Dependence modeling for recurrent event times subject to right-censoring with D-vine copulas

TL;DR

This paper introduces a flexible D-vine copula-based method for modeling dependent recurrent event times with right-censoring, allowing nonparametric margins and capturing complex dependence structures, demonstrated through simulations and an asthma study.

Contribution

It extends existing models by incorporating nonparametric margins and D-vine copulas, providing a more flexible approach to dependent recurrent event data with censoring.

Findings

D-vine copula effectively captures changing dependence over time.

Proposed methods show good finite sample performance in simulations.

Application reveals dependence patterns in recurrent asthma attacks.

Abstract

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.