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

Gastro-Esophageal Reflux Disease — Structural Causal Analysis

Gastro-esophageal reflux disease (GERD) affects roughly 20% of United States adults. Its danger is not the symptom but the progression esophagitis → Barrett’s esophagus → esophageal adenocarcinoma (a cancer with ~20% five-year survival), plus aspiration pneumonia. This oracle estimates the causal reduction in esophagitis / reflux — the proximal mediator of those hard endpoints — achievable by combining therapies, using effect sizes from named trials. Cancer/mortality endpoints are largely inferred and flagged.

Method. Structural Causal Model (SCM) using cited, confounder-adjusted effect sizes (backdoor adjustment is the source study’s) (Pearl). Interventions are not assumed independent: their heavy mechanistic overlap (nearly all act by reducing esophageal acid exposure) is removed by an eigenvalue-corrected equicorrelation model at an adjustable mean cross-correlation ρ̄ (default 0.30). Robustness to unmeasured confounding is quantified per intervention with the E-value. Probabilities of Necessity / Sufficiency (PN / PS / PNS) are reported under a monotonicity assumption. Every hazard ratio is cited to its source trial — no effect size is invented.
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 hazard ratio, 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 acid-exposure-mediator 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 10-yr risk (illustrative anchor)
Absolute risk after intervention
Absolute risk difference (RD)
Backdoor-only HR (no front-door)
Mediator (weight) overlap removed
Number needed to treat (NNT)

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). Each therapy is a distinct node; nearly all effects flow through the shared mediator esophageal acid exposure (acid-suppressants directly; fundoplication / weight loss / alginate via the reflux barrier). Acid exposure drives the esophagitis → Barrett’s → adenocarcinoma progression and the aspiration → pneumonia branch, both reaching mortality. Radiofrequency ablation is acid-independent — it ablates dysplastic tissue directly. Named confounders open back-door paths (adjusted). Illustrative of structure, not yet the identification engine.

Confounders U:age · sex · obesity / body-mass index · hiatal hernia · Helicobacter pylori · smoking · diet → back-door paths (adjusted)Proton-pump inhibitorH2-receptor antagonistFundoplicationWeight lossAlginateRadiofrequency ablationReflux / LESbarrier ↓Esophageal acidexposure ↓AspirationEsophagitisAspirationpneumoniaBarrett's /adenocarcinomaMortality (Y)Front-door: through acid exposureAcid-independent (direct)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 for this domain: incretin drugs, surgery, diet, and activity overwhelmingly share the weight-loss / insulin-sensitivity pathway, so ~30% of their nominal effects overlap. A mediation analysis of semaglutide found ~80% of its MACE benefit is not mediated by weight loss, which is why ρ̄ is user-adjustable rather than fixed.

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-hazard-ratio 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

Symptom control is NOT cancer prevention. Proton-pump inhibitors heal esophagitis (~84% at 8 weeks) and relieve symptoms superbly, but no trial shows they reduce esophageal adenocarcinoma incidence. AspECT — the best evidence — gave only a modest composite benefit (time ratio 1.27).
Barrett’s progression is rare. Non-dysplastic Barrett’s progresses to cancer at only ~0.3–0.5% per year. Most GERD patients never progress, so the absolute benefit of aggressive intervention is small and the number-needed-to-treat for cancer prevention is enormous.
PPI safety associations are mostly confounded. Observational links between long-term proton-pump inhibitors and chronic kidney disease, fracture, dementia, and enteric infection are largely confounded by indication; the one large randomised trial (COMPASS/pantoprazole) found no significant excess except enteric infection. Deprescribe where possible, but do not over-weight these signals.
Ablation is dysplasia-specific. Radiofrequency ablation reduces progression only in confirmed Barrett’s dysplasia; applying it to non-dysplastic Barrett’s or ordinary GERD is not supported and carries stricture / bleeding risk.
Stacking acid-suppressants saturates fast. Adding an H2-antagonist to a proton-pump inhibitor barely lowers already-suppressed acid — the front-door saturation is steep, so combination acid suppression yields little incremental benefit over optimised monotherapy.

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(mortality | do(∅)) — baseline
P(mortality | 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 hazard ratio 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 hazard ratio is swung across its 95% confidence interval (others held at point estimate); the bar is the resulting swing in the combined front-door HR. A long bar means the combined estimate leans heavily on that single trial's precision.

Optimistic bound (all HRs at CI-low)
Point estimate
Pessimistic bound (all HRs at CI-high)
Pooled E-value (confounding robustness)

Front-door (mediation) decomposition. Most GERD therapies act through one shared mediator — reduction of esophageal acid exposure. Each log-effect is split into an acid-mediated (indirect) and an acid-independent (direct) part. Indirect parts are pooled through the mediator with dose-response saturation (acid exposure cannot fall below zero — two acid-suppressants cannot each abolish the same acid), removing the mediator cross-correlation; direct parts keep the residual eigenvalue correlation at ρ̄. Radiofrequency ablation, which removes dysplastic tissue rather than acid, is therefore NOT discounted for overlap with the acid-suppressants.

Mediator saturation cap = 60% acid ↓
Sum of standalone acid reduction (naive)
Combined acid 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%acid↓acid-medindirect logHRdirect logHR

Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the acid-exposure saturation (currently removing of the summed acid-mediated effect when acid-suppressants are stacked — adding an H2-antagonist to a proton-pump inhibitor barely lowers already-suppressed acid). The direct overlap is the residual ρ̄. Acid-mediated fractions are transparent, adjustable priors.

Front-door caveat (antithesis): the cited endpoints are mostly esophagitis healing / reflux control — a surrogate. Whether acid suppression prevents esophageal adenocarcinoma is largely unproven: AspECT showed only a modest composite benefit (time ratio 1.27), and Barrett’s progresses to cancer at just ~0.3–0.5%/year. The acid→cancer path is confounded (obesity, smoking). Indirect mortality estimates are upper bounds.

Executive summary

Select interventions to generate a plain-language summary.