Bayesian Causal Atlas · Vol. Functional GI · Pearl Structural Causal Model

Irritable Bowel Syndrome — Structural Causal Analysis

Irritable bowel syndrome (IBS) affects an estimated 30–45 million United States adults (~10–15%). It is a disorder of gut-brain interaction: not life-threatening, but a major driver of disability, absenteeism, anxiety/depression and healthcare cost. This oracle estimates the causal reduction in symptom burden — the shared mediator — achievable by combining dietary, pharmacological and gut-brain therapies, using effect sizes from named trials and network meta-analyses. It is distinct from the inflammatory-bowel-disease oracle. For education, not individual medical advice.

Method. Structural Causal Model (SCM) with backdoor adjustment (Pearl). Interventions are not assumed independent: their overlap (most act by reducing visceral hypersensitivity / symptom severity) is removed by an eigenvalue-corrected equicorrelation model at an adjustable mean cross-correlation ρ̄ (default 0.30). Robustness to unmeasured confounding — critically, the large IBS placebo response — is quantified per intervention with the E-value. PN / PS / PNS are reported under monotonicity. Every relative risk is cited to its source meta-analysis or trial — no effect size is invented. The front door is resolved through an EXPLICIT mediator cascade (diet / fibre → gut motility / → brain-gut → 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 symptom 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)
Mediator (symptom) 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). Each therapy is a node; most act through the shared mediator visceral hypersensitivity / symptom severity, which drives disability, mood and healthcare use — the components of the morbidity burden Y. Tricyclics, SSRIs and gut-directed psychotherapy also act independently of gut symptoms (on anxiety and coping). Named confounders — especially placebo response — open back-door paths (adjusted). Illustrative of structure. Mediator cascade: interventions attach to the node they act on (diet / fibre → gut motility / → brain-gut), 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:age · sex · IBS subtype · psychiatric comorbidity · somatisation · diet · placebo response → back-door paths (adjusted)Soluble fibreAntispasmodic /peppermint oilLow-FODMAP dietTCA / SSRIneuromodulatorSecretagogue(IBS-C)Gut-directed CBT/ hypnotherapyDiet / fibreGut motility /microbiomeBrain-gutneuromodulationIBS symptomseverityQoL /burdenFront-door: through symptom reductionSymptom-independent (mood / coping)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: fibre, antispasmodics, diet and secretagogues overwhelmingly share the luminal-symptom pathway, so a substantial fraction of their nominal effects overlap. Gut-brain neuromodulators and psychotherapy retain more independent (mood-mediated) effect, which is why ρ̄ is user-adjustable rather than fixed. Note the unusually large placebo response in IBS trials, which the E-value helps bound. 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

The endpoint is symptom relief, not survival. IBS is a disorder of gut-brain interaction with essentially normal life expectancy. Every estimate here is a surrogate for morbidity, quality of life and healthcare use — there is no mortality signal to reduce, so “risk” means the risk of remaining symptomatic.
Placebo response is enormous. IBS trials show 30–40% placebo response rates. Relative risks are calculated against that high placebo bar, but real-world open-label benefit is smaller, and regression to the mean inflates apparent effect.
Subtype specificity breaks the stack. Secretagogues and (to a degree) SSRIs help IBS-C; rifaximin, low-FODMAP and TCAs favour IBS-D. A pooled “combined” estimate only applies within a subtype — you cannot add an IBS-C and an IBS-D drug in the same patient.
Neuromodulators and CBT are undersold by a symptom RR. Their largest effects are on anxiety, catastrophising and coping — partly symptom-independent — which is why the graph gives them separate gold arrows and the front-door layer does not fully discount them against the antispasmodics.
Evidence quality is low. Most component trials are small, short (4–12 weeks) and at moderate-to-high risk of bias; the network meta-analysis authors explicitly caution that the rankings are more robust than the absolute effect sizes.

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. Most IBS therapies act through one shared mediator — reduction of visceral hypersensitivity / symptom severity. Each log-effect is split into a symptom-mediated (indirect) and a symptom-independent (direct) part. Indirect parts are pooled through the mediator with dose-response saturation (symptom relief saturates — stacking a third luminal agent yields diminishing returns), removing the mediator cross-correlation; direct parts keep the residual eigenvalue correlation at ρ̄. Tricyclics, SSRIs and gut-directed psychotherapy, whose effects on mood and coping are partly symptom-independent, are therefore NOT fully discounted against the antispasmodics. 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% symptom ↓
Sum of standalone symptom reduction (naive)
Combined symptom 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%symptmed-fracindirect logdirect log

Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the symptom saturation (currently removing of the summed mediated effect when interventions are stacked). Note a domain caveat: secretagogues and SSRIs favour IBS-C, while rifaximin, low-FODMAP and tricyclics favour IBS-D — subtype-specific agents only combine within a subtype. Symptom-mediated fractions are transparent, adjustable priors.

Front-door caveat (antithesis): the endpoint is symptom relief / responder status — a surrogate with no mortality translation. Because IBS trials have a 30–40% placebo response, favourable relative risks are calculated against a high bar and overstate real-world open-label benefit.

Executive summary

Select interventions to generate a plain-language summary.