DoAtlas-2: A Foundation for Self-Evolving Causal Biomedical Discovery

1 Overview

• DoAtlas-2 starts from evidence gaps, conflicting relations, and unresolved paths to formulate and prioritize testable research questions.Selected mechanisms are evaluated in HPP and independent data; supporting, challenging, or unresolved results revise mechanism state and subsequent research priorities.Source: §1 · p. 2
• As of September 22, 2026, the evidence base contained 93,566 canonical nodes, 149,383 candidate causal relations, and 4,696,704 literature-derived records.It supported 4,014 candidate pathway questions across vascular, early-glycemic, and hepatic-metabolic systems.Source: §1 · p. 2
• Across 2,031 evaluated questions, DoAtlas-2 reports mechanistic findings linking blood pressure to adiposity, hepatic, and lipid phenotypes and an interpretable predictive foundation.Sections 3–5 report the discovery loop and representative findings.Source: §1 · p. 2

Data, Research Scope, and Resource Footprint

• 771 research resources cover more than 720,000 participants across 48 countries and span clinical, physiological, imaging, and molecular measurements.The resources contain more than 40 million resource-specific measurement dimensions across multiple physiological systems.Source: Data, Research Scope, and Resource… · p. 2, Figure 1 · p. 3
• By December 2024, HPP had enrolled 27,916 participants, with 13,072 completing a first deep-phenotyping visit.Designed for 25 years of follow-up, HPP links participant-level longitudinal phenotyping and multi-omics measurements.Source: Data, Research Scope, and Resource… · p. 2
• HPP recorded 63,004,814 field-level measurements across 37 observational domains, including 109,788 participant-days of continuous glucose monitoring.Its participant-linked records also include imaging, sleep monitoring, and food, medication, sleep, and activity logging.Source: Data, Research Scope, and Resource… · p. 3
• 2,031 independent research questions were completed, averaging 29.86 computation-complete terminal units per question over a 70-day run.The evaluations consumed approximately 1.587 trillion model tokens in total.Source: Data, Research Scope, and Resource… · p. 3, Table 1 · p. 3

2 The DoAtlas-2 Self-Evolving Causal Foundation

• Each research round is represented by the contextualized causal evidence state, discovery frontier, and external evidence requirements.Evidence gaps and conflicting findings generate candidate mechanism questions with traceable parent results.Source: §2 · p. 4
• Selected questions specify population, temporal structure, causal estimand, and identification conditions before external outcomes are revealed.Research agents report prespecified outcomes, diagnostics, and non-estimable states.Source: §2 · p. 4
• External selection records drive state transitions in which results revise evidence support and scope, reshaping later questions and evidence needs.Supported paths motivate extensions, while counterevidence, context restrictions, and unresolved results prompt competing mechanisms or boundary tests.Source: §2 · p. 4

3 Evidence for the Self-Evolution Loop

• 756 of the first 1,079 screened research questions received screening-level statistical support.Across three rounds, the candidate catalog grew to 4,014 pathway questions covering 3,941 distinct pathways and 517 candidate directed relations.Source: §3 · p. 4
• 200 of 259 relations with HPP evidence acquired population-derived states: 81 supported, 2 challenged, and 117 unresolved.Unresolved means evidence cannot yet determine direction, not that the relation is absent; the remaining uncertainty directs larger temporally ordered samples or more precise designs.Source: §3 · p. 4
• A joint analysis using ±365-day measurement windows estimated a standardized WHR–ALT–DBP–PWV path association of 0.01073 (95% CI [0.007575, 0.01389]).The follow-up adds ALT and examines the DBP branch of a liver-related pathway between adiposity and vascular phenotypes.Source: §3 · pp. 4–5
• The agent architecture links mechanism-question proposals to study execution and learning-agent revisions of evidence support, discovery frontier, and evidence needs.Figure 2 depicts candidate and challenged relations and context-dependent follow-up motifs.Source: Figure 2 · p. 5
• Follow-up questions compare serial and shorter paths, alternative mediators, vascular endpoints, and competing explanations for intermediate phenotypes.Round 3’s first 30 pathway proposals span 15 outcome constructs.Source: §3 · p. 5

4 Key Findings

• Fifteen pathways with complete serial estimates form a cross-system association network of 19 phenotype nodes and 29 connections.All models account for age and sex; serial estimates are products of adjacent edge coefficients, standardized unless stated otherwise.Source: §4 · p. 6

4.1 Blood-pressure convergence of metabolic and vascular phenotypes

• Five shorter supported paths link adiposity to cIMT or lower-limb PWV through blood pressure, while hepatic and lipid branches converge on DBP before lower-limb PWV.Hip–ALT–DBP–PWV and Hip–ApoB–DBP–PWV products are 0.01174 (95% CI [0.005539, 0.02063]) and 0.004717 (95% CI [0.001192, 0.009364]), respectively; both retain support after Holm correction.Source: §4.1 · pp. 6–7
• −0.002524 (95% CI [−0.004037, −0.001117]) and 0.02437 (95% CI [0.004872, 0.04387]) are the supported Waist–SpO2–SBP–cIMT and SpO2–GlycA–PWV serial products.Metabolic-to-pressure routes also replicate in a 912-adult cohort, with Holm-adjusted P ≤0.0012.Source: §4.1 · p. 7
• Waist circumference is negatively associated with nocturnal SpO2 and raises SBP; conditioning on waist changes the SpO2–SBP association from negative to weakly positive.Across HPP analyses, all 9 SpO2–SBP intervals excluding zero are negative without an adiposity term, while all 10 are positive with an adiposity measure; conditional SpO2–DBP associations remain predominantly negative.Source: §4.1 · p. 7

4.2 Temporal support for DBP paths and differences in ApoB associations

• ALT–DBP–PWV and TG–DBP–PWV receive support under strict temporal ordering, while selected ApoB-related serial associations differ by sex and age.The VAT–ApoB–SBP–PWV sex contrast has Holm-adjusted P = 0.005; the older-age contrast for Weight–ApoB–DBP–PWV is ∆= −0.02275 (95% CI [−0.04126, −0.00828]; Holm-adjusted P = 0.006).Source: §4.2 · p. 7

4.3 Covariate-dependent adiposity–inflammation–blood-pressure link

• Joint BMI and smoking adjustment decreases the WHR–GlycA–SBP–PWV serial estimate from 0.01218 to 0.002022, with a formal difference of ∆= −0.01016 (95% CI [−0.01537, −0.004936]).The attenuation indicates that the pathway reflects overall adiposity and smoking more than waist-to-hip-ratio-indexed fat distribution.Source: §4.3 · p. 7

• The 19-node, 29-connection vascular network is the model structure: predictions are closed-form expressions, and the node, interaction, and branch decomposition is an exact identity.For temporally ordered questions, the network also yields closed-form direct and mediated effects.Source: §5 · p. 8
• Each source equation traces to a specific network relationship, while task-specific terms and weights combine applicable source equations with observed phenotypes and covariates.The prediction equation also accounts for whether each variable is observed.Source: §5 · p. 9
• 12,492 HPP and 1,587 NHANES predictions are independently reproduced with maximum discrepancies of 1.42 × 10−14 and 5.55 × 10−16, respectively.Node and branch views are alternative summaries of the same prediction, and contributions retain the outcome’s original units.Source: §5 · p. 10
• For a BMI contrast of 22.921 →28.397 kg/m2 in 425 HPP participants, the total BMI–cIMT contrast has 95% CI [0.00400, 0.04285] mm, with direct and mediated components [0.00737, 0.04683] and [−0.00883, −0.00055] mm.The negative SpO2-mediated component partially offsets the positive direct component.Source: §5 · p. 11
• Expanded adjustment changes the total contrast to 0.01962 mm (95% CI [−0.00090, 0.03747]) in 294 participants; removing prior cIMT on the same participants gives 0.03338 mm.The paired difference is 0.01376 mm (95% CI [0.00554, 0.02572]).Source: §5 · p. 11
• Held-out R2 is 0.378 for future PWV and 0.176 for future cIMT; with 70% additional random masking, five-seed mean R2 is 0.248 and 0.136, respectively.Every prediction retains its complete contribution decomposition.Source: §5 · p. 11
• Frozen HPP relationship parameters yield NHANES 60-month mortality AUC 0.798 and IPCW Brier score 0.0473, while target-domain refitting reaches AUC 0.799.On the same NHANES split, the target-domain refit matches a generalized additive model (AUC 0.798) and a gradient-boosted tree (AUC 0.803).Source: §5 · p. 11

A Abbreviations and Measurement Definitions

• Table A.1 lists abbreviations and principal-phenotype measurements and units; pathway identifiers and figure-panel symbols are defined with Figures 4 and 5.These references support interpretation of the reported mechanistic findings.Source: A Abbreviations and Measurement… · p. 14, Table A.1 · p. 14

B.1 Scientific state and notation

• The scientific state combines contextualized causal evidence and its uncertainty, unresolved questions and pathways, and requirements for evidence needed to revise judgments.Supporting and conflicting results can coexist under their applicable conditions.Source: §B.1 · p. 15

B.2 Discovery and selection of research questions

• Candidate questions pair a testable causal-mechanism proposition with its context and retain parent results and rationale; all candidates and selection status remain in the denominator.Priority weighs causal coherence, unresolved uncertainty, and expected discriminative value.Source: §B.2 · p. 15

B.3 Study design and evidence requirements

• Prespecified designs declare population, exposure, outcome, temporal windows, estimand, and identification conditions, while analysis units distinguish ordered, ambiguous-order, and cross-sectional evidence.Non-estimability records name missing measurements, population support, follow-up, confounders, or instruments needed; some questions require external validation.Source: §B.3 · p. 15

B.4 Long-chain causal pathways

• A long-chain pathway composes evidenced adjacent relations only when shared nodes are measured consistently and segment populations cover the target context.Strictly ordered composition additionally requires the path measurements to occur in sequence for each participant.Source: §B.4 · p. 15

B.5 External scientific selection

• External selection records preserve each analysis-unit result and admitted estimate, with admission governed by the adjudication policy.An admitted HPP estimate needs an interval, declared scale and estimand, a directed concept pair, and a sample supporting the interval.Source: §B.5 · p. 16, §B.6 · p. 16

B.6 Evidence-state rules

• Evidence-state rules classify estimates using their intervals, null value, design-declared equivalence margin, multiplicity criterion, and direction relative to literature reports.Relation states aggregate evidence contexts without weighting by sample size or evidence class; unresolved means direction is not established in every context.Source: §B.6 · p. 16, Table B.1 · p. 16

B.7 Joint state revision

• Each round's joint revision records changes to evidence, questions, and evidence requirements, with every change attributable to cited selection records.A revision is joint when all three change sets are non-empty.Source: §B.7 · p. 17

C.1 Scope and counting units

• A research question is an ordered concept sequence to be tested within its context; screening tests indirect association and each link before full evaluation.Screening-level support requires false-discovery-rate significance and a path free of measurement artifacts.Source: §C.1 · p. 17
• 4,014 Round-3 pathway questions comprise 1,546 vascular, 1,329 early-glycemic, and 1,139 hepatic-metabolic questions; 61 of 86 supported Round-1 questions became Round-2 parents.None of the 89 unsupported Round-1 questions became parents, and each Round-2 question records two or three parents.Source: §C.1 · p. 17, Table C.1 · p. 17

