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

Amyotrophic Lateral Sclerosis — Structural Causal Analysis

ALS (motor neuron disease) is a relentlessly progressive degeneration of upper and lower motor neurons; median survival is roughly 2–4 years from onset, and respiratory failure is the usual cause of death. This oracle estimates the causal reduction in death / tracheostomy-free survival from each intervention, on a shared progression → respiratory/nutritional failure → death backbone, using hazard ratios from named trials. It separates the two arms with randomised survival evidence (riluzole, non-invasive ventilation) from surrogate, subgroup, observational and failed-confirmatory figures — the last exemplified by AMX0035 / Relyvrio, withdrawn from the market in 2024. For education, not individual medical advice.

Method. Structural Causal Model (SCM) with backdoor adjustment (Pearl), resolved through an EXPLICIT multi-mediator cascade rather than one lumped node: neuroprotection acts on motor-neuron preservation, ventilation on respiratory function, nutrition on nutritional status, and symptomatic agents downstream. Each intervention is attached to the mediator it acts on, which enables d-separation, per-channel dose-response saturation (same-node substitutes saturate; different-node channels compose in series), and structural cross-correlation removal. The residual eigenvalue ρ̄ (default 0.30) cleans up only the mediator-independent (direct) effects. Robustness to unmeasured confounding is quantified with the E-value — material for the observational supportive arms. PN / PS / PNS under monotonicity. Every hazard ratio is cited; surrogate, subgroup and failed-confirmatory figures are flagged. The front door is resolved through an EXPLICIT mediator cascade (motor-neuron → respiratory → nutritional → care → symptom → 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 progression 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
Life-years saved
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)
Progression / support-channel overlap removed
Number needed to treat (NNT)
Life-years saved (RMST survival gain)
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). Neuroprotective agents act through motor-neuron preservation (tofersen does so directly at the SOD1 source), ventilation and nutrition through their respective organ-support channels, all converging on ALS progression and thence death / tracheostomy (Y). Named confounders — onset site, baseline slope, forced vital capacity, genotype — open back-door paths (adjusted); channelling of fitter patients into the supportive arms is the dominant residual bias. Mediator cascade: interventions attach to the node they act on (motor-neuron → respiratory → nutritional → care → symptom), 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:onset site (bulbar vs limb) · age at onset · diagnostic delay · baseline ALSFRS-R slope · forced vital capacity · genotype (SOD1 / C9orf72) · riluzole/edaravone co-use → back-door paths (adjusted). Faster-progressing patients are enrolled and treated differently, so channelling and immortal-time bias inflate observational arms.RiluzoleEdaravoneTofersen(SOD1-ALS)AMX0035— withdrawnNon-invasiveventilationGastrostomy(PEG/RIG)High-calorienutritionMultidisciplinaryALS clinicDextromethorphan/quinidineMexiletine(cramps)Motor-neuronpreservationRespiratoryfunctionNutritionalstatusCarecoordinationSymptomcontrolALS progression(motor-neuron loss)Death /trach-free survivalFront-door: through ALS progression / organ supportDirect source knockdown (SOD1 silencing)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

The overlap is handled structurally by the mediator nodes: two neuroprotective agents on the same node are substitutes and saturate, while a neuroprotectant and non-invasive ventilation sit on different channels and compose in series. ρ̄ ≈ 0.30 governs only the residual correlation among the mediator-independent (direct) supportive effects. 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

ALS is uniformly fatal — these are survival extensions, not cures. Median survival is roughly 2–4 years from onset, and none of the disease-modifiers changes that trajectory qualitatively. Riluzole buys months; edaravone moves a functional scale in a narrow subgroup with unproven survival benefit; tofersen helps only the ~2% with SOD1 mutations. The honest framing is incremental slowing of an inexorable disease, and the combined figures here are upper bounds that assume everything works together, which it rarely does.
AMX0035 is the cautionary tale of the decade. A positive phase-2 post-hoc survival signal (HR ≈ 0.56) drove approval; the confirmatory phase-3 PHOENIX trial then failed and the drug was pulled from the market in 2024. It is retained here only as an anti-target: read every provisional entry (edaravone survival, high-calorie-diet subgroup, gastrostomy) through that lens — a striking subgroup or post-hoc result is a hypothesis, not an effect.
The supportive arms are selection machines. NIV, gastrostomy, high-calorie nutrition and multidisciplinary care are offered to — and tolerated by — fitter, slower-progressing, earlier-diagnosed patients, and much of their apparent survival advantage is that channelling plus immortal-time bias. NIV has the one randomised trial and it is bulbar-function-dependent; the rest are observational and their E-values are modest, so small unmeasured confounders erode them.
Only NIV and riluzole rest on randomised survival evidence. Everything else here is either a functional/biomarker surrogate (edaravone, tofersen), a subgroup (high-calorie diet), an observational cohort (gastrostomy, multidisciplinary care), a failed confirmatory (AMX0035), or purely symptomatic (dextromethorphan/quinidine, mexiletine). The grades and provisional flags carry that distinction; do not read them as interchangeable.
Combining across mechanisms is only partly additive. Neuroprotection, respiratory support and nutritional support act on different nodes and genuinely compose in series, but each has a ceiling and the disease overwhelms them; stacking every arm does not multiply into a large joint benefit. The eigenvalue and saturation model discounts within-node overlap, but the residual biological reality is that ALS progresses regardless.
Endpoints are not uniform. Death/tracheostomy (riluzole, NIV), a 24-week functional slope (edaravone), a neurofilament biomarker (tofersen), a subgroup survival (high-calorie diet), and observational mortality (gastrostomy, multidisciplinary care) are being placed on one axis. They are directionally comparable but not identical, and the front-door decomposition only approximates their exchangeability.

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 over the explicit cascade. Each intervention’s mediated log-effect is pooled WITHIN its node with dose-response saturation (there is a floor to how much progression can be slowed), then the nodes are composed in SERIES down the flux (neuroprotection → respiratory → nutritional → progression), with a series attenuation because supporting an already-supported system buys less. Direct (organ-level) effects keep the residual eigenvalue ρ̄. Neuroprotectants are almost wholly mediated by progression; NIV and nutrition are largely direct (they do not slow motor-neuron loss), so they do not saturate against the disease-modifiers. 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 = 45% progression ↓
Sum of standalone progression reduction (naive)
Combined progression 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%prog↓med-fracindirect logdirect log

Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the progression saturation (currently removing of the summed mediated effect when interventions are stacked). Note the failure modes on display: AMX0035 moved a post-hoc survival curve and then failed its confirmatory trial and was withdrawn; edaravone moved a 24-week functional scale without proving survival; tofersen moved a biomarker. None should be read the way an RCT survival result (riluzole, NIV) is read.

Front-door caveat (antithesis): the progression→death edge is confounded by onset site and baseline slope; effect sizes are subgroup- and stage-conditional; and ALS progresses despite everything. The combined figure is an upper bound that assumes the arms stack cleanly, which the disease rarely permits.

Executive summary

Select interventions to generate a plain-language summary.