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

The National Heart, Lung and Blood Institute Growth and Health Study (NGHS) is a large longitudinal study of childhood health. A main objective of the study is to estimate the joint distributions of cardiovascular risk outcomes at any two time points conditioning on a large number of covariates. Existing multivariate longitudinal methods are not suitable for outcomes at multiple time points. We present a dynamic copula approach for estimating an outcome's joint distributions at two time points given a large number of time-varying covariates. Our models depend on the outcome's time-varying distributions at one time point, the bivariate copula densities and the functional copula parameters. We develop a three-step procedure for variable selection and estimation, which selects the influential covariates using a machine learning procedure based on spline Lasso-regularized least squares, computes the outcome's single-time distribution using splines, and estimates the functional copula parameter of the dynamic copula models. Pointwise confidence intervals are constructed through the resampling-subject bootstrap. We apply our procedure to the NGHS cardiovascular risk data and illustrate the clinical interpretations of the conditional distributions of a set of risk outcomes. We demonstrate the statistical properties of the dynamic models and estimation procedure through a simulation study.