C.2 From results to successor questions

• The 904 Round-2 questions fall into five successor families; among 2,535 parent–child links, 2,294 share the parent's outcome and 1,441 share a directed relation.Successors insert an upstream mediator, replace blood pressure with a competing mediator, or test blood pressure as a shared intermediate node.Source: §C.2 · p. 18, Table C.2 · p. 18
• Of 120 Round-2 pathway contrasts, 81 had an unsupported serial bridge but supported nested path, 30 differed across vascular outcomes, and 9 showed the reverse pattern.Ten contrasts received scientific interpretation; the first seven yielded seven successor proposals, and further evaluation of three ApoB bridges produced 11 interpretations and 11 proposals.Source: §C.2 · p. 18
• The first 30 Round-3 proposals span 15 outcome constructs and include 19 single relations, 8 three-node paths, and 3 five-node chains.Eight proposals request common-cause, fork, or measurement diagnostics; the outcomes include earlier intermediates, earlier outcomes, and constructs not seen in prior rounds.Source: §C.2 · p. 18

C.3.1 Adiposity–liver–vascular follow-up

• The Round-2 successor shares WHR and PWV with both Round-1 parents but none of their directed relations, and the joint model estimates ALT and DBP branches alongside a direct association.Its ±365-day windows differ from the primary design's symmetric adjacent-measurement windows.Source: §C.3.1 · pp. 18–19
• The Round-2 primary design estimated a serial path of 0.01099, matching the product 0.2323 × 0.1088 × 0.4347; screening estimated an indirect association of 0.0149.The screening estimate used 7,452 participants without covariate adjustment; the primary design used symmetric windows of ±180, ±90, and ±30 days between adjacent measurements.Source: §C.3.1 · p. 19
• 0.09771 ([0.08289, 0.1125]) is the joint-model DBP bypass product, while the ALT bypass product is 0.00219 ([−0.002308, 0.006688]).The Round-2 primary design likewise estimates a DBP branch product of 0.09709 ([0.07721, 0.117]) and an ALT branch product of 0.001912 (95% CI [−0.005126, 0.008951]).Source: Table C.3 · p. 19, §C.3.1 · p. 19

C.3.2 Neck circumference, ApoB and blood pressure

• The Neck–ApoB–DBP–PWV and Neck–ApoB–SBP–PWV serial questions lacked screening support, while four nested shorter paths through DBP or SBP were supported.The serial indirect associations were 0.0049 and 0.0043 (n = 750); nested Neck–DBP–PWV and Neck–SBP–PWV gave 0.1536 and 0.2289 (n = 2,665), and ApoB–DBP–PWV and ApoB–SBP–PWV gave 0.0826 and 0.0845 (n = 1,388). Seven successor proposals followed, six deepening Round-2 questions and one new screening question.Source: §C.3.2 · p. 19

C.3.3 Waist-to-hip ratio, ApoB and vascular endpoints

• WHR–ApoB–DBP–cIMT lacked screening support, but nested WHR–DBP–cIMT and downstream ApoB–DBP–cIMT paths were supported.The same mediator sequence was supported for PWV, while WHR–ApoB–cIMT was not; four successor proposals deepened Round-2 questions.Source: §C.3.3 · p. 20

C.3.4 HbA1c, SBP and UACR

• The Round-3 HbA1c–SBP–UACR proposal tests whether blood pressure mediates the HbA1c–UACR association or is a common cause or parallel consequence.It pairs the pathway with HbA1c–UACR and requires serial, direct, and common-cause explanations to be evaluated separately.Source: §C.3.4 · p. 20
• Of 29 Round-2 screening paths containing HbA1c–SBP, 27 received screening-level support; both unsupported paths began with total sleep time.Among the first 30 Round-3 pathway proposals, five other proposals used UACR as the outcome.Source: §C.3.4 · pp. 20–21

C.4 Evidence-state revision

• 200 of 259 relations with HPP evidence acquired a population-derived state: 81 supported, 2 challenged, and 117 unresolved.The other 59 had only secondary or unspecified HPP records.Source: §C.4 · p. 21
• Of 81 supported relations, 49 had no literature-network counterpart, while 16 matched a directional literature reference and 16 had conflicted or non-directional references.Among 117 unresolved relations, 38 were supported in at least one evidence context and 78 were unresolved in every context; 52 of those 78 had no informative primary record.Source: §C.4 · p. 21

D.1 Definitions for Figure 4

• Figure 4 maps research-question outputs and analysis units by design class, then joins the liver, lipid, and sleep pathways into a directed network with shared nodes and connections marked separately.Its other panels describe reverse, within-person, and off-path analyses, plus confounding-sensitivity analyses.Source: §D.1 · pp. 23, 26

D.2 Definitions for Figure 5

• Figure 5 compares alternative timing and adjustment specifications, sex and age patterns, interactions, component coefficients, and joint-model coefficients across its panels.For R1, panel c compares extended adjustment with the primary adjustment on the same sample and standardization, isolating the change associated with adding BMI and smoking.Source: §D.2 · pp. 27, 28, 30

D.3 Sensitivity analyses of the WHR–ALT–DBP–PWV joint model

• The WHR–ALT–DBP–PWV joint model estimates a three-edge serial product alongside bypass and direct associations, with sensitivity analyses varying windows, sex, adjustment, interactions, and unmeasured-confounding assumptions.The extended adjustment adds BMI and current smoking to age and sex; robustness values quantify the partial R2 an unmeasured confounder would need with a predictor and outcome to reduce an edge estimate to zero.Source: §D.3 · pp. 30–31

D.4 Replication in external cohorts

• The external cohorts were 912 adults from a population study and 879 hospitalized patients with diabetes in Chengdu; both were cross-sectional.Source: §D.4 · p. 32
• Seven tests re-estimated five HPP paths, using BMI instead of WHR or android fat and baPWV instead of lower-limb PWV.Models adjusted for age and sex, with path variables standardized within each model.Source: §D.4 · p. 32
• A path counted as replicated when its serial estimate matched the HPP sign and was Holm-significant, with every component also matching the HPP sign and having a 95% CI excluding zero.Source: §D.4 · p. 32, Table D.24 · p. 33

E.1 Hand grip strength–GlycA–DBP–cIMT

• The serial grip strength→GlycA→diastolic blood pressure→carotid IMT analysis reports 0.1646 [0.06322, 0.266] (P=0.001521) and 0.1155 [0.0342, 0.1967] (P=0.005461).The design requires GlycA within 365 days of grip strength, blood pressure within 90 days of GlycA, and carotid IMT 30–1825 days after blood pressure.Source: §E.1 · pp. 33–34

2. Exposure–outcome association: grip strength and carotid IMT (±365 days)

• For grip strength and carotid IMT measured within ±365 days, the adjusted association coefficient βA was 0.0005656 [0.0002785, 0.0008527] (P=0.000113).The analysis used original-scale measurements and adjusted for age, BMI, and sex.Source: §2 · p. 34

3. Pairwise association: grip strength →GlycA (±365 days); 7. Pairwise association: grip strength →diastolic blood pressure (±90 days)

• Pairwise analyses estimated β=-0.2853 for grip strength→GlycA and β=0.0931 for grip strength→diastolic blood pressure, with bias-bound grids across hypothetical confounder strengths.The grids report intervals as the coefficient plus or minus a bias bound; the supplied passages do not identify a single confounder-strength scenario as definitive.Source: §3 · p. 35, §7 · p. 37

4. Pairwise association: GlycA →diastolic blood pressure (±90 days)

• For GlycA→seated diastolic blood pressure, the adjusted standardized slope was 0.08383 [0.03421, 0.1334] (P=0.0009403).The pairwise analysis used measurements within 90 days and included 1,544 participants.Source: §4 · pp. 35–36

5. Pairwise association: diastolic blood pressure →carotid IMT (30–1825 days); 6. Pairwise total association: grip strength →carotid IMT (±730 days); 8. Pairwise association: GlycA →carotid IMT (30–1825 days); 9. Single-mediator path: grip strength →GlycA →carotid IMT

• Other specified analyses examined diastolic blood pressure→carotid IMT, grip strength→carotid IMT within ±730 days, GlycA→carotid IMT, and grip strength→GlycA→carotid IMT.The supplied passages specify forward measurement windows for the blood-pressure and GlycA links to IMT and a single-mediator design through GlycA; they do not provide corresponding result values.Source: §5 · p. 36, §6 · p. 36, §8 · p. 37

10. Single-mediator path: grip strength →diastolic blood pressure →carotid IMT

• For the grip strength→diastolic blood pressure→carotid IMT path, the reported values include 0.006348 [0.0001121, 0.01371] and 0.0748 [0.0036, 0.146] (P=0.0395).The design places blood-pressure measurement within 90 days of grip strength and carotid ultrasound 30–1825 days afterward.Source: §10 · pp. 38–39
• The single-mediator analysis examined the grip strength → diastolic blood pressure → carotid IMT path and reported coefficient estimates with interval grids.The supplied result passage does not identify which estimate or interval corresponds to a particular parameter.Source: §10 · p. 39

11–15. Pairwise association analyses

• Five pairwise analyses tested grip strength–GlycA, grip strength–diastolic blood pressure, GlycA–IMT, diastolic blood pressure–IMT, and GlycA–diastolic blood pressure associations.Measurements were aligned within ±365 days and models adjusted for age, BMI, and sex; sample sizes were 10,346 for grip strength–diastolic blood pressure, 821 for GlycA–IMT, and 7,940 for diastolic blood pressure–IMT.Source: §11 · p. 39, §12 · p. 40, §13 · p. 40

Joint models

• The joint model reported 5.827 [2.3, 9.354] and 0.001203; it used the same sample as the base model (n = 804), adjusting for approximate age, closest BMI within ±365 days, and sex.Source: Joint models · p. 41, §16 · p. 41

17. Reversed measurement order: serial equations with IMT preceding diastolic blood pressure

• A reversed-order serial analysis placed IMT before diastolic blood pressure and fit four linear equations on a sample of 40 participants.The chain aligned GlycA within 365 days of grip strength, diastolic blood pressure within 90 days of GlycA, and IMT 30–1,825 days before diastolic blood pressure.Source: §17 · p. 42

18. Reversed time order: IMT and grip strength measured 366–730 days later

• A reversed-time analysis compared carotid IMT with grip strength measured 366–730 days afterward, adjusting for age, BMI, and sex.The design allowed the same participant to contribute multiple IMT-anchored measurements.Source: §18 · p. 43

19. Heterogeneity by sex: grip strength–carotid IMT slope (±365 days)

• 0.0009764 [0.0004786, 0.001474] (P = 0.0001208) was the reported grip strength–carotid IMT slope in the sex-heterogeneity analysis.The analysis modeled sex-specific slopes with adjustment for age and BMI.Source: §19 · pp. 43–44

