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from surrogate, subgroup, observational and failed-confirmatory figures — the last exemplified by AMX0035 / Relyvrio, withdrawn from the market in 2024.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.
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.
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.
Under monotonicity + exogeneity (E-value bounds the exogeneity assumption).
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.
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.
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.
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.
Intervening on the selected set S with Pearl's do-operator (setting the interventions, not merely observing them). Contrast against do(∅) = no intervention.
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 it | HR with full set | marginal 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.
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.
| Intervention | HR | %prog↓ | med-frac | indirect log | direct 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.
Select interventions to generate a plain-language summary.