A Pearl Structural Causal Model framework applied to 18 cardiovascular phenotypes across atherosclerotic, heart-failure, valvular, arrhythmic, and cardiomyopathic strata. Select a disease, configure intervention bundles, and observe Pearl-adjusted (backdoor + do-calculus) hazard reductions with channel-structured cross-correlation removal (mechanistic-overlap matrix; within-channel saturation), E-values, PNS / PN / PS, population attributable fraction, dose–response saturation, and antithetical critique.
Select category, then variant/stage. The intervention panel auto-filters to evidence-based therapies for that specific phenotype. Baseline absolute risks reflect untreated or sub-optimally managed cohorts at the corresponding stage.
Per-intervention hazard ratios are combined through mechanistic channels, not a flat product. Interventions are ordered by benefit and each contributes only its residual, channel-independent effect after discounting by its mechanistic overlap (pairwise correlation) with the strongest already-counted intervention: same-channel substitutes (two lipid agents, ACEi vs ARNI) saturate against each other, while interventions on independent channels are d-separated and compose in series. This yields the Pearl-adjusted combined HR — less optimistic than naïve multiplicative pooling for overlapping mechanisms, without over-penalising genuinely independent ones.
Active interventions (red) → mechanism nodes (gold) → endpoint (white). Edge thickness encodes do-calculus effect strength. Backdoor paths via comorbidity confounders are adjusted.
Each row decomposes per-intervention contribution: naïve HR, E-value (unmeasured confounding threshold), PNS (probability of necessity & sufficiency), PN (necessity), PS (sufficiency), and Pearl-adjusted marginal contribution after correlation removal.
| Intervention | Class | HR (95% CI) | E-value | PNS | PN | PS | Pearl-Adj Δ | PAF |
|---|
(a) Pareto frontier of marginal benefit; (b) Dose–response saturation for continuous interventions; (c) Monte Carlo uncertainty distribution; (d) Cross-correlation heatmap of active interventions.
Interventions ordered by Pearl-adjusted contribution (descending). Cumulative benefit shows diminishing returns.
Continuous-dose interventions: HR vs dose. Hill/log-saturation kinetics. Shows ceiling effects beyond k₅₀.
10,000 draws from log-normal posteriors per intervention CI, with correlation-adjusted compounding. 95% credible interval shown.
Mechanistic-overlap correlation matrix. ρ̄ ≈ 0.30 average enforces Pearl-adjusted attenuation of naïve multiplicative pooling.
Greedy forward-selection algorithm builds the full Pareto frontier for the selected phenotype: at each step k, the intervention yielding the largest marginal Pearl-adjusted hazard-ratio reduction is added to the bundle. Set a target relative risk reduction (RRR) with the slider — the minimum bundle that achieves it is highlighted, with one-click apply.
Drag the slider to set the desired RRR for the composite endpoint. The system finds the smallest evidence-supported bundle (and its Pearl-adjusted HR) that meets or exceeds the target.
| k | Greedy-selected bundle (most-recent additions in italic) | HRadj | RRR | Δ vs k−1 |
|---|
"What-if" and "if-not-for" interrogation: removing single interventions from the active set quantifies their marginal causal contribution. Tornado plot identifies leverage interventions.
| If we removed… | Combined HR (without) | Δ from full bundle | Relative impact | Tornado |
|---|
Per Commandment 07: challenge own conclusions and solve the counter-argument.
(i) Effect-modification by phenotype. The catalog HRs are pooled trial-level estimates. Individual phenotypes carry effect modifiers that may attenuate benefit: ICD in non-ischemic DCM (DANISH 2016) showed neutral effect on all-cause mortality despite SCD reduction; SGLT2i benefit in HFpEF is concentrated in LVEF ≤ 60% (PARAGON-HF post-hoc); ablation in long-standing persistent AF underperforms paroxysmal AF.
(ii) Selection bias in RCT populations. RCT cohorts are typically younger, less polypharmacy-burdened, and more adherent than real-world patients. External-validity attenuation of 20–40% is commonly observed (e.g., MERIT-HF replication in registries).
(iii) Cross-correlation handling — both directions. The Pearl ρ̄ ≈ 0.30 attenuation may over-correct when interventions act on truly orthogonal pathways (e.g., DOAC anti-thrombotic + statin anti-inflammatory). Conversely, ρ̄ may under-correct for the dominant lifestyle cluster (diet–exercise–weight–BP), where the underlying causal structure is dense.
(iv) Competing risks. All HR-based combinations assume proportional hazards; in advanced disease (HFrEF NYHA IV, severe AS unrepaired), non-cardiac competing mortality erodes attributable benefit. Subdistribution hazards (Fine-Gray) would yield more conservative estimates.
(v) Adherence decay. Real-world adherence drops to ~50% by year 1 for statin, ~60% for ARNI, ~70% for ICD-monitored populations. Multiplicative discounting by adherence retention would push Pearl-adjusted HR toward 0.55 × bundle benefit.
(vi) Why effects may nevertheless be realistic:
(vii) Recommendation. Treat the "Pearl-adjusted combined HR" as an upper bound of biologically plausible benefit. Real-world expectation should be multiplied by an adherence discount factor of 0.65–0.80 and a competing-risks attenuator of 0.85–0.95 depending on age and frailty.
Computational pipeline applied to every intervention bundle.
| Step | Procedure | Formula / Mechanism | Reference |
|---|---|---|---|
| 1 | Define SCM with disease as endpoint Y, interventions X₁…X_n, confounders Z (age, sex, comorbidity) | Y = f(X, Z, U) | Pearl 2009 §1.4 |
| 2 | Identify backdoor set Z for each X_i → Y | (Z ⫫ X_i | Y) blocks all backdoor paths | Backdoor criterion |
| 3 | Convert SMDs / odds ratios to hazard ratios where needed | HR ≈ exp(β); Chinn SMD: ln(OR) = π·SMD/√3 | Chinn Stat Med 2000 |
| 4 | Naïve compounded HR (independence assumption) | HR_naïve = Π HR_i (for active i) | — |
| 5 | Pairwise correlation ρ_ij from mechanism overlap class | ρ_ij ∈ [0.10, 0.75] | Class clustering |
| 6 | Average correlation ρ̄ across active set | ρ̄ = mean(ρ_ij), i≠j | — |
| 7 | Pearl-adjusted compounded HR | HR_adj = HR_naïve^(1 − ρ̄ · (n − 1) / n) | Custom shrinkage |
| 8 | E-value for unmeasured confounding | E = HR + √(HR(HR − 1)) where HR ≤ 1 → reciprocal | VanderWeele 2017 |
| 9 | PNS / PN / PS bounds (Tian-Pearl) | PNS = P(Y_{X=1}=0, Y_{X=0}=1); bounds via do-calculus | Pearl 2009 §9.2 |
| 10 | Population attributable fraction | PAF = p·(HR − 1)/(1 + p·(HR − 1)) | Levin 1953 |
| 11 | Dose-response saturation (continuous interventions) | HR(d) = 1 − h_max · d / (k₅₀ + d) | Hill kinetics |
| 12 | Monte Carlo posterior (10,000 draws) | HR_i ~ LogNormal(ln(HR), σ); σ = (ln(UCL) − ln(LCL))/3.92 | Bayesian compounding |
| 13 | Counterfactual leave-one-out sensitivity | Δ_i = HR_adj(full) − HR_adj(full \ {i}) | Custom |
| 14 | Antithetical critique | Adherence discount × competing-risks attenuator | §06 above |