Combining longitudinal cohort studies to examine cardiovascular risk factor trajectories across the adult lifespan

Donald M. Lloyd-Jones; Hongyan Ning; Juned Siddique; Michael J Daniels; Zeynab Aghabazaz

arxiv: 2503.17606 · v2 · submitted 2025-03-22 · 📊 stat.ME · stat.AP

Combining longitudinal cohort studies to examine cardiovascular risk factor trajectories across the adult lifespan

Zeynab Aghabazaz , Michael J Daniels , Hongyan Ning , Donald M. Lloyd-Jones , Juned Siddique This is my paper

Pith reviewed 2026-05-22 23:34 UTC · model grok-4.3

classification 📊 stat.ME stat.AP

keywords Bayesian hierarchical modelslongitudinal cohort studiescardiovascular risk factorsmissing datamultiple imputationmodel validationmultivariate random effects

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The pith

A Bayesian hierarchical model pools seven cardiovascular cohorts to map risk factor trajectories across the full adult lifespan by borrowing strength across studies and variables.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a statistical framework that merges data from seven longitudinal cohorts, each covering only portions of adulthood, to study cardiovascular risk factor changes starting in early adulthood. It uses a Bayesian hierarchical multivariate model to jointly estimate trajectories for multiple risk factors while sharing information across cohorts to handle gaps where data are missing for certain ages or variables. Novel diagnostics verify that the model preserves relationships among risk factors over time. The fitted trajectories show clear age-related shifts that differ by life stage, demographic subgroup, and original cohort, pointing to periods when prevention efforts may be most effective.

Core claim

The authors introduce a Bayesian hierarchical multivariate approach that jointly models multiple longitudinal risk factors over time and across cohorts from the Lifetime Risk Pooling Project. The model borrows information from all risk factors to improve precision for each one and borrows across cohorts to fill in unobserved values, allowing estimation of trajectories over the entire adult lifespan despite incomplete coverage by any single study. New diagnostic and validation methods confirm that critical relationships among risk factors are maintained. Application of the model reveals substantial age-related variation in the trajectories, with patterns differing across life stages, groups,

What carries the argument

Bayesian hierarchical multivariate random-effects model that jointly estimates longitudinal trajectories for multiple risk factors while borrowing information across cohorts and variables to handle incomplete data coverage.

If this is right

Risk factor trajectories vary substantially by age and life stage, identifying distinct windows for cardiovascular prevention.
Differences across subgroups and cohorts indicate that monitoring and intervention strategies should be tailored rather than uniform.
Joint modeling of multiple risk factors increases the precision of estimates for each individual factor.
Validation procedures ensure that interrelationships among risk factors remain consistent across the modeled lifespan.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The combined trajectories could be linked to later clinical events to test whether the identified age patterns predict outcomes differently by subgroup.
The borrowing strategy may be tested on other sets of health outcomes where no single study spans the full relevant time window.
Public health planning could use the life-stage differences to time screening recommendations more precisely than current age-based guidelines.

Load-bearing premise

Information borrowed from other cohorts and risk factors can fill unobserved values without introducing systematic bias.

What would settle it

Direct comparison of model-imputed trajectories in an age range covered by one cohort against independent observed data from a different long-running study covering the same range.

read the original abstract

We introduce a statistical framework for combining data from multiple large longitudinal cardiovascular cohorts to enable the study of long-term cardiovascular health starting in early adulthood. Using data from seven cohorts belonging to the Lifetime Risk Pooling Project (LRPP), we present a Bayesian hierarchical multivariate approach that jointly models multiple longitudinal risk factors over time and across cohorts. Because few cohorts in our project cover the entire adult lifespan, our strategy uses information from all risk factors to increase precision for each risk factor trajectory and borrows information across cohorts to fill in unobserved risk factors. We develop novel diagnostic testing and model validation methods to ensure that our model robustly captures and maintains critical relationships over time and across risk factors. Our modeling reveals substantial age-related variation in risk factor trajectories, with patterns that differ across life stages, subgroups, and cohorts, thereby highlighting key periods for cardiovascular prevention and monitoring. Keywords: Bayesian hierarchical models; Missing data; Model validation; Multiple imputation; Random effects.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper gives a concrete Bayesian hierarchical setup for pooling the seven LRPP cohorts to estimate joint risk-factor trajectories across the full adult span, with added diagnostics, but the exchangeability needed for borrowing strength across cohorts is the load-bearing piece.

read the letter

The new piece is the joint multivariate random-effects model that lets them borrow across both risk factors and cohorts to fill in the age ranges no single LRPP study covers. They also supply some custom diagnostic checks aimed at verifying that the imputed trajectories preserve the key cross-factor and cross-time relationships. That combination is a practical step for this kind of lifespan pooling problem, and the application to the actual LRPP data is worked out in detail rather than left as a simulation exercise. The validation methods go a bit beyond off-the-shelf multiple imputation, which is useful for readers who have to defend these kinds of combined analyses. The central results on age-related variation and life-stage differences follow directly from the fitted trajectories. The soft spot is exactly the one the stress-test flags: the model still needs the cohorts to be exchangeable once the random effects are in place. If unmeasured differences in recruitment, measurement protocols, or unmodeled confounders remain, the borrowed segments can shift the estimated age patterns in a systematic way. The paper presents the diagnostics as protection, but they do not appear to include a targeted power check against cohort-level misspecification, so it is not clear how much bias would be caught. The results on subgroup and cohort differences are therefore only as strong as that assumption. This is for cardiovascular epidemiologists who routinely combine cohorts and for statisticians who work on hierarchical longitudinal models with missing segments. It is worth sending to referees because the methods are spelled out, the data are real, and the diagnostics are a genuine addition, even though the exchangeability question will need more explicit attention in revision.

