A Judea Pearl Structural Causal Model in which every intervention acts through one shared mediator — systolic blood pressure. Because the levers are not independent causes of cardiovascular events, their per-lever event hazard ratios are never multiplied. The engine sums their published mm Hg effects, shrinks for overlap, and converts the net blood-pressure change to outcome hazard ratios once, using the BPLTTC dose–response. All effect sizes are real published values; aggregation is an upper-bound ceiling, not clinical advice.
Causal question. Across the interventions for which published blood-pressure effects and cardiovascular dose–response data exist, what is the identifiable causal contribution of each — acting through systolic blood pressure — to a reduction in major cardiovascular events and all-cause mortality, after removing confounding (randomisation) and after removing shared-mediator double-counting via cross-correlation shrinkage?
| Element | Specification |
|---|---|
| Population | Adults with hypertension (or elevated cardiovascular risk), the SPRINT/BPLTTC trial populations |
| Mediator (do-target) | Systolic blood pressure (mm Hg) — the single node every lever moves |
| Primary endpoints | Major cardiovascular events (MI / ACS / stroke / heart failure / CV death) and all-cause mortality |
| Anchor (baseline risk) | 10-year major-CVD risk, user-set (default 15%); BPLTTC comparator event rate ≈ 3.2%/yr |
| Secondary endpoints | Stroke, heart failure, ischaemic heart disease, cardiovascular death (each with its own BPLTTC slope) |
Calibration check: SPRINT's intensive arm achieved ≈ 14–15 mm Hg lower SBP than standard care and a primary-composite HR of 0.73–0.75. The BPLTTC per-5 mm Hg slope predicts 0.903 ≈ 0.73 for a 15 mm Hg reduction — the model reproduces the landmark trial.
The graph below makes the structure explicit: interventions are parents of a single mediator (SBP), and SBP is the parent of the cardiovascular outcomes. There is no direct intervention→outcome arrow that bypasses SBP, which is precisely why the engine converts once at the mediator rather than multiplying lever-specific outcome HRs.
| Operation | Method | Implementation here |
|---|---|---|
| Confounding control | Backdoor criterion (Pearl) | Drug and most lifestyle effects come from randomised trials; backdoor paths closed by design |
| Effect aggregation | Additive on the mediator, not multiplicative on outcomes | Net ΔSBP = largest lever + (1−ρ̄)·Σ(remaining levers); converted once |
| Cross-correlation removal | Shared-variance shrinkage, ρ̄ = 0.30 | Overlapping levers (DASH already embeds Na/K; exercise/weight overlap) deflated to avoid double-counting |
| Dose–response | BPLTTC per-5 mm Hg slopes | HRendpoint = (slope)ΔSBP/5, separate slope per endpoint |
| Unmeasured-confounder robustness | E-value (VanderWeele & Ding) | Computed for the composite-event HR |
| Saturation / ceiling | Physiologic cap on ΔSBP | Net ΔSBP capped at 40 mm Hg; risk floored — no implausible totals |
| Minimum-effective set | Pareto frontier (mm Hg vs burden) | Levers ranked in Section IV |
Individual-participant meta-analysis of 48 randomised trials, 344,716 participants. Effects are proportional to the size of the SBP reduction and similar with or without prior cardiovascular disease, down to baseline SBP < 120 mm Hg.
| Endpoint | Per 5 mm Hg SBP↓ (HR) | Per 5 mm Hg reduction | Source / grade |
|---|---|---|---|
| Major CV events (composite) | 0.90 | −10% | BPLTTC, Lancet 2021 A |
| Stroke | 0.87 | −13% | BPLTTC, Lancet 2021 A |
| Heart failure | 0.87 | −13% | BPLTTC, Lancet 2021 A |
| Ischaemic heart disease | 0.92 | −8% | BPLTTC, Lancet 2021 A |
| Cardiovascular death | 0.95 | −5% | BPLTTC, Lancet 2021 A |
| All-cause mortality | 0.93 | −7% | BPLTTC, Lancet 2016 (per-10 RR 0.87) A |
SPRINT anchors the upper end: intensive control (target < 120) vs standard (< 140) gave a composite HR of 0.73–0.75 and all-cause mortality HR ≈ 0.73 over ≈ 15 mm Hg of additional separation.
Each lever's published SBP effect. Drug-class monotherapy figures are from the Law / Wald analysis of 354 trials (≈ 9 mm Hg at standard dose; classes roughly additive). Lifestyle figures are the 2017 ACC/AHA guideline summary estimates.
| Lever | SBP reduction (mm Hg) | Class | Source / grade |
|---|
| Endpoint | HR | Relative reduction |
|---|
Levers ranked by systolic-BP reduction (mm Hg) — the efficient frontier trades blood-pressure effect against treatment burden and risk. Drag the threshold to set a minimum per-lever yield: levers at or above the line form the minimum-effective set; the dimmed tail below contributes diminishing returns relative to its pill / adverse-effect burden.
Because every lever works through SBP, their effects on cardiovascular events are sub-additive, not multiplicative. Two drugs that each cut events 10% in isolation do not cut events 19% together — they lower SBP a bit more and move along one dose–response curve. Naïve HR-stacking (the error this engine avoids) would have predicted impossible benefit.