Sensitivity analyses

• Sensitivity analyses included a narrower serial-path window and a separate model additionally adjusting for education and smoking.The latter used 203 participants, with IMT measured 30–1,825 days after diastolic blood pressure.Source: §19 · pp. 44–45

19. Heterogeneity by sex: grip strength–carotid IMT slope (±365 days)

• The sex-heterogeneity analysis presents bias-bound intervals for path coefficients across hypothetical confounder partial R2 values, but the supplied results do not identify sex-specific estimates.The bounds vary the partial R2 values for a hypothetical omitted confounder from 0.01 to 0.50.Source: §19 · pp. 45–46

22. Narrow window: grip strength–carotid IMT (±90 days); 23. Additional adjustment for smoking status: grip strength–carotid IMT (±365 days)

• The adjusted grip strength–carotid IMT association coefficient was 0.0005631 [0.0002759, 0.0008502]; with additional adjustment for smoking status, it was 0.0005596 [0.0002452, 0.000874].Source: §22 · p. 46, §23 · p. 46

24. Joint model: grip strength, GlycA, diastolic blood pressure and IMT (tightened windows)

• The tightened-window joint models assess grip strength, GlycA, and diastolic blood pressure against IMT, including a version additionally adjusted for smoking status.The supplied passages identify the blood-pressure coefficient and grip-strength coefficient change but do not provide their estimates.Source: §24 · pp. 47–48

E.2 Hip circumference–hepatic steatosis–DBP–PWV

• The HPP research question tests whether hip circumference is associated with thigh-to-ankle PWV through hepatic steatosis and diastolic blood pressure.Hepatic ultrasound attenuation serves as the continuous proxy for steatosis.Source: §E.2 · p. 48

1. Single-mediator path: hip circumference →hepatic ultrasound attenuation →thigh-to-ankle PWV

• A single-mediator path analysis links hip circumference, hepatic ultrasound attenuation, and thigh-to-ankle PWV using one strictly ordered measurement chain per participant (n = 43).The reported path index is the product of the hip circumference–attenuation and attenuation–PWV coefficients; supplied passages do not provide its estimate.Source: §1 · pp. 48–49

2. Serial path coefficients and bias bounds: hip circumference →hepatic attenuation →seated DBP →PWV

• The serial-path analysis reported coefficients of 0.2035, 0.2633, 0.08416, and 0.04859 for a1, a2, d21, and b1, respectively.The corresponding reported values were 0.4338 for b2, −0.02049 for c′, and 0.111 for the total-association slope c.Source: §2 · p. 49

3. Exposure–outcome association: hip circumference and bilateral thigh-to-ankle PWV

• The exposure–outcome analysis estimates the standardized hip circumference–bilateral PWV association adjusted for age and sex, but its estimate is not supplied.The analysis uses the shortest-gap hip circumference–PWV pair per participant (n = 8,956).Source: §2 · p. 50, §3 · p. 50

4. Serial segment: hip circumference →hepatic ultrasound attenuation →seated DBP

• A serial segment analysis models hip circumference, hepatic attenuation, and seated DBP in date order, with age, sex, and height as covariates.The supplied passages define the path index but do not provide its estimate.Source: §4 · p. 50

4. Serial segment: hip circumference →hepatic ultrasound attenuation →seated DBP; 6. Pairwise association: hip circumference →seated DBP (0–180 days); 7. Pairwise association: hepatic ultrasound attenuation →seated DBP (0–180 days)

• The forward serial segment and 0–180-day pairwise analyses examined hip circumference–hepatic attenuation, hip circumference–DBP, and hepatic attenuation–DBP associations, but their supplied passages lack estimates.The serial segment also specifies a path index with a bootstrap 95% percentile interval, without providing its value.Source: §4 · p. 51, §6 · p. 51, §7 · p. 51

8. Pairwise association: hepatic ultrasound attenuation →PWV (0–365 days); 9. Pairwise association: seated DBP →PWV (0–180 days); 10. Pairwise total association: hip circumference →PWV (0–365 days)

• The 0–365-day forward pairwise analyses specified hepatic attenuation→PWV and hip circumference→PWV associations, but the supplied passages do not report their estimates.A separate 0–180-day analysis specified seated DBP→PWV; its estimate is also absent.Source: §8 · p. 52, §10 · p. 52, §9 · p. 52

11. Pairwise association: hip circumference–hepatic ultrasound attenuation (±365 days); 12. Pairwise association: hip circumference–seated DBP (±365 days); 13. Pairwise association: hepatic ultrasound attenuation–PWV (±365 days); 15. Pairwise association: hepatic ultrasound attenuation–seated DBP (±365 days)

• Passages report a seated-DBP difference per 1-SD higher hip circumference at fixed age and sex, plus standardized coefficients for hip circumference–hepatic attenuation and hepatic attenuation–PWV and –seated DBP.Source: §11 · p. 53, §12 · p. 53, §13 · p. 53

14. Pairwise association: seated DBP–PWV (±365 days)

• 0.545 (95% CI [0.5104, 0.5795]; P = 8.767 × 10−172) was the seated DBP–PWV standardized coefficient in the ±365-day analysis.The analysis included 1,974 participants and adjusted for age and recorded sex.Source: §14 · p. 53

16. Joint models: hip circumference, hepatic attenuation, DBP and PWV (±365 days)

• The ±365-day joint models estimated hepatic attenuation and DBP coefficients for PWV with hip circumference, age, and sex, including a mutually adjusted model, but supplied passages omit the coefficient values.The design used a shared sample and reported 95% confidence intervals; P values were not corrected for multiple comparisons.Source: §16 · pp. 54–55

17. Joint models: hip circumference, hepatic attenuation, DBP and PWV (±180 days)

• The ±180-day joint models repeated the hepatic-proxy, DBP, and mutually adjusted PWV specifications, but the supplied passages do not provide identifiable coefficient-value pairs.The subsection also specifies a reverse PWV→hepatic attenuation→hip circumference path and its components, without estimates in the supplied passages.Source: §17 · pp. 55–56
• Joint models report reverse-direction PWV → hip circumference slopes, including a slope adjusted for hepatic attenuation and an adjusted total slope.They also report a reverse-path index with a bootstrap 95% percentile interval.Source: §17 · p. 56

19. Reverse pairing: earlier PWV and subsequently measured hip circumference

• Reverse pairing assessed whether earlier PWV was associated with hip circumference measured 1–365 days later.The reported quantity was the reverse-direction coefficient.Source: §19 · p. 57

20. Sex heterogeneity: hip circumference →hepatic ultrasound attenuation →PWV

• Sex-category-specific serial path products were 0.005615 in the first category and 0.009779 in the second.The reported bootstrap 95% percentile intervals were [0.003191, 0.008495] and [0.006492, 0.01331], respectively.Source: §20 · p. 59

25. Wide-window serial path: hip circumference →hepatic ultrasound attenuation →DBP → PWV

• 0.007426 was the estimated wide-window serial path index for hip circumference → hepatic attenuation → DBP → PWV.The bootstrap 95% percentile interval was [0.005351, 0.009601].Source: §25 · p. 61
• 0.1111 [0.08975, 0.1316] was the total hip-circumference–PWV association in the wide-window serial-path decomposition.The decomposition also reports a DBP-only path product of 0.1143 [0.1036, 0.1256], a serial path product of 0.007426 [0.005351, 0.009601], and a remaining conditional component of −0.02044 [−0.04091, −0.00164].Source: §25 · p. 61

26. Conditioning on same-day BMI: hip circumference →hepatic ultrasound attenuation → DBP →PWV

• −0.06661 [−0.1099, −0.02552] was the total hip-circumference–PWV association conditional on same-day BMI.The reported DBP-only path product was −0.02162 [−0.03936, −0.00343], and the remaining conditional component was −0.04036 [−0.0787, −0.002933].Source: §26 · p. 62

27. Hip circumference–PWV association conditional on same-day BMI

• A same-day-BMI-adjusted hip circumference–PWV association was assessed in 8,937 people, but the supplied passage does not show its estimate.The coefficient represents the PWV difference per 1 SD higher hip circumference at fixed BMI, age, and sex.Source: §27 · pp. 62–63

28. Negative-control outcome: hip circumference and left-minus-right PWV difference

• Hip circumference was evaluated against the left-minus-right PWV difference as a negative-control outcome in 8,956 people, but the supplied passage omits the estimate.The outcome was the signed left-side minus right-side PWV difference, adjusted for age and sex.Source: §28 · p. 63

E.3 WHR–LDL–DBP–PWV

• The WHR–LDL–DBP–PWV research question used HPP measures of waist-to-hip ratio, LDL cholesterol, seated DBP, and thigh-to-ankle PWV.The supplied passage defines these exposures, mediators, and outcome but does not provide a result for this overview subsection.Source: §E.3 · p. 63

1. Single-mediator path: waist-to-hip ratio →LDL cholesterol →thigh-to-ankle PWV

• The single-mediator analysis tested waist-to-hip ratio → LDL → PWV and included a bias-bound sensitivity grid spanning partial R2 values from 0.01 to 0.30.The path product was evaluated at the 25th, 50th, and 75th percentiles of waist-to-hip ratio; the supplied result fragment does not clearly pair estimates with those path components.Source: §1 · pp. 63–64

2. Main serial path: waist-to-hip ratio →LDL →diastolic blood pressure →PWV

• 0.002147 [0.0002414, 0.00442] was the estimated serial path product for waist-to-hip ratio → LDL → diastolic blood pressure → PWV.The path was evaluated using standardized measurements and adjustment for age, sex, study membership, and smoking; P values were not corrected for multiple comparisons.Source: §2 · p. 65
• 0.05173 [0.0187, 0.08475] was the adjusted standardized waist-to-hip ratio–LDL cholesterol slope (P = 0.002143).The analysis paired measurements within 365 days, with one pair per participant, and adjusted for approximate age, sex, study membership, and smoking status.Source: §2 · p. 66

6. Pairwise association: waist-to-hip ratio–seated diastolic blood pressure (±90 days)

• The waist-to-hip ratio–diastolic blood pressure and LDL cholesterol–PWV pairwise analyses used same-period measurements within 90 and 365 days, respectively.Each used one pair per participant and standardized measures, adjusting for approximate age, sex, study membership, and smoking status; the LDL–PWV sample included 5,690 participants.Source: §6 · pp. 66–67, §7 · p. 67

8. Pairwise association: seated diastolic blood pressure–PWV (±90 days)

• 0.4441 [0.4253, 0.4629] was the adjusted standardized seated diastolic blood pressure–PWV slope (P = 0).The paired-measurement analysis used readings within 90 days and adjusted for approximate age, sex, study membership, and smoking status.Source: §8 · p. 67

9. Pairwise total association: waist-to-hip ratio–PWV (±365 days)

• Additional standardized pairwise analyses specified waist-to-hip ratio–PWV within 365 days and LDL cholesterol–seated diastolic blood pressure within 90 days.Both designs paired one measurement per participant and adjusted for age, sex, study membership, and smoking status; the waist-to-hip ratio–PWV sample included 9,385 participants.Source: §9 · pp. 67–68, §10 · p. 68

