Bayesian Causal Atlas · Vol. Endocrinology / Metabolic · Pearl Structural Causal Model

Adiposity & Obesity — Upstream Structural Causal Analysis

Excess adiposity affects >100 million United States adults (41.9%) and sits upstream of cardiovascular disease, type-2 diabetes and several cancers. This oracle estimates the causal reduction in mortality / major adverse cardiovascular events (MACE) achievable by combining weight-lowering interventions, using hazard ratios from named trials. Endpoints are mixed (mortality, MACE, diabetes-prevention surrogates) and unified only as upstream effects. For education, not individual medical advice.

Method. Structural Causal Model (SCM) with backdoor adjustment (Pearl). Interventions are not assumed independent: weight-lowering options share the adiposity pathway, so their overlap is removed by an eigenvalue-corrected equicorrelation model at an adjustable mean cross-correlation ρ̄ (default 0.30). Incretins are separated by a large weight-independent direct vascular path. Robustness to unmeasured confounding is quantified with the E-value. PN / PS / PNS under monotonicity. Every hazard ratio is cited — no effect size is invented. The front door is resolved through an EXPLICIT mediator cascade (energy balance → adiposity → metabolic → disease state), not one lumped node: each intervention acts on a specific node, so same-node interventions are substitutes that saturate against each other, while different-node interventions are d-separated given the intermediate node and compose in series. The cross-correlation removal thus follows from the graph structure; the residual ρ̄ cleans up only the mediator-independent (direct) effects.
ρ̄ = 0.30
A–D (all)
A high (RCT/meta) · B cohort · C case-series/modelled · D consensus/provisional. Lower-grade interventions are excluded from the DAG, front-door pooling, Pareto, Monte‑Carlo & sensitivity.

Interventions

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.

Combined causal estimate

Headline is the front-door estimate: shared weight overlap removed via dose-response saturation; residual direct-effect overlap removed via the eigenvalue model at ρ̄.

1.00
Combined HR
0%
Relative risk ↓
Pooled E-value
Interventions selected (k)
0
Effective independent dimensions (n_eff)
0
Redundancy discount applied
0%
Baseline risk (illustrative anchor)
Absolute risk after intervention
Absolute risk difference (RD)
Backdoor-only HR (no front-door)
Weight (adiposity) overlap removed
Number needed to treat (NNT)
ρ-sensitivity band (ρ 0 → 0.6)
Interpretation

Causal attribution

Under monotonicity + exogeneity (E-value bounds the exogeneity assumption).

Probability of Necessity (PN)
Probability of Sufficiency (PS)
Prob. of Necessity & Sufficiency (PNS, lower bound)
Causal DAG
Cross-correlation
Pareto (threshold)
Monte Carlo
Front-door mediation
What-if / If-not-for
Sensitivity
Antithesis

Faithful causal directed acyclic graph (DAG). Weight-lowering therapies act through the shared mediator excess adiposity / body weight, which drives cardiometabolic risk (CVD, type-2 diabetes, cancer) and thence mortality / MACE (Y). Incretins additionally act independently of weight (direct vascular / anti-inflammatory effects — ~80% of the semaglutide benefit). Named confounders — baseline BMI, diabetes, reverse causation — open back-door paths (adjusted). Mediator cascade: interventions attach to the node they act on (energy balance → adiposity → metabolic), which converge on the disease state and thence the endpoint — drawing the intermediate mediators explicitly is what exposes d-separation and per-channel saturation.

Confounders U:age · sex · baseline BMI · diabetes status · reverse causation (illness → weight loss) · socioeconomic access → back-door paths (adjusted)Metabolic /bariatric surgerySemaglutide 2.4 mg(GLP-1 RA)Tirzepatide(dual GIP/GLP-1)GLP-1 RA class(broad)MediterraneandietPhysical activity(active vs inactive)Physical activity(+10 MET-h/wk)Intensive lifestyle(DPP)Metformin(prevention)Intensive lifestyle(Look AHEAD)Energy balance(intake / expenditure)Adiposity(fat mass)Metabolic(insulin / lipids / BP)CardiometabolicdiseaseEvents /mortalityFront-door: through weight / adiposityWeight-independent (incretin vascular) direct pathBack-door confounding (adjusted)

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.

k (selected)
0
λmax
λmin
n_eff = (Σλ)² / Σλ²
Condition number

On mechanistic grounds ρ̄ ≈ 0.30 is defensible: weight-lowering therapies share the adiposity pathway, so stacking two weight-loss agents is partly redundant on the mediated component. ρ̄ is user-adjustable because a diet and an incretin’s weight-independent vascular effect 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.

