| Removed Intervention | HR shifts to | Δ ARR (pp) | Marginal contribution | Rank-loss |
|---|
| Intervention | HR | 95% CI | Mechanism | Evidence | Source |
|---|
1 · Causal Identification Strategy
For each disease phenotype, we construct a Directed Acyclic Graph (DAG) G over intervention nodes X, mediators M, confounders U, and outcome Y. The interventional distribution P(Y | do(X = x)) is identified via Pearl's backdoor criterion when a set Z blocks all backdoor paths from X to Y and contains no descendants of X.
2 · Cross-Correlation Removal (Effective Independent Effects)
Naïve combination assumes independence: log HRcombined = Σ log HRi. To correct for shared causal pathways and overlap in mechanism (mean off-diagonal correlation ρ̄), we shrink by the effective independent count:
Default ρ̄ = 0.30 reflects the empirical mean inter-intervention correlation in pulmonary RCT meta-data (range 0.18–0.42 across COPD, asthma, lung cancer trials). Eigenvalue spectrum of the working correlation matrix ΣX is checked for positive-definiteness; if minimum eigenvalue λmin < 0.01, ridge regularisation (+0.01·I) is applied.
3 · Dose–Response Saturation
For fraction f of canonical dose, the effective log-HR is scaled by a Michaelis-Menten-like saturation kernel:
At f = 1.0, ≈95% of the asymptotic effect is realised; at f = 0.5, ≈78%. Saturation point (95% of asymptote) occurs near f ≈ 1.0 for most pharmacologic agents in the dataset.
4 · E-Value (Unmeasured Confounding Bound)
For an observed risk ratio RR < 1, the minimum strength of association on the risk-ratio scale that an unmeasured confounder would need with both treatment and outcome to fully explain away the effect:
(VanderWeele & Ding, Ann Intern Med 2017). A larger E-value implies greater robustness.
5 · Probability of Necessity & Sufficiency (PNS / PN / PS)
Following Pearl (Causality, 2009 §9.2), under the monotonicity assumption:
PN answers "How likely is the bad outcome only because the intervention was withheld?"; PS answers "How likely would the intervention have produced the good outcome?".
6 · Population Attributable Fraction (PAF)
For each risk factor / withheld intervention i with prevalence pi and adjusted HRi:
Joint PAF over multiple correlated factors uses Eide–Geffeler partitioning to avoid double-counting.
7 · Baseline Risk Calibration
Age- and sex-adjusted baseline 5-year risk is obtained from disease-specific registries (e.g., COPDGene, BODE; IASLC 8th edition for NSCLC; EmphasisHF for PH; UK CF Registry; CDC TB; OSCAR for OSA). Per-decade modifier on log-hazard: +0.04 (age > 60), male sex +0.05–0.20 depending on disease, current smoking +log(2)·(PY/40) for combustion-driven endpoints.
A1 · Independence assumption is generous, not conservative
ρ̄ = 0.30 is a working mean; true correlations between interventions targeting the same final common pathway (e.g., inhaled corticosteroids and biologics in eosinophilic asthma both reduce type-2 inflammation) can exceed 0.5. The "Pearl-adjusted" combined HR shown should be interpreted as an upper-bound benefit estimate. Push ρ̄ to 0.45 in sensitivity for realistic scenarios.
A2 · HRs are population averages, not individual treatment effects (ITEs)
A combined HR of 0.40 does not mean every patient gets 60% risk reduction. Heterogeneity of treatment effect (HTE) is substantial in COPD (eosinophil-high vs -low ICS responders), NSCLC (driver-mutation status), and IPF (rapid- vs slow-progressors). The patient-level credible interval is wider than the displayed CI.
A3 · Multiplicative HRs can over-promise on the relative scale
Stacking five HR=0.7 interventions naïvely yields HR=0.17 (83% reduction). Pearl-adjusted estimate (at ρ̄=0.30) ≈ HR 0.36. But real-world adherence, drug-drug interaction, and competing-risk decomposition typically deliver 50–70% of the projected absolute risk reduction.
A4 · The DAG itself is a model, not the territory
Omitted variables (e.g., epigenetic age, gut microbiome composition, indoor PM2.5) may confound multiple intervention arms simultaneously, creating residual bias. The E-value quantifies how strong such a hidden confounder would need to be — interpret E<2 cautiously.
A5 · Competing risks shrink benefits in older patients
For a 78-year-old with COPD GOLD 4, cardiovascular and cancer mortality compete with respiratory mortality. The marginal benefit of any single pulmonary intervention is bounded by the cause-specific hazard share — typically 0.4–0.6 of all-cause mortality at this profile. ARR projections may be 30–50% optimistic.
A6 · Some "interventions" are not modifiable in clinical time
Lifelong non-smoking, premorbid VO₂max, and early-life socioeconomic status carry the largest causal weight but cannot be "applied" to an existing patient. This tool prioritizes actionable interventions; static risk factors appear as confounders rather than levers.