12. Pairwise association: waist-to-hip ratio–seated diastolic blood pressure (±365 days)

• Separate original-scale analyses anchored measurements on each waist-to-hip ratio, blood pressure, or PWV measurement day and allowed multiple rows per participant.They paired waist-to-hip ratio with blood pressure within 365 days, and LDL cholesterol with PWV within 365 days; blood pressure and PWV were summarized as seated-reading and bilateral means, respectively.Source: §12 · pp. 68–69, §13 · p. 69

14. Pairwise association: seated diastolic blood pressure–PWV (±365 days)

• In the joint serial-path model, seated diastolic blood pressure’s adjusted association with PWV was 0.01895 [0.0005562, 0.03735], P = 0.04362.The joint model included waist-to-hip ratio, LDL cholesterol, seated diastolic blood pressure, and PWV, with the three equations sharing a sample and adjustment for age, sex, and recruitment study.Source: §14 · pp. 69–70

17. Reverse temporal order: PWV and seated diastolic blood pressure 1–365 days later

• The reverse-temporal analyses tested PWV before later diastolic blood pressure and a PWV→LDL→waist-to-hip ratio measurement chain.The blood pressure measurement followed PWV by 1–365 days; in the three-measure chain, LDL followed PWV by 30–1,095 days and waist-to-hip ratio followed LDL by 30–730 days.Source: §14 · pp. 70–71, §17 · p. 71
• The reverse-temporal analysis defined βM2 as the difference in earlier PWV per original unit higher later diastolic blood pressure.Later blood pressure was measured 1–365 days after PWV.Source: §17 · p. 71

18. Sex heterogeneity: waist-to-hip ratio →LDL cholesterol →thigh-to-ankle PWV

• A sex-heterogeneity analysis modeled the waist-to-hip ratio→LDL→PWV path product at the 25th, 50th, and 75th waist-to-hip ratio percentiles.The design included sex interactions and used a bootstrap simultaneous confidence band across both sex categories and all three percentile points; no estimates are supplied.Source: §18 · p. 71

19. Sex heterogeneity: waist-to-hip ratio →LDL →diastolic blood pressure →PWV

• Sex-specific serial-path analyses estimated waist-to-hip ratio→LDL, LDL→diastolic blood pressure, and blood pressure→PWV slopes and their product.The path product used standardized measurements; its 95% interval came from joint normal simulation, and P values were not corrected for multiple comparisons.Source: §19 · pp. 72–73

20. Sex heterogeneity: sex-specific waist-to-hip ratio–PWV slopes (±365 days)

• The waist-to-hip ratio–PWV slope was estimated separately for each sex category, with shared adjustment for age and recruitment study.The model reported the PWV difference per 0.1 higher waist-to-hip ratio; the supplied result passages identify each sex-specific estimate but provide no values.Source: §20 · p. 73

21. Age interaction: change in the waist-to-hip ratio–PWV slope with age (±365 days)

• The analysis tested whether the waist-to-hip ratio–PWV slope changed with age using a waist-to-hip ratio × age interaction.Its target was the per-year change in the PWV difference per 0.1 higher waist-to-hip ratio; the supplied result passage gives no estimate value.Source: §21 · pp. 73–74

24. Narrow-window serial path: waist-to-hip ratio →LDL →diastolic blood pressure →PWV

• 0.08287 (95% interval 0.03146–0.1343; P = 0.001582) was reported for the narrow-window serial path index.The analysis narrowed the windows to LDL within 180 days of waist-to-hip ratio, diastolic blood pressure within 30 days of LDL, and PWV within 180 days of blood pressure.Source: §21 · p. 75

25. Additional adjustment for BMI and height: waist-to-hip ratio →LDL →diastolic blood pressure →PWV

• The serial-path model additionally adjusted for same-day BMI and height when estimating the waist-to-hip ratio→LDL→blood pressure→PWV pathway.The supplied passages define the adjusted path but provide no corresponding estimates.Source: §25 · p. 76

26. Narrow-window joint path: waist-to-hip ratio →LDL →diastolic blood pressure →PWV (±90 days)

• A joint-path analysis narrowed the measurement window to ±90 days around PWV and reported adjusted waist-to-hip ratio, LDL, and blood-pressure coefficients.The passages list the coefficient labels but do not connect the reported numeric value to a specific coefficient.Source: §26 · pp. 76–77

27. Broad-window joint path: waist-to-hip ratio →LDL →diastolic blood pressure →PWV (±730 days)

• The joint-path analysis widened the matching window to ±730 days around each PWV measurement, using the closest waist-to-hip ratio, LDL, and diastolic blood pressure measurements within that window.The three equations shared one sample; confidence intervals were 95%, and P values were not corrected for multiple comparisons.Source: §27 · p. 77

28. Joint path with additional adjustment for BMI and HbA1c (±365 days)

• The ±365-day joint path additionally adjusted for same-day BMI and HbA1c, alongside approximate age, sex, and recruitment study category.Waist-to-hip ratio, LDL, and diastolic blood pressure were matched to each PWV day; confidence intervals were 95%, and P values were not corrected for multiple comparisons.Source: §28 · p. 78

E.4 Hip circumference–GGT–SBP–PWV

• The single-mediator path indices were 0.006271 [−0.00697, 0.02438] for GGT and −1.829 [−15.9, 1.813] for seated systolic blood pressure.Both intervals span zero; the pathways were tested separately using date-ordered measurements and adjustment for approximate age, sex, and recruitment cohort.Source: §E.4 · pp. 79–80

3. Serial pathway and bias bounds: hip circumference →GGT →seated systolic blood pressure →PWV

• 0.1966 [0.007984, 0.3852] was the serial path index for hip circumference → GGT → seated systolic blood pressure → PWV.The serial analysis included 64 participants; its bias-bound grid varied the omitted covariate’s partial R2 with both regressor and outcome from 0.01 to 0.20.Source: §3 · pp. 80–81

4. Exposure–outcome association: hip circumference and thigh-to-ankle PWV

• 0.02428 [0.02041, 0.02816] was the hip circumference–PWV association estimate.The analysis paired measurements within 90 days and included 9,385 participants, adjusting for age, sex, and recruitment cohort.Source: §4 · p. 81, §3 · p. 81

5. Serial segment: hip circumference →GGT →seated systolic blood pressure

• A serial segment analysis tested hip circumference → GGT → seated systolic blood pressure in 222 participants using date-ordered measurements.The analysis reported a segment path-product index and omitted-confounder robustness values, but the supplied passages do not map the displayed estimates to those labels.Source: §5 · pp. 81–82

6. Pairwise association: hip circumference →GGT (0–365 days)

• A pairwise analysis tested hip circumference → GGT using measurements up to 365 days apart, with standardized variables and adjustment for age and sex.One row was used per GGT test, and participants could contribute multiple rows; the supplied passages give no estimate value.Source: §6 · p. 82

7. Pairwise association: GGT–seated systolic blood pressure (±30 days)

• A pairwise analysis tested GGT–seated systolic blood pressure associations using measurements within 30 days in either order, standardizing variables and adjusting for age and sex.Participants could contribute multiple GGT-test rows; the supplied passages give no estimate value.Source: §7 · pp. 82–83

8. Pairwise association: seated systolic blood pressure →PWV (0–365 days)

• A pairwise analysis tested seated systolic blood pressure → PWV using measurements up to 365 days apart, standardizing variables and adjusting for age and sex.Participants could contribute multiple blood-pressure-day rows; the supplied passages give no estimate value.Source: §8 · p. 83

9. Pairwise association: hip circumference–GGT (±90 days); 10. Pairwise association: seated systolic blood pressure–PWV (±90 days)

• Two same-period pairwise analyses examined hip circumference–GGT and seated systolic blood pressure–PWV, pairing each participant’s closest measurements within 90 days.Both analyses retained original numerical scales and adjusted for age, sex, and recruitment cohort; the supplied passages give no estimate values.Source: §9 · p. 83, §10 · p. 83

10. Pairwise association: seated systolic blood pressure–PWV (±90 days)

• The pairwise seated systolic blood pressure–PWV adjusted slope was 0.05098 [0.04878, 0.05318]; hip circumference–blood pressure and GGT–PWV pairs used ±90-day windows.The hip circumference–blood pressure analysis included 10,380 participants, and the GGT–PWV analysis included 1,340; both adjusted for age, sex, and recruitment cohort.Source: §10 · p. 84, §11 · p. 84, §12 · p. 84

Joint models

• Reported slopes were b2 = 0.04917 [0.04291, 0.05543] and 0.05006 [0.0427, 0.05742], and total slope c = 0.03168 [0.02133, 0.04202].Both b2 values describe the seated systolic blood pressure–PWV slope adjusted for hip circumference and GGT; c is the hip circumference–PWV total slope adjusted for covariates only.Source: Joint models · pp. 85–86

15. Reverse measurement order: earlier PWV and subsequently measured hip circumference

• A reverse-order analysis tested whether hip circumference measured 31–365 days after PWV was associated with the earlier PWV, using the shortest-gap pair per participant.The design included 18 participants and adjusted for age, sex, and recruitment cohort; the supplied result passage identifies the reverse-measurement-order result but provides no coefficient.Source: §15 · p. 86

17. Age heterogeneity: hip circumference →GGT →PWV path product

• At median age, the age-conditional serial path index for hip circumference → GGT → systolic blood pressure → PWV was −0.002768 [−0.01772, 0.01218].The serial path analysis used age-conditional path indices at the 25th, 50th, and 75th age percentiles; the supplied passages do not provide the other estimates.Source: §17 · pp. 87–88

19. Sex modification: hip circumference–PWV slope within each sex category

• Hip circumference–PWV slopes were 0.0205 [0.01571, 0.02529] in the first sex category and 0.0306 [0.02402, 0.03719] in the second.The model estimated sex-specific slopes while adjusting for age and recruitment cohort.Source: §19 · p. 88

20. Narrow-window single-mediator pathway: hip circumference →GGT →PWV

• A narrow-window single-mediator analysis evaluated the hip circumference → GGT → PWV path product using GGT 90–365 days after hip circumference and PWV 180–730 days after GGT.The analysis used standardized variables and defined the path product as the hip circumference–GGT slope multiplied by the mutually adjusted GGT–PWV slope; no coefficient is supplied.Source: §20 · pp. 88–89
• The narrow-window single-mediator analysis examined hip circumference → GGT → PWV, including omitted-confounder robustness and additional smoking and alcohol adjustment.The additionally adjusted design used strictly ordered measurements and one chain per participant (n = 167); estimates are not identifiable from the supplied result fragments.Source: §20 · pp. 89–90

22. Wide-window serial pathway: hip circumference →GGT →seated systolic blood pressure →PWV

• The wide-window model assessed the serial hip circumference → GGT → systolic blood pressure → PWV path index and six standardized path coefficients.The measurement chain allowed multiple chains per participant, with age and sex adjustment; the supplied passages do not provide the estimates.Source: §22 · p. 90

