A transition copula model for analyzing multivariate longitudinal data with missing responses.

In multivariate longitudinal studies, several outcomes are repeatedly measured for each subject over time. The data structure of these studies creates two types of associations which should take into account by the model: association of outcomes at a given time point and association among repeated measurements over time for a specific outcome. In our approach, because of some advantageous arisen from features like flexibility of marginal distributions, a copula-based approach is used for joint modeling of multivariate outcomes at each time points, also a transition model is used for considering the association of longitudinal measurements over time. For the problem of incomplete data, missingness mechanism is assumed to be ignorable. Some simulation results are reported in different scenarios using the Gaussian, t and several commonly used copulas of the family of Archimedean copulas. Akaike information criterion (AIC) is used to select the best copula function. The proposed approach is also used for analyzing a real obesity data set.