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

Rheumatoid Arthritis — Structural Causal Analysis

Rheumatoid arthritis affects roughly 1.3 million United States adults, causing progressive joint destruction, disability and excess cardiovascular mortality driven by chronic inflammation. This oracle estimates the causal reduction in joint damage / disability and CV death on a shared synovial-inflammation backbone, using hazard ratios from named trials. It anchors on methotrexate, treats biologic effects as add-ons that saturate against one another, and flags the JAK safety signal and the glucocorticoid bridge-versus-trap trade-off. For education, not individual medical advice.

Method. Structural Causal Model (SCM) in Judea Pearl's framework. What this engine does and does not do: it does not itself perform backdoor adjustment — every hazard ratio is taken from a named trial or a confounder-adjusted study, so the backdoor adjustment is the source study's, and the named confounders below are the paths those studies adjusted for. What this engine adds is the combination rule. Interventions are not assumed independent: shared-mechanism arms overlap on synovial autoimmune inflammation, and that overlap is removed by an eigenvalue-corrected model at an adjustable mean cross-correlation ρ̄ (default 0.30). Robustness to unmeasured confounding is quantified with the E-value. 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 (conventional → biologic → jak → steroid → symptomatic → treat-to- → 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 synovial 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 risk (illustrative anchor)
Absolute risk after intervention
Absolute risk difference (RD)
Backdoor-only HR (no front-door)
Mediator 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 acting through synovial autoimmune inflammation toward the endpoint (Y); direct-mechanism arms are drawn gold. Named confounders open back-door paths (adjusted). Mediator cascade: interventions attach to the node they act on (conventional → biologic → jak → steroid → symptomatic → treat-to-), 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:seropositivity (RF / anti-CCP) · disease duration · baseline erosions · smoking · cardiovascular risk · prior DMARD exposure → back-door paths (adjusted). Biologic trials enrolled inadequate-responders on background methotrexate, so their HRs are add-on effects, not standalone.MethotrexateTriple csDMARDTNF inhibitorIL-6 inhibitorAbataceptRituximabJAK inhibitorTreat-to-targetGlucocorticoid(bridge)NSAIDConventionalDMARDBiologicDMARDJAKinhibitorSteroidbridgeSymptomaticTreat-to-targetSynovialinflammationJoint damage /disability, CVFront-door: through synovial inflammationDirect anchor DMARD (methotrexate)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

ρ̄ ≈ 0.30 is defensible on mechanistic grounds: same-mechanism arms converge on synovial autoimmune inflammation, so stacking them yields diminishing returns, while arms on distinct mechanisms share little and compose. ρ̄ is user-adjustable. 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

Cheap triple therapy rivals expensive biologics. RACAT showed methotrexate-based triple therapy non-inferior to MTX + etanercept for many patients; the biologics are not uniformly superior, and anchoring on them inverts the cost-effectiveness. On the graph, triple therapy shares the csDMARD node with methotrexate.
Biologic HRs are add-on effects, not standalone. Nearly every biologic trial randomised methotrexate-inadequate responders on background MTX, so the HR is the increment on top of methotrexate; reading it as a standalone effect double-counts. The biologics also saturate against one another on the shared node — they are sequenced, not stacked.
JAK inhibitors buy efficacy at a safety cost. ORAL Surveillance found excess cardiovascular events, malignancy and death versus a TNF inhibitor in higher-risk patients; the disease-activity HR does not capture that trade-off, which is why the drug is safety-restricted.
Glucocorticoids are a bridge that becomes a trap. Early low-dose steroid helps, but chronic use causes infection, osteoporosis and cardiovascular harm; the short-term activity HR hides the long-term damage.
Damage and disability, not just symptoms, are the endpoint. NSAIDs relieve pain without preventing erosions; controlling the ACR/EULAR endpoints requires disease modification. The excess cardiovascular mortality of RA is driven by inflammation, so inflammation control — not analgesia — is what moves the outcome.

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-structured mediation decomposition (not front-door identification). Each log-effect splits into a mediated (indirect) and a mediator-independent (direct) part. Indirect parts are routed through the mediator cascade: arms on the SAME node are substitutes and saturate against a dose-response ceiling; arms on DIFFERENT nodes are d-separated and compose in series. No correlation coefficient is applied to the mediated path. ρ̄ is applied ONLY to the un-mediated direct residual. Caveat: Pearl's front-door criterion would additionally require the mediator to be COMPLETE (no unblocked X→Y path bypassing M) and the M→Y edge to be unconfounded — neither is defended arm-by-arm here, and baseline severity routinely confounds M→Y. These are therefore structured decompositions, not identified causal effects. 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% inflammatory activity ↓
Sum of standalone synovial reduction (naive)
Combined synovial 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%act↓med-fracindirect logdirect log

Which % of cross-correlation is appropriate? Not one number. The mediator overlap is fixed empirically by the synovial saturation (currently removing of the summed mediated effect when interventions are stacked). Read every provisional (surrogate / subgroup / observational / failed-confirmatory) entry through its grade, not as an RCT survival result.

Front-door caveat (antithesis): the mediator→outcome edge is confounded by baseline severity and stage; effect sizes are stage-conditional; combined figures are upper bounds that assume the arms stack cleanly.

Executive summary

Select interventions to generate a plain-language summary.