Low back pain is the single leading global cause of years-lived-with-disability, affecting hundreds of millions at any time. This oracle estimates the causal reduction in persistent disabling low back pain across active, psychological, pharmacologic, manual and interventional options — and deliberately includes two anti-targets (long-term opioids, anticonvulsants) so the frontier shows them as dominated. Effect sizes are from named guidelines and 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 pain 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). Active, psychological and manual therapies act through the shared mediator pain processing / functional capacity, which drives activity limitation and thence persistent disabling pain (Y). Symptomatic analgesics act independently of function (they damp the pain signal). Named confounders — fear-avoidance, distress, specific pathology — open back-door paths (adjusted). Mediator cascade: interventions attach to the node they act on (active rehab / → psychological → pharmacologic → procedural), 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 active and psychological arms overlap on the biopsychosocial pathway, so stacking exercise, rehabilitation and CBT is partly redundant. ρ̄ is user-adjustable because a symptomatic analgesic and an exercise programme 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… | 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. The restorative arms act through one shared biopsychosocial mediator. Each log-effect is split into a function-mediated (indirect) and a direct symptomatic 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. Symptomatic analgesics, which relieve pain without restoring function, are NOT discounted against the active arms — and the two anti-target arms show near-null hazard ratios, exposing dominated options. 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 | %func | med-frac | indirect log | direct log |
|---|
Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the pain saturation (currently removing — of the summed mediated effect when interventions are stacked). Note a domain caveat: the active / psychological arms are partly redundant, whereas symptomatic analgesia adds a distinct (short-lived) mechanism. Function-mediated fractions are transparent, adjustable priors.
Front-door caveat (antithesis): no arm is strongly effective (exercise, the best, moves pain ~1.2–1.8/10), the endpoint is subjective and regression-prone, and two arms are anti-targets. Specific pathology (radiculopathy, stenosis, fracture, malignancy) needs a different pathway.
Select interventions to generate a plain-language summary.