24. Joint path model with same-day height adjustment (±90 days)

• The joint path model used a ±90-day window for adjacent measurements and adjusted for same-day height alongside age, sex, and recruitment cohort.It jointly modeled hip circumference, GGT, seated systolic blood pressure, and PWV on their original scales.Source: §24 · p. 91

25. Hip-measurement-day panel: hip circumference–PWV association

• The hip-measurement-day panel paired hip circumference with nearby PWV measurements and included 10,917 rows.Each hip-measurement day was paired once with the closest PWV measurement within 90 days, with adjustment for age, sex, and recruitment cohort.Source: §24 · p. 92, §25 · p. 92

E.5 Gynoid fat–LDL–SBP–PWV

• The gynoid-fat subsection frames LDL-C and systolic blood pressure as candidate mediators of the association with lower-limb arterial stiffness.It defines thigh-to-ankle PWV as the outcome and uses HPP cohort data; the supplied passage does not provide a complete result estimate.Source: §E.5 · pp. 92–93

1. Single-mediator path: gynoid fat mass →LDL-C →thigh-to-ankle PWV

• −5.313 × 10−7 was reported for the gynoid fat mass → LDL-C → PWV path-product association index.The supplied confidence interval is truncated, so it cannot be summarized completely.Source: §1 · p. 93

2. Serial path: gynoid fat mass →LDL cholesterol →systolic blood pressure →PWV

• The serial gynoid-fat model assessed pathways through LDL cholesterol and systolic blood pressure to PWV, alongside LDL-only and blood-pressure-only path products.The supplied passages describe the model and measures but do not include its result estimates.Source: §2 · pp. 93–94
• A serial gynoid-fat-mass → LDL-C → SBP → PWV analysis specified conditional path components and a path product, with age and sex adjustment and gynoid fat mass and PWV paired within 365 days.The supplied results list estimates but do not identify their parameter labels.Source: §2 · p. 94

3. Exposure–outcome association: gynoid fat mass and thigh-to-ankle PWV

• The exposure–outcome analysis modeled gynoid fat mass against thigh-to-ankle PWV with age and sex adjustment; the supplied passages do not report its estimate.The related ±365-day pairwise analysis likewise specifies a total-association slope but provides no result value here.Source: §3 · pp. 94–95, §9 · p. 96

5. Downstream serial fragment: LDL-C →seated systolic blood pressure →thigh-to-ankle PWV

• A downstream LDL-C → SBP → PWV serial fragment defined θ as the product of the LDL-C-to-SBP and mutually adjusted SBP-to-PWV slopes; no parameter label accompanies the supplied result value.The design ordered measurements in time and adjusted for age and sex.Source: §5 · p. 95

6. Pairwise association: gynoid fat mass →LDL cholesterol (±180 days)

• At fixed age and sex, each 1-original-unit higher gynoid fat mass corresponded to LDL cholesterol β=0.001683 [0.000745, 0.002622] (P=0.0004384); adjusted LDL cholesterol→seated systolic blood pressure slope was 0.01847 [0.005048, 0.0319] (P=0.006998).The adjusted seated systolic blood pressure→thigh-to-ankle PWV slope was 0.05133 [0.04929, 0.05337] (P=0).Source: §6 · pp. 95–96, §7 · p. 96, §8 · p. 96

10. Pairwise association: gynoid fat mass–LDL-C (±365 days)

• The ±365-day gynoid-fat–LDL-C and LDL-C–SBP analyses specify age- and sex-adjusted pairwise models, but their result estimates are not included in the supplied passages.The latter uses the mean of available seated SBP readings.Source: §10 · p. 97, §11 · p. 97

12. Pairwise association: gynoid fat mass–seated systolic blood pressure (±365 days)

• The ±365-day joint analysis modeled PWV against gynoid fat mass, LDL-C, and SBP together, and compared it with a reduced model containing gynoid fat mass alone plus age and sex.The same-sample comparison was repeated using a four-measurement date span of at most 180 days.Source: §12 · p. 98
• In the ±365-day joint model, βSBP was 0.05195 [0.04844, 0.05545] and αA was 0.000187 [0.0001481, 0.0002259]; in the ±180-day model, they were 0.05253 [0.04835, 0.05671] and 0.0001817 [0.000136, 0.0002274].βSBP is the seated SBP coefficient in the joint model; αA is the gynoid fat mass coefficient in the reduced model, adjusted for age and sex.Source: §12 · p. 98

15. Reverse path: PWV →LDL-C →gynoid fat mass

• A reverse PWV → LDL-C → gynoid-fat-mass path was specified in strict measurement-date order, but the supplied passages report no estimates.The reverse-path sample included 419 participants and adjusted for age and sex.Source: §15 · p. 99

15. Reverse path: PWV →LDL-C →gynoid fat mass; 16. Reverse path: PWV →seated systolic blood pressure →gynoid fat mass

• Reverse-path analyses tested PWV → LDL-C → gynoid fat mass and PWV → seated systolic blood pressure → gynoid fat mass, but supplied passages give no estimates.The SBP chain used strict date order and adjusted for age and sex.Source: §15 · p. 99, §16 · p. 99

17. Reverse pairing: earlier PWV and gynoid fat mass measured 1–365 days later; 18. Reverse pairing: earlier PWV and gynoid fat mass measured 366–730 days later

• Reverse pairings also related earlier PWV to gynoid fat mass measured 1–365 days later and 366–730 days later; no estimates are supplied.The first window used one row per PWV measurement date (n = 46); the second paired the earliest eligible gynoid measurement with the nearest PWV.Source: §16 · p. 100, §17 · p. 100, §18 · p. 100

19. Conditional path to PWV under the gynoid fat mass × LDL-C interaction

• For 138 participants with date-ordered gynoid fat mass, LDL-C, and PWV measurements, the linear-regression model’s reported quantities included an interaction coefficient βAM, but no estimate is supplied here.Source: §19 · p. 100

20. Sex heterogeneity: gynoid fat mass →LDL-C →PWV

• In the first sex category, the adjusted total slope was 8.431 × 10−5 [−5.177 × 10−5, 0.0002455], and the path-product index was 7.71 × 10−5 [−5.978 × 10−5, 0.0002394].These are the reported γA,1 and θ1 estimates for the gynoid fat mass → LDL-C → PWV analysis.Source: §20 · p. 101
• The serial gynoid fat mass → LDL cholesterol → systolic blood pressure → PWV product was evaluated at ages 40, 50, and 60, with age-related slope changes modeled per 10 years.The analysis adjusted for sex and centered age at 50 years; reported P values were not corrected for multiple comparisons.Source: §20 · p. 102
• The LDL-C → PWV slope adjusted for gynoid fat mass and systolic blood pressure was 0.001675 [0.0004082, 0.002942] (P = 0.009555).This is the reported e coefficient in the age-modified serial-path analysis.Source: §20 · p. 102

23. Gynoid fat mass × age interaction: PWV slope in the joint model; 24. Shorter-window single-mediator path: gynoid fat mass →LDL-C →PWV

• A joint model specified the gynoid fat mass × age interaction on PWV slope per year, while a separate single-mediator analysis tested gynoid fat mass → LDL-C → PWV using shorter nested windows.The joint model additionally adjusted for LDL-C, systolic blood pressure, and sex; the shorter-window analysis required LDL-C 90–365 days and PWV 180–730 days later.Source: §23 · p. 103, §24 · pp. 103–104

24. Shorter-window single-mediator path: gynoid fat mass →LDL-C →PWV

• 8.365 × 10−6 [−3.865 × 10−5, 5.58 × 10−5] was the reported θ path-product association index.The broad-window serial pathway runs from gynoid fat mass through LDL cholesterol and seated systolic blood pressure to PWV.Source: §24 · p. 104

27. Extended adjustment: gynoid fat mass →LDL →systolic blood pressure →PWV

• The extended-adjustment design additionally controlled for education, smoking status, and alcohol consumption frequency in the gynoid-fat-to-PWV pathway analysis.It matched LDL, systolic blood pressure, and PWV measurements within specified windows around each gynoid-fat measurement and used linear regressions; the supplied result value is not linked to a named parameter.Source: §27 · p. 106

28. Same-region bone mass comparator: gynoid bone mass →LDL →systolic blood pressure →PWV

• For the gynoid bone-mass comparator, c′ was 0.002679 [0.001008, 0.004349] (P=0.001672), and f was 0.002212 [0.0002764, 0.004148] (P=0.0251).Here c′ is the gynoid bone mass–PWV slope adjusted for LDL and systolic blood pressure, while f is the systolic blood pressure–PWV slope adjusted for gynoid bone mass and LDL.Source: §28 · pp. 107–108

29. Joint model with extended adjustment: additional adjustment for total fat mass, cohort and height

• The joint-model analysis additionally adjusted for total fat mass, recruitment cohort, and height; the reduced model estimated the gynoid-fat slope with those covariates.The models shared a sample and matched measurements within a 365-day span; the supplied result value is not linked to a named parameter.Source: §29 · p. 108

30. Repeated PWV measurements: joint model (±365 days)

• The repeated-measurement design treated each participant–PWV measurement date as a row and matched gynoid fat mass, LDL-C, and systolic blood pressure within a 365-day span.It selected the set with the shortest date span and compared joint and reduced models; no result value for this analysis is supplied.Source: §30 · p. 108

E.6 Gynoid fat–GGT–DBP–PWV

• The single-mediator path-product association index for gynoid fat mass → GGT → PWV was 0.02975 [−0.04817, 0.1077].The analysis used standardized variables and a temporally ordered measurement chain.Source: §E.6 · p. 109

2. Serial path: gynoid fat mass →GGT →seated diastolic blood pressure →PWV

• The serial model included paths through GGT and diastolic blood pressure; the path product through GGT only was 0.04162 [−0.03614, 0.1194].The reported serial path product through both mediators and the sum of path products are identified, but their estimates are not readable in the supplied passages.Source: §2 · p. 110

5. Pairwise association: gynoid fat mass →GGT (0–365 days)

• Pairwise analyses assessed gynoid fat mass → GGT, GGT → seated diastolic blood pressure, and seated diastolic blood pressure → PWV in forward windows, with estimates not readable here.The windows were 0–365 days for gynoid fat–GGT and blood pressure–PWV, and ±90 days for GGT–blood pressure.Source: §5 · p. 111, §6 · p. 111, §7 · p. 112

3. Exposure–outcome association: gynoid fat mass and thigh-to-ankle PWV

• The section also reports labels for the adjusted total gynoid fat–PWV association and the gynoid fat–diastolic blood pressure serial segment, without readable estimates.The exposure–outcome analysis used a 0–730-day forward window; the serial segment assessed gynoid fat mass → GGT → seated diastolic blood pressure.Source: §4 · p. 111, §8 · p. 112

8. Pairwise total association: gynoid fat mass →PWV (0–730 days)

• A separate pairwise analysis reports the total gynoid fat mass → PWV association over a 0–730-day forward window, without a readable estimate.Another pairwise analysis labels the gynoid fat mass–GGT association for a ±180-day window, also without a readable estimate.Source: §8 · p. 112, §9 · p. 112

