Each analysis in this atlas is built on the same scaffold. A directed acyclic graph encodes the causal hypotheses; hazard ratios and standardised mean differences from the literature are converted to a common scale; eigenvalue-corrected correlation matrices strip the double-counting that arises when interventions share mechanism.
The framework follows Pearl (2009) and Pearl & Mackenzie (2018), with Chinn's SMD-to-OR transform
where trial endpoints differ from the target outcome. Confounders satisfying the
backdoor criterion are conditioned on; mediators are not, to avoid blocking the very paths
under study. Sensitivity is reported as the E-value: the minimum strength an unmeasured
confounder would need to explain away an observed effect. Each entry closes with an antithesis
section — what would falsify the inferred causal effect.
| Stage | Operation |
|---|---|
| Graph | Specify DAG G = (V, E) encoding mechanistic hypotheses. Distinguish confounders, mediators, colliders. |
| Identification | Use the backdoor criterion to identify the confounders the source studies adjusted for (this atlas consumes their adjusted estimates; it does not re-adjust raw data) Z such that P(Y | do(X)) = Σz P(Y | X, Z) P(Z). |
| Effect scaling | Convert SMD → HR via Chinn (2000); aggregate by inverse-variance weighting; flag publication bias. |
| De-correlation | Eigenvalue-corrected correlation matrix; remove redundant shared-mechanism variance (typical residual ρ̄ ≈ 0.30). |
| Counterfactuals | Compute Probability of Necessity, Sufficiency, and Necessity-and-Sufficiency per Tian & Pearl (2000). |
| Robustness | E-value, tipping-point analysis, leave-one-out sensitivity, dose-response saturation modelling. |
| Antithesis | Explicit counter-argument section: what would falsify the inferred causal effect? |
1. It does not perform backdoor adjustment — and it cannot. Backdoor adjustment operates on individual-level data: you condition on a confounder set so that, within its levels, treatment is as-if random. A published hazard ratio is already a summary statistic — the adjustment is baked in and cannot be undone or redone. You cannot re-adjust HR = 0.64 (UKPDS‑34); there is no distribution left to condition on. Every effect size here is taken from a named trial or a confounder-adjusted study, so the backdoor adjustment is the source study’s, and the confounders named in each DAG are the paths those studies adjusted for. What this engine contributes is the combination rule, not the adjustment.
2. What it audits instead: adjustment-set adequacy. The question that can be answered is whether each source’s adjustment set blocks the backdoor paths this DAG posits — the source chose confounders for its estimand, not ours. Every intervention now carries an adequacy verdict beside its evidence grade: RCT randomisation severs confounder→treatment arrows, so no backdoor path is open and adjustment is unnecessary by design; ADJ~ the source adjusted for its own set, but adequacy for this DAG’s paths is not established; ADJ! a named, documented bias plausibly explains part of the effect. Across the 287 arms audited: 129 not required (randomised), 140 partial, 18 insufficient. The named biases include healthy-vaccinee (influenza vaccine), immortal-time (medication for opioid use disorder), confounding by indication or severity (antibiotics in pneumonia; reliever overuse in asthma), ecological design (naloxone distribution, supervised consumption), and selection-for-surgery (bariatric, cataract). Hover any badge for the specific bias. A note on the “partial” class: adjustment adequacy is a question about design, not endpoint quality — an arm can be randomised (no open backdoor path) and still be provisional for a surrogate endpoint or a subgroup finding, which is an external-validity caveat carried by the evidence grade, not by this axis. Of the 140 “partial” arms, roughly a quarter are genuinely observational; the remainder are arms whose design is not stated in the cited source and which are therefore treated conservatively rather than assumed adequate. Resolving those requires verifying each source paper’s design and adjustment set against this DAG — work in progress, and deliberately not guessed at.
3. Downgrades are proportionate, and adequacy is a separate axis from strength. An ADJ! verdict costs exactly one evidence grade (A→B, B→C) — never a cliff. Conflating the two axes would be misleading and, in places, unsafe: methadone’s mortality hazard ratio is cohort-derived (immortal-time bias), but randomised evidence supports its retention and abstinence effects and it remains the standard of care for a fatal condition. Stamping it “grade C” would misrepresent the evidence base. The adequacy verdict is therefore shown beside the grade, never instead of it.
4. The combination is front-door-structured, not front-door-identified. Interventions are routed through an explicit mediator cascade: arms acting on the same mediator are substitutes and saturate against a dose-response ceiling; arms on different mediators are d-separated and compose in series. No correlation coefficient is applied to the mediated path. The mean cross-correlation ρ̄ is applied only to the un-mediated direct residual, and each oracle displays a ρ-sensitivity band so you can see exactly how much ρ moves its answer.
5. The honest limit. Pearl’s front-door criterion would additionally require each mediator to be complete (no unblocked path from intervention to outcome that bypasses it) and the mediator→outcome edge to be unconfounded. Neither is defended arm-by-arm, and baseline severity and stage routinely confound the mediator→outcome edge. Genuine backdoor estimation is possible only where individual-level data exist — which is the role of the MIMIC / NHANES harness, not of these literature-derived oracles. Combined figures are therefore within-model upper bounds under the stated cascade, saturation and monotonicity assumptions — not identified causal effects.