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.

翻译：在多元纵向研究中，不同结局变量间的关联常呈现时变性及个体异质性，这促使我们将相关性建模为时间和协变量的显式函数。然而，现有大多数相关性分析方法难以同时捕捉时变效应与协变量依赖效应。本文提出一种时变协变量依赖相关性模型，该模型能够联合刻画协变量对相关性的影响随时间发生的灵活平滑变化。该模型采用二元高斯建模框架，通过惩罚样条对协变量依赖的相关性进行半参数化建模。我们开发了一种基于惩罚极大似然的牛顿-拉弗森算法，并借助同步置信带对时变效应进行统计推断。模拟研究表明，在二元与连续协变量、稀疏至密集观测计划、多种相关轨迹模式等广泛场景下，该模型在相关性估计精度方面均持续优于现有方法。我们将该模型应用于包含291名双相I型障碍患者的精神病学案例研究，将抑郁与焦虑评分间的时变相关性建模为其临床变量的函数。分析结果揭示了与性别及神经系统药物使用相关的显著异质性，且这种异质性随年龄变化，从而展现了双相障碍中抑郁与焦虑间复杂的动态关联。