Analysis of longitudinal data with unmeasured confounders

Area of Science:

• Epidemiology
• Biostatistics
• Longitudinal Data Analysis

Background:

• Confounding in longitudinal or clustered data poses unique challenges due to varying relationships between confounders and covariates.
• Cohort and period effects in aging research exemplify such confounding in longitudinal data.

Purpose of the Study:

• To formulate a data-generating model with confounding and derive the response variable's distribution.
• To examine the properties of regression coefficients when confounders are omitted.
• To analyze the impact of within- and between-individual confounding on statistical models.

Main Methods:

• Formulated a data-generating model incorporating confounding.
• Derived the unconditional distribution of the response variable.
• Analyzed regression coefficient properties under omitted confounder scenarios.
• Investigated multivariate cases combining within- and between-individual information based on covariance structure.

Main Results:

• Expected regression coefficient values differ between across- and within-individual regressions.
• In multivariate analysis, bias-variance trade-offs depend on numerous parameters and the assumed covariance structure.
• Minimizing between-individual confounding (e.g., cohort effects) often benefits from fitting correlations slightly above the true value.
• Period effects may necessitate fitting correlations below the true correlation.

Conclusions:

• The choice of analytical method for longitudinal data involves inherent trade-offs between bias and variance.
• Optimal method selection depends on identifying the primary concern: within- or between-individual confounding.
• Understanding these trade-offs is crucial for accurate interpretation of longitudinal study findings.