Referee Report

2 major / 2 minor

Summary. The paper introduces a Bayesian hierarchical multivariate model to combine data from seven LRPP cohorts for studying longitudinal cardiovascular risk factor trajectories across the adult lifespan. It jointly models multiple risk factors, borrows strength across cohorts and factors to impute unobserved segments, develops novel diagnostics for validation, and reports substantial age-related variation in trajectories that differ by life stages, subgroups, and cohorts.

Significance. If the imputation and exchangeability assumptions hold, the framework would enable analysis of long-term trajectories from early adulthood onward and identification of key prevention periods, extending beyond single-cohort limitations. The joint modeling and multiple-imputation approach via random effects is a methodological strength when supported by the diagnostics.

major comments (2)

[§3] §3 (random-effects structure and joint modeling): The central claim of substantial age-related variation (and life-stage/subgroup differences) depends on the model correctly imputing missing segments by borrowing across the seven cohorts. The manuscript does not report sensitivity analyses or explicit checks for violations of exchangeability arising from cohort-specific selection, measurement protocols, or unmeasured confounders, which could systematically bias the estimated trajectories.
[§4] §4 (novel diagnostics and model validation): The diagnostics are presented as safeguards against misspecification, yet the paper provides no power analysis, simulation study, or targeted evaluation demonstrating their ability to detect bias from unmodeled cohort-level differences. This leaves the robustness of the reported patterns unverified on the load-bearing assumption.

minor comments (2)

[Abstract] The abstract states that the model 'uses information from all risk factors to increase precision' but does not quantify the precision gain or compare to single-factor models; a brief numerical illustration would clarify the benefit.
Notation for the multivariate random effects and imputation steps could be made more explicit (e.g., distinguishing cohort-level vs. individual-level effects) to aid reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments on our manuscript. We address each major comment below and will incorporate revisions to strengthen the presentation of the exchangeability assumptions and validation of the diagnostics.

read point-by-point responses

Referee: [§3] §3 (random-effects structure and joint modeling): The central claim of substantial age-related variation (and life-stage/subgroup differences) depends on the model correctly imputing missing segments by borrowing across the seven cohorts. The manuscript does not report sensitivity analyses or explicit checks for violations of exchangeability arising from cohort-specific selection, measurement protocols, or unmeasured confounders, which could systematically bias the estimated trajectories.

Authors: We agree that explicit sensitivity analyses for the exchangeability assumption would strengthen the manuscript. The hierarchical model includes cohort-specific random effects to allow for heterogeneity in intercepts and slopes, and the joint multivariate structure borrows strength via the shared covariance across risk factors. However, to directly address potential systematic biases from cohort selection or measurement differences, we will add sensitivity analyses in the revision. These will include refitting the model after excluding individual cohorts, adding cohort-level covariates where available, and comparing trajectory estimates under alternative prior specifications on the cohort random effects. The results will be reported in a new subsection of the results and an expanded appendix. revision: yes
Referee: [§4] §4 (novel diagnostics and model validation): The diagnostics are presented as safeguards against misspecification, yet the paper provides no power analysis, simulation study, or targeted evaluation demonstrating their ability to detect bias from unmodeled cohort-level differences. This leaves the robustness of the reported patterns unverified on the load-bearing assumption.

Authors: The diagnostics were constructed to verify preservation of within- and between-factor relationships observed in the data and have been applied to the LRPP cohorts with consistent results. We acknowledge that a dedicated simulation study would provide stronger evidence of their ability to detect unmodeled cohort-level bias. In the revised manuscript we will add a simulation study that introduces controlled violations of exchangeability (e.g., cohort-specific shifts in means or variances) and evaluates the power of the proposed diagnostics to flag these departures. The simulation design, results, and power curves will be included in a new methods subsection and supplementary material. revision: yes

Circularity Check

0 steps flagged

No circularity; standard Bayesian hierarchical modeling with independent validation steps

full rationale

The paper presents a Bayesian hierarchical multivariate model that jointly models risk factors across cohorts using random effects and borrowing strength for missing segments. This relies on established Bayesian methods rather than any self-definitional loop, fitted parameter renamed as prediction, or load-bearing self-citation chain. The novel diagnostics in §4 are described as external checks on the model fit and relationships, not internal to the estimation itself. No equation reduces to its own input by construction, and the age-related variation claim is derived from the fitted trajectories on the LRPP data rather than assumed or renamed from prior results. The framework is self-contained against external benchmarks with no reduction to tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available, so specific free parameters and additional axioms cannot be identified from the text. The central modeling approach rests on the domain assumption that cohorts are combinable under a shared hierarchical structure.

axioms (1)

domain assumption Data from different cohorts can be jointly modeled using a hierarchical structure that allows borrowing of information across cohorts and risk factors.
This is necessary to fill in unobserved risk factors and increase precision for each trajectory.

pith-pipeline@v0.9.0 · 5706 in / 1205 out tokens · 45469 ms · 2026-05-22T23:34:47.361455+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

We present a Bayesian hierarchical multivariate approach that jointly models multiple longitudinal risk factors over time and across cohorts... piecewise linear function with P pre-selected breakpoints... random effects b(p)_iℓ and b(p)_ℓk
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Σ = Δ ⊛ Γ... inverse-Wishart priors... posterior predictive probability (PPP)

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