Uncorrected refractive error affects roughly 1.1 billion people and is the leading cause of visual impairment worldwide; myopia is projected to reach ~4.8 billion people by 2050. This oracle separates two problems on two causal paths: immediate correction (spectacles, surgery) of the vast uncorrected burden, and childhood progression control (atropine, orthokeratology, defocus optics, red-light, outdoor time) to prevent future high / pathologic myopia. Effect sizes 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 axial 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). Control therapies act through the shared mediator axial elongation / refractive-error progression, which drives high / pathologic myopia and thence visual impairment (Y). Correction (spectacles, surgery) acts directly on current acuity, bypassing progression. Named confounders — onset age, parental myopia, near-work — open back-door paths (adjusted). Mediator cascade: interventions attach to the node they act on (refractive → environmental → pharmacologic → optical), 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 optical control arms (ortho-k, DIMS, MiSight) all exploit peripheral myopic defocus, so combining two of them is largely redundant. ρ̄ is user-adjustable because atropine (pharmacologic) and red-light act through partly distinct mechanisms, which is why atropine+ortho-k is additive. 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… | RR without it | RR 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. Control therapies act through one shared mediator — axial elongation. Each log-effect is split into an elongation-mediated (indirect) and a 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. Correction (spectacles / surgery), which restores acuity without touching elongation, is NOT discounted against the control options. 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 | RR | %ctrl | med-frac | indirect log | direct log |
|---|
Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the axial saturation (currently removing — of the summed mediated effect when interventions are stacked). Note a domain caveat: the optical defocus arms are mutually redundant (shared mechanism), whereas atropine and red-light add mechanism. Elongation-mediated fractions are transparent, adjustable priors from published axial-length data.
Front-door caveat (antithesis): the endpoint is a surrogate — millimetres of axial length, not lifetime blindness — and rebound on stopping erodes durability. The largest real-world win is simply correcting the ~1.1 billion with uncorrected refractive error; progression control addresses a smaller, future, childhood-specific burden.
Select interventions to generate a plain-language summary.