Bayesian Causal Atlas · Vol. Neurology / Cardiology · Pearl Structural Causal Model

Stroke / Cerebrovascular Disease — Structural Causal Analysis

Stroke is the second leading cause of death and a top cause of disability worldwide (~12 million events and ~6.5 million deaths a year). This oracle estimates the causal reduction in stroke death or dependency (modified Rankin Scale 3–6) across acute reperfusion, systems-of-care and secondary-prevention strategies, all acting through cerebral ischaemic injury — with decompressive surgery separated as a life-saving mass-effect path. Effect sizes are from named trials. For education, not individual medical advice.

Method. Structural Causal Model (SCM) with backdoor adjustment (Pearl). Interventions are not assumed independent: the reperfusion and prevention arms act on the shared ischaemic-injury pathway, so their overlap is removed by an eigenvalue-corrected equicorrelation model at an adjustable mean cross-correlation ρ̄ (default 0.30). Decompressive hemicraniectomy is separated as a mass-effect (survival) path. 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. The front door is resolved through an EXPLICIT mediator cascade (acute → secondary → organised → decompressive → 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 infarct 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)
Ischaemic-injury 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). Prevention (avoid the infarct) and acute reperfusion (salvage tissue) act through the shared mediator cerebral ischaemic injury / infarct burden, which drives neurological deficit and thence death or dependency (Y). Decompressive hemicraniectomy acts by relieving mass effect (survival), not by reducing infarct. Named confounders — subtype, time-to-treatment, baseline severity — open back-door paths (adjusted). Mediator cascade: interventions attach to the node they act on (acute → secondary → organised → decompressive), 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:stroke subtype (LVO / lacunar / haemorrhagic) · time-to-treatment · age · baseline NIHSS / infarct core · comorbidity · access to care → back-door paths (adjusted)Anticoagulation(DOAC, AF)Mechanicalthrombectomy (LVO)Carotid endarterectomy(symptomatic)Blood-pressureloweringIV thrombolysis(tenecteplase)Organisedstroke-unit careAntiplatelet(aspirin/clopidogrel)High-intensitystatinDecompressivehemicraniectomyAcutereperfusionSecondarypreventionOrganisedstroke careDecompressivesurgeryIschaemicinfarct burdenDeath /disabilityFront-door: through reduced ischaemic injury / infarctMass-effect relief (survival, not infarct reduction)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 reperfusion arms (thrombolysis, thrombectomy) and the antithrombotic prevention arms overlap on the ischaemic pathway, so combining them is partly redundant. ρ̄ is user-adjustable because acute reperfusion and long-term risk-factor control act at very different times and mechanisms. 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

Acute reperfusion is exquisitely time-dependent and narrow. Thrombolysis benefit is largely gone by ~4.5 h without imaging selection, and thrombectomy applies only to the large-vessel-occlusion minority with salvageable tissue. These headline therapies reach a small, fast-triaged fraction of patients; the numbers do not generalise to the average stroke.
Survival is not the same as good outcome. Decompressive hemicraniectomy halves mortality but leaves many survivors with moderate-to-severe disability — it moves patients from “dead” to “dependent,” not to “recovered.” A mortality relative risk hides this trade-off, which is why the endpoint here is death OR dependency, not death alone.
Anticoagulation’s benefit is offset by bleeding. The 64–70% AF stroke reduction is a NET figure only in patients whose stroke risk exceeds their bleeding risk; in low-CHA₂DS₂-VASc or high-bleeding patients the balance shrinks or reverses. The relative risk is not portable across risk strata.
Carotid surgery helps only a narrow group. Endarterectomy benefits recently symptomatic severe stenosis operated early by low-complication surgeons; for asymptomatic or mild stenosis, or high perioperative risk, it is net harmful. The trial relative risk does not apply outside that window.
The global burden is an access problem. Most of the world’s stroke deaths occur where thrombectomy, thrombolysis and even organised stroke units are unavailable. Blood-pressure control and stroke-unit care — the broadest, cheapest levers — avert far more disability globally than the high-technology acute therapies that dominate attention.

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. Prevention and reperfusion act through one shared mediator — cerebral ischaemic injury. Each log-effect is split into an infarct-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. Decompressive hemicraniectomy, which improves survival by relieving mass effect rather than reducing infarct, is NOT discounted against the reperfusion / prevention arms. 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% ischaemic-injury control
Sum of standalone infarct reduction (naive)
Combined infarct 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%infarct↓med-fracindirect logdirect log

Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the infarct saturation (currently removing of the summed mediated effect when interventions are stacked). Note a domain caveat: reperfusion and antithrombotic arms are partly redundant on the ischaemic pathway, whereas hemicraniectomy adds a distinct mass-effect mechanism. Infarct-mediated fractions are transparent, adjustable priors.

Front-door caveat (antithesis): the acute therapies reach only a fast-triaged minority (thrombolysis <4.5 h; thrombectomy LVO-only), survival from hemicraniectomy often means dependency, anticoagulation’s benefit is offset by bleeding, and globally the burden is an access problem best addressed by blood-pressure control and stroke units.

Executive summary

Select interventions to generate a plain-language summary.