Erectile dysfunction (ED) affects an estimated ~30 million United States men and rises steeply with age and vascular risk. It is a morbidity condition — but a clinically important cardiovascular sentinel: organic ED reflects endothelial disease and precedes coronary events by years. This oracle estimates the causal improvement in erectile / endothelial function — the shared mediator — from oral, lifestyle, hormonal and procedural options, separating symptomatic relief from the ED-independent cardiovascular benefit of root-cause therapy. 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 erectile 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 endothelial function / penile perfusion, driving erectile function, wellbeing and — for root-cause therapies — cardiovascular risk. Lifestyle, statin and smoking cessation also act independently of erectile function on atherosclerotic CVD. Symptomatic drugs (PDE5 inhibitors, injections, prosthesis) have NO cardiovascular arrow. Named confounders open back-door paths (adjusted). Mediator cascade: interventions attach to the node they act on (vascular risk → hormonal → on-demand → mechanical), 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: vasoactive and vascular-risk interventions overlap on the same endothelial / nitric-oxide pathway, so stacking a PDE5 inhibitor onto lifestyle change yields diminishing incremental erectile benefit. ρ̄ is user-adjustable because mechanically distinct options (oral vasodilator vs implant) 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 — improved endothelial / erectile function. Each log-effect is split into a function-mediated (indirect) and a function-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. Lifestyle, statin and smoking cessation, which lower cardiovascular risk independently of erections, are therefore NOT fully discounted against the symptomatic drugs — and the symptomatic drugs carry no cardiovascular credit at all. 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 | %funct | med-frac | indirect log | direct log |
|---|
Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the erectile saturation (currently removing — of the summed mediated effect when interventions are stacked). Note the key distinction: PDE5 inhibitors, injections, vacuum devices and prostheses are purely symptomatic — they restore erections but do not treat the vessel. Function-mediated fractions are transparent, adjustable priors.
Front-door caveat (antithesis): the endpoint is erectile function (IIEF response) — a surrogate. ED’s real prognostic value is as a cardiovascular sentinel; the mortality benefit comes only from the root-cause arm, not from making erections work.
Select interventions to generate a plain-language summary.