10. Pairwise association: GGT–seated diastolic blood pressure (±180 days)

• The ±180-day pairwise analyses include GGT–diastolic blood pressure and gynoid fat mass–diastolic blood pressure associations, whose estimates are not readable.The gynoid fat mass–blood pressure analysis included 8,927 observations.Source: §10 · p. 113, §12 · p. 113
• The adjusted association coefficient (β1) for seated diastolic blood pressure–PWV was 0.07883 [0.07577, 0.08188]; the supplied entry also lists a separate 0.Source: §10 · p. 113

14. Joint model: gynoid fat mass, GGT, diastolic blood pressure, PWV (±180 days)

• The section additionally labels a GGT–PWV pairwise association and a mutually adjusted model’s diastolic blood pressure coefficient, but their estimates are not readable.The joint model included gynoid fat mass, GGT, and seated diastolic blood pressure as predictors of PWV.Source: §13 · p. 114, §14 · p. 114

15. Gynoid fat mass coefficient: before and after adding GGT and diastolic blood pressure (±180 days)

• The ±180-day analysis compared gynoid fat mass coefficients for PWV before and after mutual adjustment for GGT and seated diastolic blood pressure.The supplied passages describe the two models but provide no coefficient estimates.Source: §15 · pp. 114–115

17. Reverse serial path: PWV →diastolic blood pressure →GGT →gynoid fat mass

• A reverse serial model evaluated PWV → diastolic blood pressure → GGT → gynoid fat mass, but the supplied passages do not provide its path-product estimate.The design used one measurement chain per participant and standardized the path variables.Source: §17 · pp. 115–116

18. Reverse pairing: earlier PWV and subsequently measured gynoid fat mass

• 76.66 [36.56, 116.8] was the adjusted association coefficient for earlier PWV and gynoid fat mass measured 366–1095 days later.The reported P value was 0.0001792; the analysis adjusted for age, sex, and sub-study.Source: §18 · p. 116

20. Slopes by sex: gynoid fat mass–thigh-to-ankle PWV

• The gynoid fat mass–PWV slopes were 0.0001622 [0.0001283, 0.0001962] in the first sex category and 0.0002295 [0.0001858, 0.0002733] in the second.The reported sex-category sample sizes were 4,304 and 4,145, respectively.Source: §20 · p. 118

21. Narrower windows: gynoid fat mass →GGT →thigh-to-ankle PWV

• 0.03807 [−0.0521, 0.1282] was the path-product association index for gynoid fat mass → GGT → PWV under narrower measurement windows.The interval includes zero; the section also reports a GGT-only path product of −0.009157 [−0.05363, 0.03531].Source: §21 · pp. 118–119
• The narrower-window gynoid-fat analysis decomposed the association with PWV into GGT- and diastolic-blood-pressure-mediated path products and a conditional direct slope.Source: §21 · p. 119

23. Additional adjustment for BMI, smoking and alcohol consumption: gynoid fat mass serial path

• With additional BMI, smoking, and alcohol adjustment, the GGT-only path product was −0.2854 [−0.5342, −0.03669], versus −0.04195 [−0.1902, 0.1063] in the minimal model.Both models used the same sample; the design included 22 complete chains.Source: §23 · pp. 119–120

24. Joint model: gynoid fat mass, GGT, diastolic blood pressure, PWV (±90 days)

• The ±90-day joint model related gynoid fat mass, GGT, and seated diastolic blood pressure to thigh-to-ankle PWV using 905 measurement sets.Measurements were selected so all four measures were pairwise no more than 90 days apart.Source: §24 · p. 121

E.7 Waist circumference–TG–DBP–PWV

• The waist-circumference analyses examined PWV associations through triglycerides and seated diastolic blood pressure, including single-mediator paths and bias bounds.The stated research question used HPP data and treated waist circumference as the exposure, the two biomarkers as mediators, and PWV as the outcome.Source: §E.7 · p. 122, §2 · p. 123

1. Single-mediator path: waist circumference →triglycerides →thigh-to-ankle PWV

• The waist-circumference–triglyceride path-product index was 0.003205 [−0.003298, 0.01037].The analysis used one measurement chain per participant and adjusted for approximate age and sex.Source: §1 · pp. 122–123

2. Single-mediator path and bias bounds: waist circumference →seated diastolic blood pressure →PWV

• The serial waist-circumference–triglyceride–diastolic-blood-pressure–PWV design allowed adjacent measures in either order within 365 days and included 6,266 chains.Participants could contribute multiple chains; models adjusted for approximate age and recorded sex.Source: §2 · p. 124
• For the serial triglycerides→seated diastolic blood pressure→thigh-to-ankle PWV segment, the estimated path product was 0.002001 [0.001399, 0.002696], with age-and-sex adjustment.Blood pressure was measured 30–365 days after triglycerides, and PWV 90–1095 days after blood pressure; all three equations were linear regressions.Source: §2 · pp. 125–126

7. Pairwise association: waist circumference–triglycerides (±90 days)

• Waist circumference and triglycerides were paired within ±90 days for an adjusted association analysis involving 4,048 participants.The analysis adjusted for age, sex, and height; the supplied passages do not report its association estimate.Source: §7 · p. 126

8. Pairwise association: waist circumference–seated diastolic blood pressure (±90 days)

• Waist circumference and seated diastolic blood pressure were paired within ±90 days for an adjusted association analysis involving 12,899 participants.The supplied passages describe the design and adjustment for age, sex, and height but do not provide an association estimate.Source: §8 · p. 126

9. Pairwise association: triglycerides–seated diastolic blood pressure (±30 days)

• Triglycerides and seated diastolic blood pressure were paired within ±30 days for an adjusted association analysis involving 1,916 participants.The supplied passages specify adjustment for age, sex, and height but do not provide an association estimate.Source: §9 · p. 127

10. Pairwise association: triglycerides–PWV (±90 days)

• Triglycerides and PWV were paired within ±90 days for an adjusted association analysis involving 3,296 participants.The supplied passages specify adjustment for age, sex, and height but do not provide an association estimate.Source: §10 · p. 127

11. Pairwise association: seated diastolic blood pressure–PWV (±30 days)

• 0.07859 [0.07555, 0.08163] was the adjusted seated diastolic blood pressure–PWV association coefficient.The pairwise analysis used measurements within 30 days and adjusted for age, sex, and height.Source: §11 · pp. 127–128
• The reverse PWV→triglycerides→waist circumference analysis reported a triglycerides-to-waist slope of 0.06983 [0.04548, 0.09814].A separate joint model included waist circumference, triglycerides, diastolic pressure, and PWV measured within ±90 days; the supplied passages give its design but not its estimates.Source: §11 · pp. 128–129

14. Reverse path: PWV →seated diastolic blood pressure →waist circumference

• The reverse-path design tested PWV → seated diastolic blood pressure → waist circumference using one date-ordered measurement chain per participant, adjusted for age and sex.The supplied passages describe the design and bootstrap intervals but do not provide estimates.Source: §14 · p. 129

15. Reversed measurement order: serial path with triglycerides preceding waist circumference

• The reversed-order serial analysis began with triglycerides and linked later waist circumference, with diastolic blood pressure and PWV measured near that triglyceride date and subsequent steps.Participants could contribute multiple chains; estimates are not included in the supplied passages.Source: §15 · pp. 129–130

Heterogeneity and interaction

• The sex-heterogeneity analysis modeled category-specific slopes for waist circumference → triglycerides → diastolic blood pressure → PWV and their serial path products.It used pooled-sample linear regressions with sex interactions and adjusted for approximate age; confidence intervals were bootstrap 95% percentile intervals, and P values were not corrected for multiple comparisons.Source: Heterogeneity and interaction · pp. 130–131

17. Sex heterogeneity: sex-specific waist circumference–PWV slopes (±90 days)

• The sex-specific waist circumference–PWV model used measurements within ±90 days and estimated slopes by sex while holding triglycerides, diastolic blood pressure, age, and height fixed.The supplied passages describe the model and 95% confidence intervals but provide no estimates.Source: §17 · p. 131

18. Longer minimum intervals: waist circumference →triglycerides →PWV

• 0.003839 [−0.002721, 0.01121] was the path-product association index under longer minimum intervals; the interval spans zero.With genetic principal-component adjustment, the index was 0.003784 [−0.003173, 0.0112], also spanning zero.Source: §18 · p. 132
• Under a ±180-day measurement window, the serial chain included waist circumference, triglycerides, diastolic blood pressure, and PWV in 4,846 participant-contributed chains.The reported path-component estimates were 0.02075 [0.01606, 0.02611], 0.07505 [0.07006, 0.08002], and 0.003162 [0.002424, 0.004015], in chain order.Source: §18 · pp. 132–133

21. Triglycerides after waist circumference: waist circumference →triglycerides →diastolic blood pressure →PWV

• The triglycerides-after-waist-circumference design linked waist circumference → triglycerides → diastolic blood pressure → PWV in 567 participant-contributed chains.It used original recorded values and adjusted for approximate age and sex; no results are included in the supplied passages.Source: §21 · p. 133
• 0.02938, 0.07855, and 0.004529 were reported for the waist circumference → triglycerides → diastolic blood pressure → PWV analysis.The supplied passages do not identify which estimate corresponds to each path component.Source: §21 · pp. 133–134

22. Added smoking adjustment: waist circumference →triglycerides →diastolic blood pressure →PWV

• 0.0199, 0.07424, and 0.002798 were the three reported estimates for the waist circumference → triglycerides → diastolic blood pressure → PWV analysis with smoking adjustment.The design included 4,881 participants and adjusted for approximate age, sex, and current smoking; the supplied passages do not identify which estimate corresponds to each path component.Source: §22 · p. 134

25. PWV-anchored pairing: waist circumference–PWV (±180 days)

• The waist circumference–PWV exposure–outcome analysis paired measurements within ±180 days and adjusted for age, sex, and height.Each PWV measurement date anchored a row; the supplied passages include the design but no association estimate.Source: §25 · p. 136

E.8 Hip circumference–TG–DBP–PWV

• The hip-circumference analysis framed a serial pathway through triglycerides and seated diastolic pressure to lower-limb arterial stiffness, measured by thigh-to-ankle PWV.The cohort was the HPP; measurements were defined as SD changes per 1 SD unless otherwise stated.Source: §E.8 · p. 136

1. Single-mediator path: hip circumference →triglycerides →thigh-to-ankle PWV

• 0.1111 [0.04553, 0.1779] was the decomposed total association for hip circumference → triglycerides → PWV; direct and indirect associations were 0.08811 and 0.02295, respectively.The analysis standardized hip circumference, triglycerides, and PWV within the analysis sample and used weighted regressions.Source: §1 · p. 137
• 0.4458 [0.06639, 0.8252] was the serial path product association index for hip circumference → triglycerides → seated diastolic pressure → PWV.The analysis used standardized measures and adjusted for age, sex, and study membership.Source: §1 · p. 138

