  In many time-to-event studies, the event of interest is recurrent. Here, the
data for each sample unit corresponds to a series of gap times between the
subsequent events. Given a limited follow-up period, the last gap time might be
right-censored. In contrast to classical analysis, gap times and censoring
times cannot be assumed independent, i.e. the sequential nature of the data
induces dependent censoring. Also, the recurrences typically vary between
sample units leading to unbalanced data. To model the association pattern
between gap times, so far only parametric margins combined with the restrictive
class of Archimedean copulas have been considered. Here, taking the specific
data features into account, we extend existing work in several directions: we
allow for nonparametric margins and consider the flexible class of D-vine
copulas. A global and sequential (one- and two-stage) likelihood approach are
suggested. We discuss the computational efficiency of each estimation strategy.
Extensive simulations show good finite sample performance of the proposed
methodology. It is used to analyze the association in recurrent asthma attacks
in children. The analysis reveals that a D-vine copula detects relevant
insights, on how dependence changes in strength and type over time.
