A time-heterogeneous D-vine copula model for unbalanced and unequally spaced longitudinal data

In many longitudinal studies, the number and timing of measurements differ across study subjects. Statistical analysis of such data requires accounting for both the unbalanced study design and the unequal spacing of repeated measurements. This paper proposes a time-heterogeneous D-vine copula model that allows for time adjustment in the dependence structure of unequally spaced and potentially unbalanced longitudinal data. The proposed approach not only offers flexibility over its time-homogeneous counterparts but also allows for parsimonious model specifications at the tree or vine level for a given D-vine structure. It further provides a robust strategy to specify the joint distribution of non-Gaussian longitudinal data. The performance of the time-heterogeneous D-vine copula models are evaluated through simulation studies and by a real data application. Our findings suggest improved predictive performance of the proposed approach over the linear mixed-effects model and time-homogeneous D-vine copula model.