Chronic pain affects roughly 50 million United States adults and migraine ~40 million. Beyond suffering, chronic pain drives disability and deconditioning, depression and suicide, and — critically — opioid dependence and overdose death. This oracle estimates the causal reduction in pain — the shared mediator — achievable by combining non-opioid and opioid therapies, using effect sizes from named trials. The opioid competing-harm path is modelled explicitly; downstream disability/mortality links are partly observational. For clinical education, not individual medical advice.
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 pain-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; most act through the shared mediator pain sensitization / intensity, which drives disability / deconditioning and depression → suicide, both routes to mortality. Physical therapy and cognitive behavioural therapy also act independently of pain (on function and mood). Opioids are double-edged: they reduce pain, but carry a competing-harm path to dependence / overdose. 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. Most pain therapies act through one shared mediator — reduction of pain sensitization / intensity. Each log-effect is split into a pain-mediated (indirect) and a pain-independent (direct) part. Indirect parts are pooled through the mediator with dose-response saturation (pain relief saturates — stacking a third analgesic on two others yields diminishing returns), removing the mediator cross-correlation; direct parts keep the residual eigenvalue correlation at ρ̄. Cognitive behavioural therapy and exercise, whose effects on mood and function are partly pain-independent, are therefore NOT fully discounted for overlap with the analgesics. The opioid competing-harm is a SEPARATE path, not netted into the pain hazard ratio.
| Intervention | HR | %pain↓ | pain-med | indirect logHR | direct logHR |
|---|
Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the pain-relief saturation (currently removing — of the summed pain-mediated effect when analgesics are stacked). Note a domain caveat: migraine-specific agents (CGRP antibody, topiramate, onabotulinumtoxin) and chronic-pain agents only combine in a patient with both syndromes. Pain-mediated fractions are transparent, adjustable priors.
Front-door caveat (antithesis): the cited endpoint is pain relief / responder status — a surrogate. The disability, depression, suicide and mortality translations are partly observational. Critically, the opioid pain hazard ratio reflects SHORT-TERM analgesia only: the randomised SPACE trial found opioids no better than non-opioids over 12 months, so a favourable opioid pain HR must be read alongside its competing-harm path, not instead of it.
Select interventions to generate a plain-language summary.