Gout affects an estimated ~9 million United States adults and is the most common inflammatory arthritis. Beyond painful flares and destructive tophi, hyperuricaemia is linked to chronic kidney disease and cardiovascular risk. This oracle estimates the causal reduction in serum urate — the shared mediator — and separates disease-modifying urate-lowering therapy from purely symptomatic anti-inflammatory flare control, using effect sizes from named trials and guidelines. 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 urate 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; urate-lowering options act through the shared mediator serum urate, which drives flares/tophi, CKD progression and cardiovascular risk — the components of Y. Colchicine, NSAIDs and steroids act independently of urate (anti-inflammatory flare control). Named confounders — renal function, diuretics, alcohol — open back-door paths (adjusted). Mediator cascade: interventions attach to the node they act on (urate lowering → anti-inflammatory), 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: urate-lowering therapies all converge on serum urate, so stacking two xanthine-oxidase inhibitors is pointless and add-on uricosurics give diminishing returns near target. ρ̄ is user-adjustable because an anti-inflammatory flare agent shares essentially no mechanism with a urate-lowering drug. 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. Urate-lowering therapies act through one shared mediator — reduction of serum urate below the ~6 mg/dL saturation point at which crystals dissolve. Each log-effect is split into a urate-mediated (indirect) and a urate-independent (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. Anti-inflammatory flare agents, which control attacks without lowering urate, are NOT discounted against the urate-lowering drugs. 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 | %urate | med-frac | indirect log | direct log |
|---|
Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the urate saturation (currently removing — of the summed mediated effect when interventions are stacked). Note the key distinction: only urate-lowering therapy is disease-modifying (it dissolves crystal stores over months); NSAIDs, steroids and acute colchicine are symptomatic. Urate-mediated fractions are transparent, adjustable priors.
Front-door caveat (antithesis): the flare/tophus endpoint improves only after months of sustained target urate, and the cardiovascular/renal benefit of urate lowering was NOT confirmed in randomised CKD trials (CKD-FIX, PERL). Asymptomatic hyperuricaemia should generally not be treated.
Select interventions to generate a plain-language summary.