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

Technical Summary: Combining Longitudinal Cohort Studies to Examine Cardiovascular Risk Factor Trajectories

Problem Statement
Cardiovascular disease (CVD) development is a life-course process, yet existing epidemiological understanding often relies on risk factor measurements taken at single time points, typically in middle age. While recent literature emphasizes the importance of cumulative exposure and long-term trajectories starting in early adulthood, no single study has collected detailed phenotypic data spanning the entire adult lifespan (young adulthood through old age) on a broadly representative US population. Furthermore, individual longitudinal cohorts often have limited age coverage (e.g., starting in middle age or ending before old age) and contain missing data for specific risk factors at certain exams. Traditional meta-analyses, which aggregate results from separate studies, fail to leverage individual-level data to harmonize definitions, adjust for covariates consistently, or examine heterogeneity at the individual or subgroup level. The challenge lies in combining data from multiple cohorts with overlapping but non-identical age ranges and missing risk factor measurements while accounting for between-study heterogeneity (geography, historical period, sample characteristics).

Methodology
The authors propose a Bayesian hierarchical multivariate approach to jointly model multiple longitudinal cardiovascular risk factors across seven cohorts belonging to the Lifetime Risk Pooling Project (LRPP). The dataset includes over 256,000 observations from cohorts such as ARIC, CARDIA, CHS, MESA, FHS, FOS, and JHS, covering seven key risk factors: Systolic Blood Pressure (SBP), Diastolic Blood Pressure (DBP), BMI, Glucose, Total Cholesterol, HDL, and Triglycerides.

The core of the methodology is a piecewise linear spline model with breakpoints at 10-year intervals (ages 18, 28, ..., 78) to capture age-dependent changes in risk factor slopes. The model structure includes:

1. Multivariate Modeling: At a given age, the model captures correlations between the slopes of different risk factors within the same individual.
2. Longitudinal Modeling: It captures the correlation of risk factor trends over time within individuals.
3. Hierarchical Structure:
   • Fixed Effects: Include overall intercepts, global age slopes, and interactions with baseline covariates (race, education, birth year, cohort). Birth year is categorized into quartiles to adjust for secular trends and generational differences.
   • Random Effects:
     • Individual-level: Random intercepts and global age slopes ($p=0, 1$) allow for subject-specific deviations and capture within-individual correlations across risk factors.
     • Cohort-level: Random effects for spline-based slope increments ($p \ge 2$) capture cohort-specific deviations and correlations in trend changes across different studies.
4. Error Distribution: Residuals are modeled using a skew-normal distribution with age-window-specific scale and skewness parameters to account for potential asymmetry and heteroscedasticity.
5. Missing Data Handling: The framework treats risk factors at ages not covered by a specific cohort, or missing at specific exams, as missing data. It utilizes multiple imputation by borrowing strength across risk factors, age windows, and cohorts to fill in unobserved measurements.
6. Inference: Parameters are estimated using Markov Chain Monte Carlo (MCMC) via Stan. To ensure robust convergence in this high-dimensional setting (842 parameters), the authors employ a nested $\hat{R}$ approach using superchains and subchains.

Key Contributions

• Novel Statistical Framework: The paper introduces a method to combine multiple longitudinal cohorts with non-overlapping age ranges, treating unobserved ages as missing data rather than excluding them.
• Borrowing Strength: The model leverages information from all risk factors to increase precision for individual trajectories and borrows information across cohorts to impute unobserved risk factors, effectively extending the observable lifespan of risk factor trajectories.
• Robust Validation: The authors develop and implement novel diagnostic methods, including:
  • Posterior Predictive Checks (PPC): Comparing test statistics of observed data against replicated data to validate residual variability, mean trajectories, and variance ratios.
  • Correlation Structure Validation: Assessing the model's ability to capture correlations between risk factors at the same and different ages, as well as correlations in trend increments across cohorts.
  • Imputation Validation: Systematically deleting observed data (e.g., ages <40 in FOS, or DBP values in FOS) and evaluating the model's ability to recover the deleted values and preserve associations with other risk factors and time-to-event outcomes.

Results

• Model Fit: Posterior predictive checks indicated that the model accurately captured the variability around mean risk trajectories, with standardized residuals aligning closely with observed data. Variance ratios between observed and replicated residuals clustered near 1.0, and posterior predictive probabilities for correlation structures were generally close to 0.5, indicating the model's covariance structure mirrored observed data patterns.
• Trajectory Estimation: The model produced smooth, biologically plausible mean trajectories for all seven risk factors across the adult lifespan (ages 18–88), revealing substantial age-related variation and distinct patterns across life stages, subgroups (sex, race, education), and cohorts.
• Imputation Performance:
  • When risk factors were deleted (e.g., DBP in FOS), the imputed values preserved the expected distribution and fixed-effect coefficients (intercept, slope, spline increments) with posterior probabilities near 0.5.
  • In a joint modeling analysis of Total Cholesterol (TOTCHL) and time-to-CVD death, the Area Under the Curve (AUC) coefficients derived from imputed datasets (where ages <40 were deleted in CARDIA) closely matched those from the complete observed data (e.g., 0.41 vs. 0.42 for men), demonstrating the reliability of the imputed trajectories for downstream survival analysis.
• Simulation: A simulation study confirmed that the model could accurately recover cohort-level correlation structures even under partial age-coverage scenarios, with low bias and mean squared error compared to full-coverage scenarios.

Significance and Claims
The paper claims that this integrated framework addresses the critical limitation of single-cohort studies by enabling the study of long-term cardiovascular health starting in early adulthood. By pooling data from the LRPP, the authors demonstrate that it is possible to:

1. Identify critical periods for cardiovascular prevention and monitoring that might be missed by single-cohort analyses (e.g., midlife rises in glucose or late-life declines in HDL).
2. More precisely define thresholds for known risk factors and elucidate the role of lifestyle behaviors and demographic differences.
3. Generate robust, imputed risk factor trajectories for ages not covered by specific cohorts, facilitating the use of synthetic data for broader research.

The authors emphasize that while the model relies on structural assumptions (e.g., piecewise linear trends, specific random effect structures), it successfully balances flexibility with parsimony to maintain identifiability in high-dimensional settings. They conclude that this approach provides a foundation for future work, including joint modeling of risk factors, medication use, and time-to-event outcomes, and offers a pathway to disseminate synthetic LRPP data for the broader research community.