Target combined risk ↓ ≥ 50%

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.

Median combined HR
95% simulation interval
Standard deviation of combined HR
P(combined HR < 0.90)

Antithesis — challenging this oracle's own conclusions

Weight loss is not the mechanism. ~80% of semaglutide’s MACE benefit is not weight-mediated, so an “adiposity” model attributing all benefit to weight mis-specifies the graph. The incretins carry a large weight-independent vascular arm (gold), which is why their mediated fraction is set low.
Endpoints are mixed, not a single scale. Arms report all-cause mortality (bariatric, physical activity), 3-point MACE (semaglutide, GLP-1 class, tirzepatide) and diabetes-prevention surrogates (DPP lifestyle, metformin). These are unified only as “upstream” effects and are not strictly commensurable; the diabetes-prevention HRs in particular must NOT be read as mortality reductions.
Look AHEAD was null. Intensive lifestyle did not reduce cardiovascular events overall in type-2 diabetes (HR ~0.95, CI crossing 1); benefit appeared only in the ≥10% weight-loss subgroup. Weight loss is not a guaranteed mortality lever, and this arm is kept as an explicit counter-example.
Tirzepatide’s mortality figure is comparator-relative and provisional. The 0.84 all-cause-mortality HR is from SURPASS-CVOT versus dulaglutide — an already-effective GLP-1 comparator, not placebo — so it understates the placebo-relative effect, while the placebo-controlled obesity CVOT (SURMOUNT-MMO) is still pending. It is flagged provisional and is deliberately NOT the headline estimate.
Reverse causation confounds weight→mortality. Illness causes weight loss, so observational adiposity–mortality associations are confounded; the front-door path assumes an unconfounded mediator→outcome edge that does not hold perfectly. Observational arms (habitual physical activity) are additionally healthy-mover biased.
Trial rigor caveat (PREDIMED). PREDIMED was retracted and republished after randomisation errors; the republished hazard ratios were materially unchanged, but the episode is a caution against over-reading any single dietary trial.

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.

P(outcome | do(∅)) — baseline
P(outcome | do(S)) — intervened
Absolute risk reduction (ARR)
Number needed to treat (NNT)

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.

If not for…HR without itHR with full setmarginal 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.

Optimistic bound (all at CI-low)
Point estimate
Pessimistic bound (all at CI-high)
Pooled E-value (confounding robustness)

Front-door (mediation) decomposition. Weight-lowering therapies act through one shared mediator — excess adiposity. Each log-effect is split into a weight-mediated (indirect) and a weight-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. The incretins’ large weight-independent vascular benefit is NOT discounted against the weight-loss 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.

Mediator saturation cap = 55% TBWL
Sum of standalone weight reduction (naive)
Combined weight reduction after saturation
Mediator overlap removed (1 - saturation)
Direct-effect redundancy removed (1 - n_eff/k)
Front-door combined HR
Backdoor-only combined HR (comparison)
InterventionHR%TBWLmed-fracindirect logdirect log

Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the weight saturation (currently removing of the summed mediated effect when interventions are stacked). Note a domain caveat: endpoints are mixed (mortality, MACE, diabetes-prevention surrogates) and not strictly commensurable; weight-mediated fractions are transparent, adjustable priors set from published mediation analyses.

Front-door caveat (antithesis): textbook front-door identification requires full mediation and an unconfounded mediator→outcome path. Neither holds perfectly — mediation is partial (~80% of incretin benefit is weight-independent) and weight→mortality is confounded by reverse causation (illness causes weight loss). Look AHEAD was null overall.

Executive summary

Select interventions to generate a plain-language summary.