Type 2 Diabetes Mellitus — Structural Causal Analysis

Eigenvalue diagnostics for the selected interventions under an equicorrelation matrix (off-diagonal ρ̄). A large λ_max 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 hyperglycaemia, adiposity and cardiorenal 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.

Antithesis — challenging this oracle's own conclusions

What-if — the do-operator: P(Y | do(S))

Intervening on the selected set S with Pearl's do-operator (setting the interventions, not merely observing them). Contrast against do(∅) = no intervention.

If-not-for — but-for counterfactual (leave-one-out)

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.

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.

Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the cardiometabolic 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.