Modeling recurrent event times subject to right-censoring with D-vine copulas

In several time-to-event studies, the event of interest occurs more than once for some sample units, a feature termed recurrent events. The data for a sample unit then corresponds to a series of gap times between subsequent events. Most time to event studies only have a limited follow-up period, causing the last gap time to be subject to right-censoring. Compared to classical analysis, the gap times and the censoring times cannot be assumed independent, i.e. due to the sequential nature of the event times dependence is induced. Also, the number of occurrences may differ between sample units, making gap time data unbalanced. To unravel the association pattern of gap times, these data features need to be taken into account. The class of D-vine copulas serves this purpose and, moreover, captures in a natural way the serial dependence inherent in gap time data. One- and two-stage global likelihood based estimation are discussed. To reduce the computational demand, typically present for high-dimensional data, we introduce one- and two-stage sequential likelihood based estimation. In the two-stage procedures we discuss nonparametric estimation of the survival margins under dependent right-censoring. Our work thus extends existing work in several directions: for recurrent event time data, so far only the combination of parametric survival margins and the restrictive class of Archimedean copulas has been considered. Simulations in three and four dimensions are used to evaluate the finite sample performance of the proposed estimation strategies and to compare their limits and strengths with regard to diverse data features. The analysis of real data on recurrent asthma attacks in children stresses the need for flexible copula models as to detect a possibly complex dependence pattern. New and relevant insights are provided by showing how the strength and the type of dependence changes over time.