Tension-type headache is the second most prevalent condition on Earth (~2.0 billion people) and the most common headache disorder — benign, but a major cause of lost productivity and quality of life. This oracle estimates the causal reduction in chronic tension-type headache burden across preventive, behavioural, physical and acute options, with a deliberate focus on the paradox that the acute analgesics can, when overused, cause the chronic disease. Effect sizes are from named trials and Cochrane reviews. 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 tension 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). Preventive, behavioural and physical therapies act through the shared mediator pericranial tension + central sensitisation, which drives headache frequency and thence chronic-TTH burden (Y). Acute analgesics act symptomatically — and, overused, drive chronification. Named confounders — stress, sleep, comorbid migraine / mood — open back-door paths (adjusted). Mediator cascade: interventions attach to the node they act on (preventive → non-pharm → acute → medication-overuse), 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 preventive and behavioural arms overlap on the tension-sensitisation pathway, so stacking amitriptyline, CBT and physiotherapy is partly redundant. ρ̄ is user-adjustable because acute analgesia and preventive therapy act through distinct (and, for overuse, opposing) mechanisms. 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. Preventive / behavioural arms act through one shared mediator — tension and central sensitisation. Each log-effect is split into a tension-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. Acute analgesics, which relieve attacks without treating the disorder (and chronify on overuse), are NOT discounted against the preventive arms — and their non-monotonicity is the intended lesson. 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 | %freq↓ | med-frac | indirect log | direct log |
|---|
Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the tension saturation (currently removing — of the summed mediated effect when interventions are stacked). Note a domain caveat: the preventive / behavioural arms are partly redundant, whereas medication-overuse withdrawal reverses harm from the acute arms. Tension-mediated fractions are transparent, adjustable priors.
Front-door caveat (antithesis): there is essentially no mortality; the acute analgesics can CAUSE chronic headache when overused; placebo response is very large; and comorbid migraine / mood / sleep confound the mediator. Effect sizes are modest, imprecise and self-reported.
Select interventions to generate a plain-language summary.