Analysis of multivariate longitudinal data using dynamic lasso-regularized copula models with application to large...

Area of Science:

• Biostatistics
• Cardiovascular Epidemiology
• Longitudinal Data Analysis

Background:

• The National Heart, Lung and Blood Institute Growth and Health Study (NGHS) tracks childhood health longitudinally.
• Estimating joint distributions of cardiovascular risk outcomes across multiple time points with numerous covariates is challenging.
• Existing multivariate longitudinal methods are inadequate for multi-time point outcome analyses.

Purpose of the Study:

• To develop and validate a novel dynamic copula approach for estimating joint distributions of cardiovascular risk outcomes at two time points.
• To handle a large number of time-varying covariates in longitudinal health studies.
• To provide a method for clinical interpretation of conditional risk outcome distributions.

Main Methods:

• A dynamic copula model is proposed, incorporating time-varying outcome distributions, bivariate copula densities, and functional copula parameters.
• A three-step procedure is developed for variable selection and estimation: spline Lasso-regularized least squares for covariate selection, spline-based single-time outcome distribution computation, and functional copula parameter estimation.
• Resampling-subject bootstrap is used for constructing pointwise confidence intervals.

Main Results:

• The dynamic copula approach effectively estimates joint distributions of cardiovascular risk outcomes.
• The three-step procedure successfully identifies influential covariates and estimates model parameters.
• Application to NGHS data provides clinically relevant interpretations of conditional risk outcome distributions.

Conclusions:

• The dynamic copula approach offers a suitable method for analyzing longitudinal cardiovascular risk data with multiple time points and covariates.
• The proposed estimation procedure demonstrates statistical validity through simulation studies.
• This methodology enhances the understanding of complex relationships between cardiovascular risk factors over time.