5. Serial segment: hip circumference →triglycerides →seated diastolic pressure

• The hip circumference → triglycerides → seated diastolic pressure serial segment used measurements in strict date order and weighted eligible chains to give each participant equal weight.The supplied passages describe its design and bootstrap intervals but provide no result estimate.Source: §5 · p. 139
• 0.2232 [0.15, 0.2987] was the total association in the hip circumference → triglycerides → diastolic pressure serial segment; the direct association was 0.03541 [0.01888, 0.05435].The direct association compares diastolic pressure across a 1 SD hip-circumference difference with triglycerides fixed; the total is decomposed into direct and indirect components.Source: §5 · p. 139

6. Serial segment: triglycerides →seated diastolic pressure →PWV

• 0.1189 [0.07573, 0.1607] was the total association in the triglycerides → diastolic pressure → PWV serial segment; its direct association was 0.07377 [0.05691, 0.09393].The analysis used strictly ordered measurements, weighted eligible chains to give participants equal weight, and adjusted for age and sex.Source: §6 · pp. 139–140

7. Pairwise association: hip circumference →triglycerides (1–365 days)

• Forward-window analyses paired each hip-circumference measurement with the earliest triglyceride measurement 1–365 days later, and each triglyceride measurement with the earliest seated blood-pressure measurement 1–365 days later (n = 8784).Both windows had inclusive bounds, and participants could contribute several pairs.Source: §7 · p. 140, §8 · p. 140

10. Pairwise association: hip circumference–triglycerides (±180 days)

• Concurrent-window analyses specified hip circumference–triglycerides, hip circumference–diastolic pressure, triglycerides–PWV, and diastolic pressure–PWV associations, without estimates in the supplied passages.Measurements were paired within ±180 days; the diastolic pressure–PWV analysis included n = 9401, and the hip circumference–diastolic pressure analysis included n = 12922.Source: §10 · p. 141, §11 · p. 141, §12 · p. 141

Joint models

• 0.07881 [0.07575, 0.08186] (P = 0) was reported immediately before the joint hip circumference → triglycerides → diastolic pressure → PWV model description.The joint model used a shared sample of n = 4846 with measurements within ±180 days, unrestricted in order, and adjusted for age and sex.Source: Joint models · p. 142

Reverse direction

• The reverse-direction analysis reported 0.000879 [0.0002241, 0.001534] (P = 0.008532), but the supplied passage does not identify the corresponding parameter.Source: Reverse direction · p. 143

15. Reverse path: PWV →triglycerides →hip circumference

• 0.08035 [−0.02412, 0.1819] was the total association for the reverse PWV → triglycerides → hip circumference path; its direct association was 0.04734 [0.02027, 0.0877].This decomposition used strictly ordered measurements, weighted eligible chains equally by participant, and adjusted for age and sex.Source: §15 · p. 143

16. Reverse path: PWV →seated diastolic pressure →hip circumference

• A reverse PWV → seated diastolic pressure → hip circumference path was also specified, but its result is not included in the supplied passages.The design required strict measurement order and used bootstrap 95% percentile intervals.Source: §16 · p. 144
• 0.7495 [−1.367, 4.536] is the decomposed total association for the reverse path from PWV through seated diastolic pressure to hip circumference.The total association is defined as the direct plus indirect path associations.Source: §16 · p. 144

17. Reverse pairing: earlier PWV and subsequently measured hip circumference

• 0.3772 [−0.1471, 0.9015] (P = 0.1581) estimates the association of earlier PWV with hip circumference measured 365–730 days later.The interval includes zero in this reverse temporal pairing, adjusted for age and sex.Source: §17 · p. 144

19. Age modification: hip circumference →seated diastolic pressure slope

• The age-modification analysis estimates hip circumference’s conditional standardized slope for seated diastolic pressure at −1, 0, and +1 SD of age.Measurements were ordered from hip circumference to seated blood pressure to PWV, with age and sex adjustment; no slope estimates are supplied in these passages.Source: §19 · p. 146

20. Sex heterogeneity: hip circumference →triglycerides →diastolic pressure →PWV

• 0.5914 [0.05517, 1.128] (P = 0.03167) is the serial path product association index reported for the second sex category.The tested path runs from hip circumference through triglycerides and seated diastolic pressure to PWV.Source: §20 · p. 147

21. Sex heterogeneity: hip circumference–PWV slope adjusted for both mediators

• The sex-heterogeneity analysis evaluates hip circumference–PWV slopes adjusted for triglycerides, seated diastolic pressure, and age, separately by recorded sex category.The supplied passages describe the model and first-category slope but do not provide numerical slope estimates.Source: §21 · p. 147

22. Narrower time window: hip circumference →triglycerides →thigh-to-ankle PWV

• 0.03096 [0.0005886, 0.07036] is the direct association, while the decomposed total association is 0.09623 [−0.00465, 0.2046] in the narrower-window analysis.The analysis follows hip circumference → triglycerides → PWV with triglycerides measured 90–365 days later and PWV 180–730 days after triglycerides.Source: §22 · p. 148

23. Concurrent-window serial path: hip circumference →triglycerides →diastolic pressure → PWV

• 0.03246 [0.007954, 0.05697] (P = 0.009439) and 0.01757 [0.01384, 0.02164] are reported for the concurrent-window serial pathway analysis.The pathway links hip circumference to PWV through triglycerides and seated diastolic pressure; P values were not adjusted for multiple comparisons.Source: §23 · pp. 148–149

24. Extended-adjustment serial path: hip circumference →triglycerides →diastolic pressure →PWV

• The extended-adjustment serial path standardized hip circumference, triglycerides, diastolic pressure, and PWV, adjusting for smoking and genetic principal components, with bootstrap intervals.Measurements followed the specified sequence, with triglycerides 1–365 days after hip circumference, blood pressure within 180 days of triglycerides, and PWV 1–730 days after blood pressure.Source: §24 · p. 149

25. Narrow-window joint path (±90 days): hip circumference →triglycerides →diastolic pressure →PWV

• The narrow-window joint path used 3,219 rows with all four measurements within ±90 days, adjusted for age and sex, and reported confidence intervals with unadjusted P values.Continuous variables remained on their original scale.Source: §25 · pp. 149–150

26. Extended-adjustment joint path: smoking and medication added (±180 days)

• The ±180-day joint path used 1,425 participants and added smoking and antihypertensive and lipid-lowering medication indicators to age and sex adjustment.Its confidence intervals were 95%, and P values were not adjusted for multiple comparisons.Source: §26 · p. 150

1. Single-mediator path: visceral fat mass →serum uric acid →thigh-to-ankle PWV

• The reported path-product association indices were θ = 0.03831 [−0.04437, 0.1257] and θ = 0.01723 [0.0024, 0.03242], respectively.Source: §1 · p. 152

3. Mutually adjusted model: visceral fat and uric acid on PWV (±180 days)

• A mutually adjusted model estimated visceral-fat and uric-acid associations with PWV in 2,063 participants using measurements within 180 days and age- and sex-adjustment.The reported coefficients represent PWV SD differences per 1 SD higher exposure, with the other exposure held fixed.Source: §3 · p. 152

5. Pairwise association: serum uric acid and thigh-to-ankle PWV (within 365 days)

• The uric-acid–PWV pairwise analysis used measurements within 365 days and adjusted standardized slopes for age and sex.The paired analysis included 3,830 participants; visceral-fat–PWV measurements were also paired within 365 days in a separate analysis.Source: §5 · p. 153

6. Pairwise total association: visceral fat mass and PWV (within 365 days)

• The separate pairwise total-association model related standardized visceral fat to PWV, adjusting for age and sex.The supplied passage describes the model but gives no estimate.Source: §6 · pp. 153–154

7. Pairwise association: visceral adipose tissue mass–serum uric acid (±180 days)

• The visceral-fat–urate pairwise analysis selected measurements within ±180 days and estimated standardized associations adjusted for age and sex.The supplied passages describe the design and model but provide no estimate.Source: §7 · p. 154

8. Pairwise association: serum uric acid–thigh-to-ankle PWV (±180 days)

• 0.1289 [0.002218, 0.2482] for the standardized PWV → subsequent serum uric acid slope, and 0.04657 [0.0009421, 0.08922] for the adjusted total PWV → later visceral fat mass slope.The reverse sequence used one chain per person and adjusted for age, sex, study of origin, and serum creatinine.Source: §8 · pp. 154–155

10. Reversed measurement order: PWV before visceral fat and serum uric acid

• The reversed-order analysis specified PWV before visceral fat and serum uric acid, estimating path components and a path product for the sequence.It used linear regressions with visceral fat mass, serum uric acid, and PWV standardized; the supplied passages provide no estimates for this analysis.Source: §10 · p. 155

11. Conditional PWV slopes under the visceral fat mass × serum uric acid interaction

• The conditional-slope analysis modeled the serum uric acid–PWV slope at mean visceral fat mass and 1 SD above the mean.The outcome model included a visceral fat mass × serum uric acid interaction; no estimates are supplied here.Source: §11 · pp. 155–156

12. Sex heterogeneity: visceral fat mass →serum uric acid →PWV (strict date order)

• The strict-order analysis estimated visceral-fat-to-uric-acid and mutually adjusted uric-acid-to-PWV and visceral-fat-to-PWV slopes separately by recorded sex category.It also specified a path-product index for each category; no estimates are supplied here.Source: §12 · p. 156

13. Age heterogeneity: visceral fat mass →serum uric acid →PWV

• The age-heterogeneity analysis modeled age interactions with visceral fat and serum uric acid and defined conditional path components at mean age and 1 SD below and above it.The sequence required visceral fat measurement before uric acid and PWV; no estimates are supplied here.Source: §13 · p. 157

14. Sex heterogeneity: visceral fat mass →serum uric acid →PWV (same period)

• The same-period analysis estimated within-category visceral-fat-to-uric-acid, mutually adjusted PWV slopes, and path products by recorded sex category.Measurements were required to fall within 365 days of one another; no estimates are supplied here.Source: §14 · pp. 157–158

15. Exposure × mediator interaction: visceral fat mass →serum uric acid →PWV

• The exposure × mediator analysis evaluated conditional path products at visceral fat mass 1 SD below, at, and 1 SD above the analysis-sample mean.The PWV model included a visceral fat mass × serum uric acid product term.Source: §15 · p. 158

16. Age interaction: variation of the PWV slopes of visceral fat and uric acid with age

• The age-interaction analysis estimated how standardized visceral-fat–PWV and uric-acid–PWV slopes changed per 10 years of higher age.Measurements were required to fall within 180 days of one another; no estimates are supplied here.Source: §16 · p. 159

17. Visceral fat × uric acid interaction: non-additivity in the PWV model

• A visceral-fat-by-uric-acid interaction model tested non-additivity in the PWV association, defining the interaction coefficient as the change in standardized slope per 1 SD higher uric acid.The supplied passages describe the model but provide no interaction estimate.Source: §17 · p. 159

18. Narrow-window path: visceral fat mass →serum uric acid →PWV

• 0.04605 [−0.06337, 0.1736] was the path-product association index in the strict-order narrow-window analysis (n = 52).Visceral fat preceded uric acid, which preceded PWV; the sequence windows were 90–365 days and 180–730 days.Source: §18 · pp. 159–160

