

Structural Causal Model — Directed Acyclic Graph

Solid arrows = causal pathways; dashed = confounding paths blocked by back-door adjustment. Nodes scale with current path strength.
active intervention node mediator confounder outcome

Minimum Effective Set (MES) — Pareto Frontier

Trade-off between cumulative HR reduction and intervention burden (cost · complexity · pill count). MES marks the inflection at which marginal HR reduction per additional intervention falls below 0.02 absolute.

MES Recommendation

Tornado — One-at-a-Time Sensitivity

Each row varies a single intervention HR through its 95% CI and shows the impact on the combined HR. Wider bars = greater leverage. Most-leveraged interventions deserve the strongest evidence scrutiny.

Monte Carlo Distribution (10,000 draws)

Each draw samples each active HR from its CI (log-normal) and multiplies under the ρ̄-decorrelated covariance. Histogram shows distribution of the combined HR.

Dose–Response Saturation Curves (Hill model)

Fractional effect = Dn / (EC50n + Dn). Current intervention adherence (slider) is marked as a point on each curve. Beyond saturation, additional dose buys little; the cross-correlation between mechanism-overlapping interventions becomes the limiting factor.

Cross-Correlation Heatmap

Pairwise mechanism-overlap correlation matrix (eigenvalue-corrected). Darker = greater mechanistic redundancy; the do-operator subtracts the redundant share.

Methodology — Pearl Structural Causal Model Pipeline

Step 1 — Literature Extraction

Hazard ratios are drawn from large randomized controlled trials and high-quality meta-analyses indexed in PubMed, Cochrane, and ClinicalTrials.gov. Where only standardized mean differences (SMD) are reported (e.g., proteinuria outcomes), conversion to HR follows the Chinn transformation: log HR ≈ π/√3 · SMD.

Step 2 — Causal DAG Construction

Nodes are partitioned into {exposures, mediators, confounders, outcome}. The back-door criterion identifies the minimum adjustment set Z such that (X ⫫ Y | Z)GX̄. Front-door-structured mediation is reserved for partially identifiable mediators (e.g., proteinuria along the SGLT2i → KFRE pathway).

Step 3 — Cross-Correlation Matrix

The pairwise correlation matrix Σ is constructed from mechanism overlap (shared pathway dummies) and trial co-randomization data when available. If Σ is not positive semi-definite, the nearest-PSD matrix is obtained via Higham's eigenvalue projection: negative eigenvalues are clipped to ε = 10-6 and the matrix re-symmetrized.

Step 4 — Do-Operator Application

For the joint intervention set S = {X1, ..., Xk}, the log-HR is decomposed as:

log HRdo(S) = Σᵢ wᵢ · log HRᵢ − (ρ̄ · Σᵢ<ⱼ √(wᵢwⱼ) · log HRᵢ · log HRⱼ)

where wᵢ is the adherence-weighted dose-response fraction (Hill model). The subtraction term removes the shared mechanism variance attributable to ρ̄.

Step 5 — Confidence Propagation

Each log HRᵢ is assigned a normal prior centered on its trial estimate with σᵢ = (log U − log L)/3.92 from the reported 95% CI. The combined log HR variance is Σᵢ wᵢ² σᵢ² + 2 ρ̄ Σᵢ<ⱼ wᵢwⱼ σᵢσⱼ.

Step 6 — E-value Computation

For the combined HR, E-value = HR + √(HR · (HR − 1)) for HR < 1, or its reciprocal form for HR > 1 (VanderWeele & Ding 2017). This is the minimum strength an unmeasured confounder would require on both the exposure-confounder and confounder-outcome associations to nullify the observed effect.

Step 7 — Counterfactual Quantities

Probability of Necessity (PN), Probability of Sufficiency (PS), and PNS are computed under the monotonicity assumption (treatments are not harmful to those who would benefit), giving:

PNS = max(0, P(Y₁) − P(Y₀));   PN = PNS/P(Y₁);   PS = PNS/(1 − P(Y₀))

Step 8 — Population Attributable Fraction

PAF = (P(Y) − P(Y|do(S))) / P(Y), evaluated at population baseline prevalence for the selected disease/stage strata.

Step 9 — Antithetical Critique

For each intervention, the model presents the strongest counter-argument (publication bias, surrogate endpoint reliance, generalizability, adverse-event trade-off) in the Antithesis tab. The user may demote any intervention's effective HR toward 1.0 to model skeptical priors.

Primary Evidence Base