Thyroid dysfunction affects an estimated ~20 million United States adults (hypothyroidism most common, with hyperthyroidism, nodular and autoimmune disease). Mostly morbidity, but untreated dysfunction is linked to atrial fibrillation, cardiovascular events, fracture and, in extremes, mortality. This oracle estimates the causal effect of restoring euthyroid control — the shared mediator — across replacement, anti-thyroid, ablative and surgical options, using effect sizes from named guidelines and 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 thyroid-control 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; each acts through the shared mediator euthyroid restoration, which drives atrial-fibrillation/cardiovascular risk, bone loss and symptoms — the components of the morbidity/mortality burden Y. Beta-blockade acts independently of thyroid state (symptomatic). Named confounders — especially disorder type — open back-door paths (adjusted). Mediator cascade: interventions attach to the node they act on (restore thyroid → symptomatic → adjunct), 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 within a disorder: replacement, anti-thyroid, ablative and surgical options all converge on the euthyroid set-point, so combining two definitive therapies is redundant. ρ̄ is user-adjustable, but the more important caveat is that hypo- and hyper-thyroid therapies are never stacked. 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. Each therapy acts through one shared mediator — restoration of euthyroid control. Each log-effect is split into a control-mediated (indirect) and an independent (direct) part. Indirect parts are pooled through the mediator with dose-response saturation (you cannot become more than euthyroid), removing the mediator cross-correlation; direct parts keep the residual eigenvalue correlation at ρ̄. Beta-blockade, a thyroid-state-independent symptomatic bridge, is not discounted against the disease-modifying 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 thyroid-control saturation (currently removing — of the summed mediated effect when interventions are stacked). Note the overriding domain caveat: hypothyroid and hyperthyroid therapies treat opposite disorders and are never combined; and treating subclinical hypothyroidism is contested (TRUST was null). Control-mediated fractions are transparent, adjustable priors.
Front-door caveat (antithesis): the endpoint is thyroid control — a process surrogate. The atrial-fibrillation, cardiovascular and fracture benefits are largely inferred from association, not proven in randomised trials, and over-replacement is itself harmful.
Select interventions to generate a plain-language summary.