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

Epilepsy — Structural Causal Analysis (SUDEP endpoint)

Epilepsy affects an estimated ~3.4 million people in the United States and roughly 50 million worldwide. Unlike the morbidity-framed conditions in this atlas, epilepsy carries a genuine mortality endpoint: SUDEP — sudden unexpected death in epilepsy — the leading cause of epilepsy-related death, driven overwhelmingly by convulsive (generalised/bilateral tonic-clonic) seizures. This oracle estimates the causal reduction in SUDEP risk across pharmacological, surgical, neuromodulation and peri-ictal-rescue options, using effect sizes from named trials. For education, not individual medical advice.

Method. Structural Causal Model (SCM) with backdoor adjustment (Pearl). Interventions are not assumed independent: seizure-suppression therapies share the convulsive-burden pathway, so their overlap is removed by an eigenvalue-corrected equicorrelation model at an adjustable mean cross-correlation ρ̄ (default 0.30). Nocturnal supervision and detection devices are separated as a frequency-independent peri-ictal rescue 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 (anti-seizure → surgery / → adherence / → 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 GTCS 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)
Convulsive-burden 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). Seizure-suppression therapies act through the shared mediator convulsive (GTCS) seizure burden, which drives the peri-ictal cardio-respiratory collapse that terminates in SUDEP (Y). Nocturnal supervision and detection devices act independently of seizure frequency — they shorten time-to-rescue on the collapse→death transition. Named confounders — syndrome, drug-resistance severity, intellectual disability — open back-door paths (adjusted). Mediator cascade: interventions attach to the node they act on (anti-seizure → surgery / → adherence /), 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:epilepsy syndrome / aetiology · drug-resistance severity · baseline GTCS frequency · intellectual disability · access to care · adherence → back-door paths (adjusted)First-line ASMmonotherapyAdjunctive ASM(efficacious dose)Resectiveepilepsy surgeryVagus nervestimulationCannabidiol(Dravet / LGS)Adherence + trigger/ sleep controlNocturnalsupervisionSeizure-detection/ listening deviceAnti-seizuremedicationSurgery /neuromodulationAdherence /supervisionConvulsiveseizuresSUDEP /mortalityFront-door: through convulsive-seizure suppressionFrequency-independent peri-ictal rescueBack-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 drug/surgery/neuromodulation options overwhelmingly share one final common pathway — reducing convulsive-seizure burden toward freedom — so stacking two seizure-suppression modalities is partly redundant. ρ̄ is user-adjustable because a rescue device shares essentially no mechanism with a seizure medication. 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

Only convulsive seizures drive the endpoint. SUDEP risk tracks generalised/bilateral tonic-clonic (convulsive) seizure frequency (odds ratios ~14–27 for frequent GTCS); people with exclusively non-convulsive seizures show essentially no excess risk (OR ~1.15). Every mortality estimate here is conditional on there being convulsive seizures to suppress — for focal-only epilepsy the whole frame nearly collapses.
SUDEP is rare in absolute terms. Overall SUDEP incidence is ~1.2/1000 person-years, rising to ~4.6–6.2/1000 in refractory / surgery-ineligible groups. Large relative risks act on a small absolute base, so number-needed-to-treat to avert one death is high outside the highest-risk strata. The relative figures are upper-bound ceilings.
Supervision and devices do not treat epilepsy. Nocturnal supervision (OR ~0.4) and detection devices (OR ~0.1) reduce death without reducing a single seizure — they act on the terminal collapse→death transition. Modelling them through the seizure-burden mediator would be wrong, which is why they carry a gold, frequency-independent arrow. Their evidence is observational and confounded by care setting.
VNS mortality benefit is contested. SUDEP rates fall over time in some VNS series, but a UK cohort found no reduction in overall premature death and the confidence interval crosses 1. VNS is palliative (seizure reduction, rarely freedom); its survival claim is the weakest in this set and is shown with a CI that includes no effect.
Surgery benefit is candidate-selected and time-limited. The surgical-vs-medical mortality gap partly reflects that better-prognosis patients are chosen for surgery, and the SUDEP advantage attenuates after ~10 years. The relative risk is a seizure-freedom effect, not a scalpel effect — non-seizure-free operated patients keep dying of SUDEP.

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. Seizure-suppression therapies act through one shared mediator — convulsive (GTCS) seizure burden. Each log-effect is split into a convulsive-burden-mediated (indirect) and a frequency-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. Nocturnal supervision and detection devices, which avert death without reducing seizures, are NOT discounted against the seizure-suppression 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% GTCS ↓
Sum of standalone GTCS reduction (naive)
Combined GTCS 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%GTCSmed-fracindirect logdirect log

Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the GTCS saturation (currently removing of the summed mediated effect when interventions are stacked). Note a domain caveat: seizure-suppression options are partly redundant (shared freedom pathway), whereas rescue interventions are additive because they act on a different step. Convulsive-burden mediated fractions are transparent, adjustable priors.

Front-door caveat (antithesis): the endpoint is SUDEP — driven by convulsive seizures only, so for focal-only epilepsy the mediator carries almost no mortality signal (OR ~1.15). SUDEP is rare in absolute terms, VNS survival benefit is contested (CI crosses 1), and the surgical effect is candidate-selected and attenuates after ~10 years.

Executive summary

Select interventions to generate a plain-language summary.