Bayesian Causal Atlas · Vol. Environmental / Emergency · Pearl Structural Causal Model

Heat Stroke — Structural Causal Analysis (all variants & stages)

Heat stroke — core temperature >40°C with central-nervous-system dysfunction — is a time-critical emergency spanning the exertional variant (young, healthy; ~3–5% mortality) and the classic / non-exertional variant (elderly, comorbid, heat-wave; 10–65% mortality), through stages from heat exhaustion to multi-organ failure. As climate change drives heat mortality upward, this oracle estimates the causal reduction in heat-stroke mortality across cooling methods, systems-of-care, organ support and prevention — with antipyretics and dantrolene included as dominated anti-targets. Effect sizes are from named consensus statements and trials. For education, not individual medical advice.

Method. Structural Causal Model (SCM) with backdoor adjustment (Pearl). Interventions are not assumed independent: the cooling methods share the core-temperature pathway, so their overlap is removed by an eigenvalue-corrected equicorrelation model at an adjustable mean cross-correlation ρ̄ (default 0.30). Organ support and prevention are separated as temperature-independent paths. Robustness to unmeasured confounding is quantified with the E-value. PN / PS / PNS under monotonicity. Every relative risk is cited — no effect size is invented; where only cooling-rate–survival relationships exist, that surrogate basis is flagged. The front door is resolved through an EXPLICIT mediator cascade (prevention / → cooling → organ → pharmacologic → 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 Tc overlap removed via dose-response saturation; residual direct-effect overlap removed via the eigenvalue model at ρ̄.

1.00
Combined RR
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 RR (no front-door)
Core-temperature 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). Cooling methods act through the shared mediator core body temperature / thermal load, which drives the systemic inflammatory response, multi-organ injury and thence mortality (Y). Organ support and prevention act independently of core temperature (downstream cascade / upstream thermal load). Named confounders — variant, time-to-cooling, age — open back-door paths (adjusted). Mediator cascade: interventions attach to the node they act on (prevention / → cooling → organ → pharmacologic), 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:variant (classic vs exertional) · time-to-cooling · age / comorbidity · magnitude & duration of hyperthermia · baseline organ reserve · access to care → back-door paths (adjusted)Cold-water immersion(CWI)Rapid recognition“cool first” <30 minIce-sheet / tarpcooling (TACO)Endovascularcooling (ICU)Evaporative /convective coolingCold IV fluidsSupportive ICU/ organ supportAcclimatisation /WBGT modificationAntipyretics(paracetamol/NSAID)DantrolenePrevention /recognitionCooling(lower core temp)OrgansupportPharmacologic(ineffective)Core temp /thermal injuryOrgan failure /deathFront-door: through lowering core temperatureMediator-independent (organ support / prevention)Back-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: the cooling methods all act through the same final pathway — lowering core temperature — so applying two simultaneously is largely redundant (you cannot cool the same body twice). ρ̄ is user-adjustable because organ support and prevention share little mechanism with acute cooling. 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 RR
95% simulation interval
Standard deviation of combined RR
P(combined RR < 0.90)

Antithesis — challenging this oracle's own conclusions

Time-to-cooling dominates everything else. Mortality is directly proportional to the duration × magnitude of hyperthermia, so the same cooling method can yield near-zero or catastrophic mortality depending only on how fast it starts. The relative risks here are conditional on rapid application — a cooling method applied late is not the method that was studied.
Two of the arms are anti-targets. Antipyretics do not work (no set-point change) and are hepatotoxic in heat stroke; dantrolene is ineffective (wrong physiology). They are included precisely so the Pareto frontier shows them dominated — selecting them wastes the golden half-hour and, for antipyretics, adds harm.
Cooling does not reverse the cascade once it locks in. Normalising core temperature does not undo the systemic inflammatory response, coagulopathy and multi-organ injury once triggered — which is why organ support (gold) is needed downstream and why classic heat stroke, recognised late in frail elderly, still carries 10–65% mortality despite cooling.
The two variants are not interchangeable. Exertional heat stroke (young, healthy, witnessed) carries ~3–5% mortality with rapid cooling; classic / non-exertional heat stroke (elderly, comorbid, unwitnessed during heat waves) carries 10–65%. A single relative risk cannot be transported across these populations — the baseline and the feasible interventions differ.
Most evidence is observational and cooling-rate-based. Randomising heat-stroke patients to no cooling is unethical, so the strongest “evidence” is cooling-rate physiology and case series, not mortality RCTs. Effect sizes are inferred from the cooling-rate–survival relationship and carry that surrogate uncertainty.

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…RR without itRR 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. Cooling methods act through one shared mediator — core temperature. Each log-effect is split into a temperature-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. Organ support (downstream) and prevention (upstream), which act off core temperature, are NOT discounted against the cooling arms — and the two anti-target arms surface as near-null / harmful. 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 = 60% thermal-load reduction
Sum of standalone Tc reduction (naive)
Combined Tc reduction after saturation
Mediator overlap removed (1 - saturation)
Direct-effect redundancy removed (1 - n_eff/k)
Front-door combined RR
Backdoor-only combined RR (comparison)
InterventionRR%coolmed-fracindirect logdirect log

Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the Tc saturation (currently removing of the summed mediated effect when interventions are stacked). Note a domain caveat: the cooling arms are strongly redundant (one final pathway — core temperature), whereas organ support and prevention add distinct mechanisms. Temperature-mediated fractions are transparent, adjustable priors reflecting cooling rate.

Front-door caveat (antithesis): effect sizes are conditional on RAPID application (a late method is not the method studied), two arms are anti-targets, cooling does not reverse the cascade once locked in, and the two variants are not interchangeable. Most evidence is cooling-rate physiology and case series, not mortality RCTs.

Executive summary

Select interventions to generate a plain-language summary.