Vision-threatening eye disease — glaucoma, age-related macular degeneration (AMD), and diabetic retinopathy — affects tens of millions of United States adults. Vision loss is not merely disability: it independently raises the risk of falls / fractures, depression, and mortality. This oracle estimates the causal reduction in vision loss — the shared mediator of those downstream harms — achievable by disease-specific therapies (intraocular-pressure lowering for glaucoma; vascular-endothelial-growth-factor [VEGF] suppression for AMD / diabetic retinopathy). Downstream mortality links are largely observational and flagged.
Tick the interventions to combine. Each shows its trial hazard ratio, 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 vision-loss-mediator 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). Disease-specific therapies act through different proximal mediators — intraocular pressure (glaucoma) and VEGF / macular leakage (AMD, diabetic retinopathy) — which converge on the shared mediator vision loss. Vision loss then drives depression, falls / fractures and mortality. Low-vision rehabilitation is vision-independent: it reduces falls without restoring acuity. Named confounders open back-door paths (adjusted). Illustrative of structure, not yet the identification engine.
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 for this domain: incretin drugs, surgery, diet, and activity overwhelmingly share the weight-loss / insulin-sensitivity pathway, so ~30% of their nominal effects overlap. A mediation analysis of semaglutide found ~80% of its MACE benefit is not mediated by weight loss, which is why ρ̄ is user-adjustable rather than fixed.
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-hazard-ratio 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 hazard ratio 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 hazard ratio is swung across its 95% confidence interval (others held at point estimate); the bar is the resulting swing in the combined front-door HR. A long bar means the combined estimate leans heavily on that single trial's precision.
Front-door (mediation) decomposition. Most therapies act through one shared mediator — prevention of vision loss (reached via disease-specific proximal mediators: intraocular pressure or VEGF leakage). Each log-effect is split into a vision-mediated (indirect) and a vision-independent (direct) part. Indirect parts are pooled through the mediator with dose-response saturation (vision can only be preserved up to its baseline — you cannot restore the same lost letters twice), removing the mediator cross-correlation; direct parts keep the residual eigenvalue correlation at ρ̄. Low-vision rehabilitation, which reduces falls WITHOUT improving acuity, is therefore NOT discounted for overlap with the sight-preserving therapies.
| Intervention | HR | %vision↓ | vis-med | indirect logHR | direct logHR |
|---|
Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the vision-preservation saturation (currently removing — of the summed vision-mediated effect when sight-preserving therapies are combined). Note an important caveat unique to this domain: an intraocular-pressure drug and an anti-VEGF injection only combine if the same patient has BOTH glaucoma and a retinal disease — otherwise the pooled estimate is hypothetical. Vision-mediated fractions are transparent, adjustable priors.
Front-door caveat (antithesis): the cited endpoints are vision outcomes (acuity / field) — well proven. Their link to mortality is largely observational: the cataract-surgery mortality benefit (hazard ratio ~0.6) is confounded by healthy-patient selection, and vision→mortality associations may reflect frailty rather than causation. Falls→fracture→mortality is better supported. Downstream mortality estimates are upper bounds.
Select interventions to generate a plain-language summary.