Obstructive sleep apnoea (OSA) affects roughly 20–30 million United States adults (an estimated 80–90% undiagnosed) and is linked to hypertension, cardiovascular disease, and motor-vehicle crashes. This oracle estimates the causal reduction in mortality / major adverse cardiovascular events (MACE) achievable by combining OSA therapies, using hazard ratios (HRs) from named published trials — and flagging where only surrogate apnoea-hypopnoea-index (AHI) evidence exists.
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 AHI-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 intervention is a distinct node; effects flow through the shared apnoea-hypopnoea-index (AHI) mediator (front-door) and AHI-independent paths into two outcome branches — cardiovascular disease, and (via daytime sleepiness) motor-vehicle crashes — both reaching mortality / injury. Named confounders open 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 airway therapy acts through one shared mediator — reduction of the apnoea-hypopnoea index (AHI, events/hour). Each log-hazard-ratio is split into an AHI-mediated (indirect) and an AHI-independent (direct) part. Indirect parts are pooled through the mediator with dose-response saturation (you cannot abolish the same apnoea twice), removing the mediator cross-correlation; direct parts keep the residual eigenvalue correlation at ρ̄. A largely AHI-independent intervention (e.g. physical activity, whose benefit is mostly weight-/fitness-mediated) is therefore NOT fully discounted for overlap with airway therapies.
| Intervention | HR | AHI↓ (/h) | AHI-med | indirect logHR | direct logHR |
|---|
Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the AHI dose-response saturation (currently removing — of the summed AHI-mediated effect when airway therapies are stacked — two devices cannot each abolish the same apnoeas); the direct overlap is the residual ρ̄. AHI-mediated fractions are transparent, adjustable priors — never presented as measured facts.
Front-door caveat (antithesis): AHI is a surrogate. Randomised CPAP trials (SAVE, RICCADSA, ISAACC) cut AHI yet showed NULL effects on hard cardiovascular endpoints — largely an adherence problem, but also a warning that surrogate improvement need not become mortality benefit. Several outcome HRs here are provisional (surrogate-derived); indirect estimates are bounds.
Select interventions to generate a plain-language summary.