Estimation and inference on the joint conditional distribution for bivariate longitudinal data using Gaussian copula

In this paper we study estimating the joint conditional distributions of bivariate longitudinal outcomes using regression models and copulas. For the estimation of marginal models we consider a class of time-varying transformation models and combine the two marginal models using Gaussian copulas. Our models and estimation method can be applied in many situations where the conditional mean-based models are not good enough. Gaussian copulas combined with time-varying transformation models may allow convenient and easy-to-interpret modeling for the joint conditional distributions for bivariate longitudinal data. We derive the asymptotic properties for the copula based estimators of the joint conditional distribution functions. For illustration we apply our estimation method to an epidemiological study of childhood growth and blood pressure and also investigate finite sample properties of our procedures through a simulation study.