Tobacco smoking is the single largest modifiable cause of death — over 480,000 deaths a year in the United States and ~8 million worldwide, with ~1.1 billion smokers. This oracle estimates the causal reduction in smoking-attributable mortality across cessation pharmacotherapies, nicotine replacement, behavioural support and non-combustible harm reduction, all mediated by achieving sustained abstinence. Effect sizes are from named trials and Cochrane network meta-analyses. 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 abst 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). Cessation aids act through the shared mediator sustained abstinence from combustible tobacco, which lowers tobacco-smoke exposure and thence smoking-attributable mortality (Y). Switching to a non-combustible source acts independently of nicotine abstinence — it removes combustion, the actual killer. Named confounders — dependence severity, comorbidity, motivation — open back-door paths (adjusted). Mediator cascade: interventions attach to the node they act on (pharmacotherapy → behavioural → unaided), 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: the cessation aids share the final common pathway of achieving abstinence, so stacking two pharmacotherapies is partly redundant (though medication + behavioural support IS additive). ρ̄ is user-adjustable because a non-combustible switch and a nicotinic partial agonist 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. The cessation aids act through one shared mediator — sustained abstinence. Each log-effect is split into an abstinence-mediated (indirect) and a 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. Non-combustible switching, which removes combustion without requiring nicotine abstinence, is NOT discounted against the abstinence aids. 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 | %abst | med-frac | indirect log | direct log |
|---|
Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the abst saturation (currently removing — of the summed mediated effect when interventions are stacked). Note a domain caveat: the pharmacotherapy aids are partly redundant (shared abstinence pathway), whereas behavioural support multiplies medication and non-combustible switching adds a distinct mechanism. Abstinence-mediated fractions are transparent, adjustable priors.
Front-door caveat (antithesis): quitting at all — and before ~40 — dwarfs the choice among aids (~90% of smoking mortality is avoidable by early cessation). The e-cigarette arm is genuinely contested (long-term safety, dual use, youth uptake), and the mortality hazards are modelled from abstinence efficacy, not measured in cessation trials.
Select interventions to generate a plain-language summary.