Endometriosis affects an estimated ~6.5 million United States women and is a leading cause of pelvic pain, dysmenorrhoea and infertility, with long diagnostic delays. Benign, with essentially no mortality — the burden is chronic pain, quality of life and fertility. This oracle estimates the causal reduction in estrogen-driven lesion activity — the shared mediator — across analgesic, hormonal and surgical options, using effect sizes 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 lesion 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). Each therapy is a node; hormonal and surgical options act through the shared mediator estrogen-driven lesion activity, which drives pelvic pain, fertility/quality-of-life and recurrence — the components of the morbidity burden Y. NSAIDs act independently of lesion activity (prostaglandin-mediated pain). Named confounders — disease stage, central sensitisation, fertility goals — open back-door paths (adjusted). Mediator cascade: interventions attach to the node they act on (hormonal → symptomatic → surgical), 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: hormonal therapies overwhelmingly share the estrogen-suppression / menstrual-suppression pathway, so combining two hormonal agents is largely redundant. ρ̄ is user-adjustable because a prostaglandin-blocking analgesic and lesion excision share little mechanism. 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. Hormonal and surgical therapies act through one shared mediator — suppression of estrogen-driven lesion activity. Each log-effect is split into a lesion-mediated (indirect) and a lesion-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. NSAIDs, which relieve prostaglandin pain without touching the lesion, are NOT discounted against the hormonal 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 | %lesion | med-frac | indirect log | direct log |
|---|
Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the lesion saturation (currently removing — of the summed mediated effect when interventions are stacked). Note a domain caveat: hormonal options are mutually redundant and all prevent pregnancy, so the fertility-desired arm relies on surgery / assisted reproduction. Lesion-mediated fractions are transparent, adjustable priors.
Front-door caveat (antithesis): the endpoint is pelvic pain — a surrogate poorly correlated with lesion burden because of central sensitisation and adenomyosis. Hormonal control reverses on stopping, and surgery recurs without post-operative suppression, so on-treatment relative risks overstate durable benefit.
Select interventions to generate a plain-language summary.