Excess adiposity affects >100 million United States adults (41.9%) and sits upstream of cardiovascular disease, type-2 diabetes and several cancers. This oracle estimates the causal reduction in mortality / major adverse cardiovascular events (MACE) achievable by combining weight-lowering interventions, using hazard ratios from named trials. Endpoints are mixed (mortality, MACE, diabetes-prevention surrogates) and unified only as upstream effects. 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 weight 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). Weight-lowering therapies act through the shared mediator excess adiposity / body weight, which drives cardiometabolic risk (CVD, type-2 diabetes, cancer) and thence mortality / MACE (Y). Incretins additionally act independently of weight (direct vascular / anti-inflammatory effects — ~80% of the semaglutide benefit). Named confounders — baseline BMI, diabetes, reverse causation — open back-door paths (adjusted). Mediator cascade: interventions attach to the node they act on (energy balance → adiposity → metabolic), 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: weight-lowering therapies share the adiposity pathway, so stacking two weight-loss agents is partly redundant on the mediated component. ρ̄ is user-adjustable because a diet and an incretin’s weight-independent vascular effect 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… | HR without it | HR 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. Weight-lowering therapies act through one shared mediator — excess adiposity. Each log-effect is split into a weight-mediated (indirect) and a weight-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. The incretins’ large weight-independent vascular benefit is NOT discounted against the weight-loss 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 | HR | %TBWL | med-frac | indirect log | direct log |
|---|
Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the weight saturation (currently removing — of the summed mediated effect when interventions are stacked). Note a domain caveat: endpoints are mixed (mortality, MACE, diabetes-prevention surrogates) and not strictly commensurable; weight-mediated fractions are transparent, adjustable priors set from published mediation analyses.
Front-door caveat (antithesis): textbook front-door identification requires full mediation and an unconfounded mediator→outcome path. Neither holds perfectly — mediation is partial (~80% of incretin benefit is weight-independent) and weight→mortality is confounded by reverse causation (illness causes weight loss). Look AHEAD was null overall.
Select interventions to generate a plain-language summary.