Bayesian Causal Atlas · Vol. Women’s Health · Pearl Structural Causal Model

Uterine Fibroids — Structural Causal Analysis

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.

Method. Structural Causal Model (SCM) with backdoor adjustment (Pearl). Interventions are not assumed independent: most reduce fibroid volume or menstrual bleeding, so their overlap is removed by an eigenvalue-corrected equicorrelation model at an adjustable mean cross-correlation ρ̄ (default 0.30). Robustness to unmeasured confounding is quantified with the E-value. PN / PS / PNS are reported under monotonicity. Every relative risk is cited — no effect size is invented. The front door is resolved through an EXPLICIT mediator cascade (medical → procedural → disease state), not one lumped node: each intervention acts on a specific node, so same-node interventions are substitutes that saturate against each other, while different-node interventions are d-separated given the intermediate node and compose in series. The cross-correlation removal thus follows from the graph structure; the residual ρ̄ cleans up only the mediator-independent (direct) effects.
ρ̄ = 0.30
A–D (all)
A high (RCT/meta) · B cohort · C case-series/modelled · D consensus/provisional. Lower-grade interventions are excluded from the DAG, front-door pooling, Pareto, Monte‑Carlo & sensitivity.

Interventions

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.

Combined causal estimate

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.

1.00
Combined RR
0%
Relative risk ↓
Pooled E-value
Interventions selected (k)
0
Effective independent dimensions (n_eff)
0
Redundancy discount applied
0%
Baseline risk (illustrative anchor)
Absolute risk after intervention
Absolute risk difference (RD)
Backdoor-only RR (no front-door)
Mediator (bleeding) overlap removed
Number needed to treat (NNT)
ρ-sensitivity band (ρ 0 → 0.6)
Interpretation

Causal attribution

Under monotonicity + exogeneity (E-value bounds the exogeneity assumption).

Probability of Necessity (PN)
Probability of Sufficiency (PS)
Prob. of Necessity & Sufficiency (PNS, lower bound)
Causal DAG
Cross-correlation
Pareto (threshold)
Monte Carlo
Front-door mediation
What-if / If-not-for
Sensitivity
Antithesis

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.

Confounders U:age · fibroid size/number/location · parity · fertility goals · anaemia · BMI → back-door paths (adjusted)Tranexamic acidLNG-IUSCombined oralcontraceptiveGnRH antagonistcomboUterine arteryembolizationMyomectomyHysterectomyMedical(bleeding / size)Procedural(remove / ablate)Fibroid bleeding& bulkSymptomburdenFront-door: through fibroid/bleeding reductionFibroid-independent (antifibrinolytic bleeding)Back-door confounding (adjusted)

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.

k (selected)
0
λmax
λmin
n_eff = (Σλ)² / Σλ²
Condition number

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.

Target combined risk ↓ ≥ 50%

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.

Median combined RR
95% simulation interval
Standard deviation of combined RR
P(combined RR < 0.90)

Antithesis — challenging this oracle's own conclusions

The endpoint is symptom control, not survival. Fibroids are benign; leiomyosarcoma is rare. Estimates are surrogates for bleeding, anaemia, bulk symptoms and quality of life — there is essentially no mortality to reduce.
Medical control reverses on stopping. GnRH antagonists, ulipristal and hormonal options suppress bleeding while taken but fibroids regrow after discontinuation; only surgery/embolization gives durable structural change. The on-treatment relative risk overstates lasting benefit.
Definitive is not free. Hysterectomy cures fibroids but ends fertility and carries operative risk; the near-zero relative risk ignores the irreversibility and the competing harms of major surgery.
Fertility goals split the options. A woman wanting pregnancy cannot use hysterectomy, and embolization’s fertility effect is uncertain; the pooled estimate is only meaningful once fertility intent and fibroid location are fixed.
Ulipristal carries a rare severe harm. Ulipristal is highly effective but its use is restricted after cases of severe liver injury — a competing harm the efficacy relative risk does not capture.

What-if — the do-operator: P(Y | do(S))

Intervening on the selected set S with Pearl's do-operator (setting the interventions, not merely observing them). Contrast against do(∅) = no intervention.

P(outcome | do(∅)) — baseline
P(outcome | do(S)) — intervened
Absolute risk reduction (ARR)
Number needed to treat (NNT)

If-not-for — but-for counterfactual (leave-one-out)

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 itRR with full setmarginal 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.

Optimistic bound (all at CI-low)
Point estimate
Pessimistic bound (all at CI-high)
Pooled E-value (confounding robustness)

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.

Mediator saturation cap = 60% bleeding ↓
Sum of standalone bleeding reduction (naive)
Combined bleeding reduction after saturation
Mediator overlap removed (1 - saturation)
Direct-effect redundancy removed (1 - n_eff/k)
Front-door combined RR
Backdoor-only combined RR (comparison)
InterventionRR%bleedmed-fracindirect logdirect 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.

Executive summary

Select interventions to generate a plain-language summary.