Falls are the leading cause of injury death in United States adults over 65, and fall-related hip fracture carries high one-year mortality. This oracle estimates the causal reduction in falls and fall-related injury / fracture on a shared balance-strength + injury-risk backbone, using effect sizes from named trials. It anchors on exercise (the best-evidenced lever), separates fall PREVENTION from injury PROTECTION (hip protectors, bisphosphonates), and flags vitamin D as contested — not recommended for non-deficient community-dwellers and harmful at high dose. 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 fall 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 node acting through balance/strength and injury risk toward the endpoint (Y); direct-mechanism arms are drawn gold. Named confounders open back-door paths (adjusted). Mediator cascade: interventions attach to the node they act on (exercise / → medication → environment / → injury), 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.
ρ̄ ≈ 0.30 is defensible on mechanistic grounds: same-mechanism arms converge on balance/strength and injury risk, so stacking them yields diminishing returns, while arms on distinct mechanisms share little and compose. ρ̄ is user-adjustable. 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-structured mediation decomposition (not front-door identification). Each log-effect splits into a mediated (indirect) and a mediator-independent (direct) part. Indirect parts are routed through the mediator cascade: arms on the SAME node are substitutes and saturate against a dose-response ceiling; arms on DIFFERENT nodes are d-separated and compose in series. No correlation coefficient is applied to the mediated path. ρ̄ is applied ONLY to the un-mediated direct residual. Caveat: Pearl's front-door criterion would additionally require the mediator to be COMPLETE (no unblocked X→Y path bypassing M) and the M→Y edge to be unconfounded — neither is defended arm-by-arm here, and baseline severity routinely confounds M→Y. These are therefore structured decompositions, not identified causal effects. 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 | %risk↓ | med-frac | indirect log | direct log |
|---|
Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the fall saturation (currently removing — of the summed mediated effect when interventions are stacked). Read every provisional (surrogate / subgroup / observational / failed-confirmatory) entry through its grade, not as an RCT survival result.
Front-door caveat (antithesis): the mediator→outcome edge is confounded by baseline severity and stage; effect sizes are stage-conditional; combined figures are upper bounds that assume the arms stack cleanly.
Select interventions to generate a plain-language summary.