19. Extended covariate adjustment: visceral fat mass →serum uric acid →PWV

• 0.327 [0.04569, 0.5557] was the visceral-fat decomposition sum, while its path-product index was 0.03831 [−0.0471, 0.1239] under extended covariate adjustment.The model adjusted for age, sex, study of origin, creatinine, systolic blood pressure, smoking, and medication indicators.Source: §19 · pp. 160–161
• Visceral-fat and subcutaneous-fat path-product indices were 0.03831 [−0.0471, 0.1239] and 0.02912 [−0.01623, 0.09113], respectively.The corresponding decomposition sums were 0.327 [0.04569, 0.5557] for visceral fat and 0.04052 [−0.1264, 0.2259] for subcutaneous fat.Source: §19 · p. 161
• Within 180 days, the uric-acid slope on PWV adjusted for visceral fat was 0.06631 [0.01255, 0.1201], and the path-product index was 0.0209 [0.003782, 0.03803].This model adjusted for age and sex.Source: §19 · pp. 161–162

22. Visceral fat measured first: visceral fat mass →serum uric acid →PWV

• A visceral-fat-to-uric-acid-to-PWV path was also specified with visceral fat measured first and additional adjustment for creatinine and brachial blood pressure; no estimates are supplied here.The additional-adjustment model used age, sex, creatinine, and brachial blood pressure as covariates.Source: §22 · pp. 162–163

24. Mutually adjusted model: visceral fat and uric acid on PWV (±30 days)

• The mutually adjusted visceral-fat and uric-acid associations with PWV were modeled using measurements within 30 days, with adjustment for age and sex; estimates are not supplied.Source: §24 · p. 163

25. Mutually adjusted model: visceral fat and uric acid on PWV (±365 days)

• The same mutually adjusted PWV model was also specified for measurements within 365 days, adjusting for age and sex; estimates are not supplied.Source: §25 · p. 163

E.10 ALT–TG–DBP–PWV

• 0.2205 [0.03882, 0.7663] was the ALT→TG slope and 0.003957 [0.002663, 0.005308] the TG→PWV slope adjusted for ALT in the ALT–TG–PWV analysis.The path components were estimated for strictly time-ordered measurements.Source: §E.10 · p. 165
• 0.0008726 [0.0001607, 0.002892] was the path-product association index for ALT→TG→PWV; the decomposed total was −0.0004307 [−0.003079, 0.007891].The analysis concerned ALT, TG, and thigh-to-ankle PWV measured in strict date order.Source: §E.10 · p. 165

2. Single-mediator path: ALT →seated DBP →thigh-to-ankle PWV

• 0.1092 [0.0656, 0.1619] was the ALT→DBP slope and 0.05255 [0.04525, 0.06046] the DBP→PWV slope adjusted for ALT.The measurements followed strict date order, with DBP 7–365 days after ALT and PWV 30–1095 days after DBP.Source: §2 · pp. 165–166
• 0.005739 [0.003361, 0.008694] was the path-product association index for ALT→DBP→PWV, with a decomposed total of 0.01154 [0.005263, 0.01876].The design required ALT before seated blood pressure and blood pressure before PWV.Source: §2 · pp. 165–166

4. Adjacent segment: ALT →TG →seated DBP

• 0.002392 [−0.0004518, 0.01516] was the path-product association index for ALT→TG→DBP, and its interval spans zero.The decomposed total was 0.01833 [−0.002025, 0.08176].Source: §4 · p. 167

5. Adjacent segment: TG →seated DBP →thigh-to-ankle PWV

• 0.001942 [0.001466, 0.002483] was the path-product association index for TG→DBP→PWV, with a decomposed total of 0.003417 [0.002249, 0.004612].The chain used TG, seated DBP, and PWV measured in strict date order; n = 1663.Source: §5 · p. 167

6. Pairwise association: ALT →TG (same blood test); 7. Pairwise association: ALT–TG (same-day blood test)

• 0.5177 [0.2391, 0.9076] was the recorded-scale ALT–TG association, while 0.156 [0.05355, 0.2584] was the standardized association.Both analyses used same-day measurements and adjusted for age, sex, and BMI.Source: §6 · p. 167, §7 · p. 168

13. ALT coefficient before and after adding TG and DBP (±30 days)

• 0.09657 [0.006087, 0.1871] was the ALT coefficient for PWV in the full model adding TG and DBP (n = 108).The model adjusted for age, sex, and BMI; the interval was 95% and the P value was not adjusted for multiple comparisons.Source: §13 · pp. 169–170

15. Reverse path: thigh-to-ankle PWV →seated DBP →ALT

• 0.2099 [−0.6153, 1.018] was the path-product association index for the reverse PWV → seated DBP → ALT analysis.Measurements were ordered PWV, blood pressure, then ALT; the bootstrap 95% interval includes zero.Source: §15 · p. 170

18. Sex heterogeneity: ALT →TG →thigh-to-ankle PWV

• 0.004593 [0.002675, 0.006541] was the ALT → TG slope within the first sex category in the sex-heterogeneity analysis.The analysis also estimated sex-specific TG → PWV and ALT → PWV slopes and path products.Source: §18 · p. 172

19. Sex heterogeneity: ALT →seated DBP →thigh-to-ankle PWV

• −0.0004763 [−0.006175, 0.005117] and −0.005492 [−0.01874, 0.007006] were the sex differences in the ALT → DBP → PWV path product and decomposed total.Both bootstrap 95% intervals include zero.Source: §19 · p. 173

20. Exposure × mediator interaction: ALT, TG and PWV

• 0.2205 [0.03518, 0.751] was the ALT → TG slope in the mediator equation for the ALT, TG, and PWV interaction analysis.The PWV equation included an ALT × TG product term; the estimate's interval was a bootstrap 95% percentile interval.Source: §20 · p. 173

21. Exposure × mediator interaction: ALT, seated DBP and PWV

• 0.1092 [0.06578, 0.1575] was the ALT → DBP slope, while the DBP → PWV slope at ALT = 0 was 0.07269 [0.05837, 0.08958].The ALT × DBP interaction coefficient was −0.0009153 [−0.001608, −0.0003361].Source: §21 · p. 174

22. ALT × sex interaction: sex-specific ALT–PWV slopes

• In the ALT×sex interaction analysis, the TG→PWV slope adjusted for ALT was 0.003458 [0.001458, 0.006596], and the path-product association index was 0.000304 [−0.000247, 0.003227].The decomposed total was −0.003707 [−0.005103, 0.003405].Source: §22 · p. 175

24. Narrow time windows: ALT →seated DBP →thigh-to-ankle PWV

• The ALT→DBP→PWV path-product association index was 0.009123 [0.003557, 0.01643], while its decomposed total was 0.01654 [−0.002814, 0.03767].The analysis ordered ALT, seated DBP, and PWV in time and adjusted for approximate age and recorded sex; the total interval includes zero.Source: §24 · p. 175

25. Extended confounder adjustment: ALT →TG →thigh-to-ankle PWV

• With adjustment for age, sex, BMI, smoking, and drinking frequency, the ALT→TG→PWV path-product association index was 0.002629 [0.0002741, 0.007509].The decomposed total was 0.005049 [−0.007573, 0.01796].Source: §25 · pp. 175–176

26. Adjustment for prior PWV: ALT →TG →thigh-to-ankle PWV

• After adjustment for prior PWV, the ALT→TG→PWV path-product association index was 0.003664 [0.0003396, 0.01125], while the decomposed total was −0.01003 [−0.02526, 0.007694].The PWV equation additionally adjusted for the most recent PWV before the ALT test; intervals were bootstrap 95% percentile intervals.Source: §26 · p. 176

27. Within-participant fixed effects: ALT →TG →PWV; 28. Within-participant fixed effects: ALT →seated DBP →PWV

• The within-participant ALT→TG→PWV path-product association index was 1.426 × 10−5 [−1.919 × 10−5, 0.0001908]; a parallel within-participant ALT→DBP→PWV model was also specified.The TG-path analysis used participant fixed effects and n = 1711; the supplied passages give no numerical result for the DBP-path model.Source: §27 · pp. 176–177, §28 · p. 177

29. Serial path with symmetric windows: ALT →TG →DBP →PWV

• 0.08414 [0.06345, 0.1019] was the reported seated DBP→PWV slope adjusted for ALT and TG in the serial-path analysis.Measurements used symmetric windows; bootstrap 95% percentile intervals were reported, and P values were not adjusted for multiple comparisons.Source: §29 · pp. 177–178

30. Joint model: ALT, TG, DBP and PWV (±90 days)

• 0.1033 [0.02722, 0.1794] and 0.1266 [0.03439, 0.2188] were reported in the ±90-day and smoking-adjusted joint models, respectively.The ±90-day model used n = 167; the smoking-adjusted specification used ±30-day windows and n = 90.Source: §30 · p. 178

F.1 The equation system of the network

• The network equations use source pathway analyses or extended specifications; fitted source equations and task terms are trained on the HPP training split, with tuning used for model selection.Inputs and targets are the latest measurements at or before prediction time, and the source-analysis equation forms and covariates are retained.Source: §F.1 · p. 179, Table F.1 · p. 179

F.2 HPP multi-phenotype prediction

• 10,401 participants were split into training (5,759), tuning (1,548), calibration (1,012) and test (2,082) sets for six prediction tasks.The 12,492 predictions are the six task predictions for each of 2,082 test participants; calibration included 71 future-PWV and 79 future-cIMT labels.Source: §F.2 · p. 179
• The 90% prediction intervals use split-conformal calibration, while reported table intervals are 95% bootstrap percentile intervals over test participants.The intervals are conditional on the fitted model.Source: §F.2 · p. 179
• Random masking hides each observed network node independently at rates of 10%, 30%, 50% or 70%; structural tests hide individual nodes, modalities or restrict inputs to nine NHANES-measured nodes.Under random masking, the predictor, calibration-set interval radius and test labels stay fixed; five fixed seeds are used at each masking rate.Source: §F.2 · p. 180

F.3 The BMI–SpO2–cIMT decomposition and other effect queries

• The BMI–SpO2–cIMT decomposition uses the 25th- and 75th-percentile training-split BMI values as contrasts and fixes SpO2 at its analysis-sample median for the controlled direct contrast.With exposure–mediator interaction, T − CDE(m*) need not equal I; the alternative decomposition instead uses T = D′ + I′.Source: §F.3 · p. 181, Table F.6 · p. 182, Table F.7 · p. 182
• Causal interpretations of D, I and T require consistency, positivity, no unmeasured confounding, specified measurement and selection conditions, and correct conditional-mean models.Other queries include the ALT–TG–PWV decomposition and GGT–PWV, TG–PWV and SpO2–cIMT contrasts; the L7 chains number 196 from 147 participants.Source: §F.3 · pp. 181–182
• The analyses also examine sex and age subgroups and L7 sensitivity to residual correlation; the supplied sensitivity result reports M = 0.23801 (95% CI [0.08147, 0.37299]).For L7 age subgroups, age is measured at each chain’s exposure date, so a participant can contribute to both groups.Source: §F.3 · p. 183, Table F.10 · p. 184, Table F.11 · p. 184