HPV is near-universal over the sexual lifetime and causes essentially all cervical cancer plus a rising share of oropharyngeal, anal and penile cancers — ~350,000 cervical-cancer deaths a year, ~90% in low- and middle-income countries. This oracle estimates the causal reduction in HPV-attributable cancer death across vaccination, screening and precancer-treatment strategies, all acting through the persistent-HPV → CIN → cancer axis. Effect sizes are from named trials and national linkage studies. 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 HPV 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). Vaccination, screening and precancer treatment act through the shared mediator persistent high-risk HPV → cervical intraepithelial neoplasia, which drives invasive HPV cancer and thence cancer death (Y). Gender-neutral / male vaccination acts outside the cervical CIN pathway (oropharyngeal / anal cancers). Named confounders — age at exposure, screening attendance, HIV — open back-door paths (adjusted). Mediator cascade: interventions attach to the node they act on (vaccination → barrier → screening → precancer), 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: vaccination (primary), screening (secondary) and excision (tertiary) act at different points on the same HPV→CIN→cancer axis, so they are partly redundant — a fully vaccinated cohort needs less screening. ρ̄ is user-adjustable because male vaccination and cervical screening address partly different cancers. 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. Vaccination, screening and treatment act through one shared axis — persistent HPV → CIN. Each log-effect is split into an HPV/CIN-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. Gender-neutral / male vaccination, which prevents non-cervical HPV cancers, is NOT discounted against the cervical arms. 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 | %HPV↓ | med-frac | indirect log | direct log |
|---|
Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the HPV saturation (currently removing — of the summed mediated effect when interventions are stacked). Note a domain caveat: primary, secondary and tertiary cervical arms are partly redundant on the same axis (a vaccinated cohort needs less screening), whereas male vaccination adds a distinct non-cervical benefit. HPV/CIN-mediated fractions are transparent, adjustable priors.
Front-door caveat (antithesis): the vaccine is prophylactic (benefit collapses after exposure), first-generation vaccines miss ~30% of cancers, the endpoint is decades downstream, and ~90% of deaths are in low-resource settings — so the dominant real-world lever is access and equity, not tool choice.
Select interventions to generate a plain-language summary.