Uterine fibroids are extremely common; symptomatic disease affects an estimated ~26 million United States women, driving heavy menstrual bleeding, anaemia, bulk/pressure symptoms, fertility problems and a large share of hysterectomies. Benign, with essentially no mortality — the burden is morbidity and quality of life. This oracle estimates the causal reduction in fibroid bleeding / bulk burden — the shared mediator — across medical and procedural 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 bleeding 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; most act through the shared mediator fibroid burden / uterine bleeding, which drives anaemia, bulk symptoms and fertility/quality-of-life outcomes — the components of the morbidity burden Y. Tranexamic acid acts independently of fibroid volume (antifibrinolytic bleeding reduction). Named confounders — especially fibroid size and location — open back-door paths (adjusted). Mediator cascade: interventions attach to the node they act on (medical → procedural), 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 medical options share the estrogen-suppression / endometrial pathway, and volume-reducing procedures share the fibroid-infarction pathway, so within a class stacking gives diminishing returns. ρ̄ is user-adjustable because a non-hormonal antifibrinolytic and a volume-reducing procedure share little. 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. Most therapies act through one shared mediator — reduction of fibroid burden / uterine bleeding. Each log-effect is split into a fibroid/bleeding-mediated (indirect) and an 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. Tranexamic acid, which reduces bleeding without shrinking fibroids, is therefore NOT fully discounted against the hormonal/procedural 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 | %bleed | med-frac | indirect log | direct log |
|---|
Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the bleeding saturation (currently removing — of the summed mediated effect when interventions are stacked). Note a domain caveat: definitive surgery (hysterectomy) and uterus-sparing options are mutually exclusive within a treatment plan, and fertility goals plus fibroid location constrain which options are eligible. Fibroid/bleeding-mediated fractions are transparent, adjustable priors.
Front-door caveat (antithesis): the endpoint is bleeding / symptom control — a surrogate with no mortality translation. Medical control reverses on stopping (fibroids regrow), so on-treatment relative risks overstate durable benefit relative to structural procedures.
Select interventions to generate a plain-language summary.