Periodontitis affects roughly 42% of United States adults over 30 (severe disease ~8%). Beyond tooth loss, chronic periodontal inflammation is linked to systemic inflammation, cardiovascular disease, worse glycaemic control, and aspiration pneumonia. This oracle estimates the causal reduction in periodontal inflammation — the shared mediator — achievable by combining treatments, using effect sizes from named trials and meta-analyses. The systemic-disease and mortality links are largely observational and heavily confounded by shared risk factors, so they are flagged throughout.
Tick the interventions to combine. Each shows its trial hazard ratio, 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 inflammation-mediator 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 distinct node; nearly all effects flow through the shared mediator periodontal inflammation (probing depth / bleeding), which drives tooth loss, systemic inflammation (→ cardiovascular disease / diabetes), and aspiration pneumonia — each a route to mortality. Smoking cessation additionally lowers cardiovascular risk independently of periodontitis. Named confounders (notably smoking and diabetes, which cause BOTH periodontitis and cardiovascular disease) open strong back-door paths (adjusted). Illustrative of structure, not yet the identification engine.
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 for this domain: incretin drugs, surgery, diet, and activity overwhelmingly share the weight-loss / insulin-sensitivity pathway, so ~30% of their nominal effects overlap. A mediation analysis of semaglutide found ~80% of its MACE benefit is not mediated by weight loss, which is why ρ̄ is user-adjustable rather than fixed.
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-hazard-ratio 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 hazard ratio 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 hazard ratio is swung across its 95% confidence interval (others held at point estimate); the bar is the resulting swing in the combined front-door HR. A long bar means the combined estimate leans heavily on that single trial's precision.
Front-door (mediation) decomposition. Nearly every periodontal therapy acts through one shared mediator — reduction of periodontal inflammation (probing depth / bleeding on probing). Each log-effect is split into an inflammation-mediated (indirect) and an inflammation-independent (direct) part. Indirect parts are pooled through the mediator with dose-response saturation (pockets can only close so far — adding a third adjunct to mechanical debridement yields diminishing pocket reduction), removing the mediator cross-correlation; direct parts keep the residual eigenvalue correlation at ρ̄. Smoking cessation, whose cardiovascular benefit is partly independent of periodontitis, is therefore NOT fully discounted for overlap with the local therapies.
| Intervention | HR | %perio↓ | infl-med | indirect logHR | direct logHR |
|---|
Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the periodontal-inflammation saturation (currently removing — of the summed inflammation-mediated effect when therapies are stacked — mechanical debridement, antibiotics and antiseptics all act on the same pockets). This domain has an unusually LARGE back-door problem: smoking and diabetes cause both periodontitis and cardiovascular disease, so a high ρ̄ is defensible. Inflammation-mediated fractions are transparent, adjustable priors.
Front-door caveat (antithesis): the cited endpoints are periodontal (probing depth, tooth loss) — well proven. The link to cardiovascular mortality is largely UNproven: the randomised PAVE trial of periodontal treatment for secondary cardiovascular prevention was null, and the periodontitis–cardiovascular association is confounded by shared causes (smoking, diabetes, socioeconomic status). The inflammation→cardiovascular path here is a plausible mechanism, not a demonstrated causal effect; downstream mortality estimates are upper bounds.
Select interventions to generate a plain-language summary.