Anaemia affects roughly a third of the world’s population (~2 billion people) and is the single clearest example in this atlas of a surrogate trap: correcting the number (haemoglobin) is not the same as correcting mortality. This oracle estimates the causal reduction in mortality across iron, erythropoiesis-stimulating, HIF-PH-inhibitor and transfusion strategies, framed through the CKD, heart-failure and obstetric pathways where anaemia actually drives death. Hazard ratios are from named trials. For education, not individual medical advice.
Tick the interventions to combine. Each shows its trial effect estimate, 95% confidence interval (CI), E-value, mechanism, and citation. ★ = in the current Pareto effective set but not yet ticked.
Headline is the front-door estimate: shared Hb overlap removed via dose-response saturation; residual direct-effect overlap removed via the eigenvalue model at ρ̄.
Under monotonicity + exogeneity (E-value bounds the exogeneity assumption).
Faithful causal directed acyclic graph (DAG). Haemoglobin-raising therapies act through the shared mediator haemoglobin / red-cell mass, which drives tissue oxygen delivery and thence mortality (Y). Iron additionally acts independently of haemoglobin (direct myocardial / skeletal-muscle tissue-iron effects). Named confounders — underlying illness (reverse causation), inflammation, CKD stage — open back-door paths (adjusted). The mediator is non-monotonic: over-correcting it with an ESA adds thrombotic harm. Mediator cascade: interventions attach to the node they act on (underlying cause → iron substrate → erythropoietic → haemoglobin), which converge on the disease state and thence the endpoint — drawing the intermediate mediators explicitly is what exposes d-separation and per-channel saturation.
Eigenvalue diagnostics for the selected interventions under an equicorrelation matrix (off-diagonal ρ̄). A large λmax relative to k signals redundancy; n_eff is the effective number of independent interventions actually contributing.
On mechanistic grounds ρ̄ ≈ 0.30 is defensible: the haemoglobin-raising agents (ESA, HIF-PH inhibitor, transfusion) share one final common pathway — raising the number — so stacking them is largely redundant and, past target, harmful. ρ̄ is user-adjustable because iron’s tissue effect and “treat-the-cause” share little mechanism with pharmacological Hb-raising. Most of the overlap is now handled structurally by the mediator nodes (same-node substitutes saturate); ρ̄ governs only the residual correlation among direct effects.
Minimum-effective-set analysis. Set a target combined risk reduction; the model finds the smallest set of interventions — accounting for front-door mediator overlap — that reaches it, and highlights them. If the target exceeds what all interventions together can achieve, the full set is shown (never an empty one). "Apply" ticks exactly that set.
Monte Carlo propagation. Each selected intervention's log-effect is sampled from a normal distribution implied by its 95% CI; samples are combined with the same eigenvalue overlap discount. 5,000 draws.
Intervening on the selected set S with Pearl's do-operator (setting the interventions, not merely observing them). Contrast against do(∅) = no intervention.
For each intervention: "if not for this one, the combined front-door effect would be…". Isolates each intervention's marginal causal contribution after mediator-overlap removal, so shared-pathway agents are not double-credited.
| If not for… | HR without it | HR with full set | marginal RRR lost |
|---|
One-at-a-time sensitivity. Each intervention's effect is swung across its 95% confidence interval (others held at point estimate); the bar is the resulting swing in the combined front-door effect. A long bar means the combined estimate leans heavily on that single trial's precision.
Front-door (mediation) decomposition. Haemoglobin-raising therapies act through one shared mediator. Each log-effect is split into a haemoglobin-mediated (indirect) and a haemoglobin-independent (direct) part. Indirect parts are pooled through the mediator with dose-response saturation, removing the mediator cross-correlation; direct parts keep the residual eigenvalue correlation at ρ̄. Iron’s haemoglobin-independent tissue benefit is NOT discounted against the ESA / HIF-PHI / transfusion options — and, crucially, a high mediated fraction with a null hazard ratio (the ESA arms) exposes a mediator that moves without protecting. Here mediated effects are pooled WITHIN each cascade node (dose-response saturation of substitutes) and composed in SERIES across nodes (d-separated channels), with the per-node reductions reported so the channel structure is visible.
| Intervention | HR | %Hb↑ | med-frac | indirect log | direct log |
|---|
Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the Hb saturation (currently removing — of the summed mediated effect when interventions are stacked). Note a domain caveat: the ESA and HIF-PHI arms have a high haemoglobin-mediated fraction yet a null-to-harmful hazard ratio — the model therefore shows a mediator that is strongly moved but not protective. That is the intended lesson, not a bug.
Front-door caveat (antithesis): textbook front-door identification requires an unconfounded mediator→outcome edge; here it is confounded by reverse causation (illness→anaemia→death), and the mediator is non-monotonic (over-correction with an ESA increased stroke, TREAT HR 1.92). Iron trials were neutral on cardiovascular death alone, and transfusion strategy is mortality-neutral.
Select interventions to generate a plain-language summary.