The relative effect of a 5 mm Hg reduction is constant across baseline BP, but the absolute benefit scales with underlying risk. The same regimen prevents far more events in a 75-year-old with prior CVD than in a low-risk 50-year-old — which is why the anchor slider, not the HR, drives NNT.
Hypertension is the single largest modifiable contributor to cardiovascular mortality worldwide. A small population-wide SBP shift (e.g. dietary sodium reformulation) acting on ~1.3 billion people reaches a scale no individual prescription can — a public-health do(·) on the mediator itself.
BPLTTC found proportional benefit down to < 120 mm Hg, but a SPRINT subgroup with very high baseline SBP and low Framingham risk showed possible harm from intensive control. The dose–response is not unconditional; very low pressures in frail or low-risk patients may cross a threshold the population slope hides.
| Challenge | Why it threatens the conclusion | Mitigation here |
|---|---|---|
| Adverse events of intensive control | SPRINT's intensive arm had more hypotension, syncope, electrolyte abnormality and acute kidney injury — benefit is not free | Engine reports a ceiling on benefit only; harms are named and the BP target is left to a clinician |
| J-curve / subgroup harm | Intensive control in patients with SBP ≥ 160 and low Framingham risk was associated with higher mortality (HR 3.12, 1.00–9.69) | Flagged explicitly; the population slope is not applied as if unconditional |
| Additivity of mm Hg | Lifestyle levers overlap (DASH embeds sodium and potassium); summing them raw overstates the net effect | ρ̄ shrinkage deflates overlapping secondary levers; net ΔSBP capped at a physiologic ceiling |
| Real-world adherence | Trial BP reductions are best-case; sustained adherence to drugs and especially lifestyle is much lower | NNT shown to expose absolute scale; figures framed as an upper bound, not an expected outcome |
| Lifestyle evidence grade | Some lifestyle mm Hg estimates rest on shorter trials with heterogeneity | Drug classes graded A from large RCTs; lifestyle summarised from guideline meta-analyses and labelled accordingly |
levers sorted by mm Hg descending; s₁ = largest
ΔSBP_eff = min( 40 , s₁ + (1 − ρ̄) · Σi≥2 sᵢ )
HR_endpoint = slope_endpoint ^ (ΔSBP_eff / 5)
slope: composite 0.90 · stroke 0.87 · HF 0.87 · IHD 0.92 · CV-death 0.95 · all-cause 0.933
risk_treated = anchor · HR_composite ; ARR = anchor − risk_treated ; NNT = 1 / ARR
E-value (HR<1): RR* = 1/HR ; E = RR* + √(RR*·(RR*−1))
Worked example: thiazide (−9) + DASH (−11) + sodium (−5), ρ̄ = 0.30 → ΔSBP_eff = 11 + 0.7·(9+5) = 20.8 mm Hg → composite HR = 0.90^(20.8/5) = 0.65; all-cause HR = 0.933^(4.16) = 0.75. At 15% anchor: treated 9.8%, ARR 5.2%, NNT ≈ 19.
1. SPRINT Research Group. A Randomized Trial of Intensive versus Standard Blood-Pressure Control. N Engl J Med 2015;373:2103–2116. Primary composite HR 0.75 (0.64–0.89); all-cause mortality HR 0.73.
2. SPRINT Research Group. Final Report of a Trial of Intensive versus Standard Blood-Pressure Control. N Engl J Med 2021;384:1921–1930. Composite HR 0.73; all-cause mortality HR 0.75 (0.61–0.92).
3. Blood Pressure Lowering Treatment Trialists' Collaboration. Pharmacological blood pressure lowering... an individual participant-level data meta-analysis. Lancet 2021;397:1625–1636. Per 5 mm Hg SBP↓: major CV events −10%, stroke −13%, heart failure −13%, ischaemic heart disease −8%, CV death −5%.
4. BPLTTC. Blood pressure lowering for prevention of cardiovascular disease and death: a systematic review and meta-analysis. Lancet 2016;387:957–967. Per 10 mm Hg SBP↓: major CVD RR 0.80, stroke 0.73, heart failure 0.72, all-cause mortality RR 0.87.
5. Wald DS, Law M, et al. Combination therapy versus monotherapy in reducing blood pressure: meta-analysis on 11,000 participants from 42 trials; and Law MR, et al. BMJ 2003;326:1427 (354 trials). Standard-dose class monotherapy ≈ 9.1 mm Hg SBP; classes approximately additive.
6. Whelton PK, Carey RM, et al. 2017 ACC/AHA/... Guideline for the Prevention, Detection, Evaluation, and Management of High Blood Pressure in Adults. Hypertension 2018;71:e13–e115. Nonpharmacologic SBP effects: DASH ≈ −11, weight loss ≈ −5 (1 mm Hg/kg), aerobic exercise ≈ −5 to −8, sodium reduction ≈ −5 to −6, potassium ≈ −4 to −5, alcohol moderation ≈ −4 mm Hg.
Longevity Research Initiative — Bayesian Causal Atlas. SCM methodology after Judea Pearl; E-values after VanderWeele & Ding. All effect sizes are published values cited above; none were fabricated. Outputs are upper-bound ceilings for research, not clinical guidance. Report generated .