A Time-Varying and Covariate-Dependent Correlation Model for Multivariate Longitudinal Studies

TL;DR

This paper introduces TiVAC, a novel semiparametric model for capturing how correlations between outcomes change over time and with covariates in multivariate longitudinal data, improving accuracy over existing methods.

Contribution

The paper develops a flexible, smooth, covariate-dependent correlation model using penalized splines and provides an efficient inference algorithm, advancing correlation analysis in longitudinal studies.

Findings

TiVAC outperforms existing methods in simulation studies.

Identifies significant heterogeneity in depression-anxiety correlation related to clinical variables.

Reveals dynamic relationships in bipolar disorder data.

Abstract

In multivariate longitudinal studies, associations between outcomes often exhibit time-varying and individual level heterogeneity, motivating the modeling of correlations as an explicit function of time and covariates. However, most existing methods for correlation analysis fail to simultaneously capture the time-varying and covariate-dependent effects. We propose a Time-Varying and Covariate-Dependent (TiVAC) correlation model that jointly allows covariate effects on correlation to change flexibly and smoothly across time. TiVAC employs a bivariate Gaussian model where the covariate-dependent correlations are modeled semiparametrically using penalized splines. We develop a penalized maximum likelihood-based Newton-Raphson algorithm, and inference on time-varying effects is provided through simultaneous confidence bands. Simulation studies show that TiVAC consistently outperforms existing methods in accurately estimating correlations across a wide range of settings, including binary and continuous covariates, sparse to dense observation schedules, and across diverse correlation trajectory patterns. We apply TiVAC to a psychiatric case study of 291 bipolar I patients, modeling the time-varying correlation between depression and anxiety scores as a function of their clinical variables. Our analyses reveal significant heterogeneity associated with gender and nervous-system medication use, which varies with age, revealing the complex dynamic relationship between depression and anxiety in bipolar disorders.