Vine copula based likelihood estimation of dependence patterns in multivariate event time data

TL;DR

This paper develops a likelihood-based estimation method for vine copulas to model complex dependence in multivariate event time data with right-censoring, supported by simulations and real data application.

Contribution

It introduces a two-stage likelihood estimation approach for vine copulas in censored data, including a sequential estimation procedure to handle computational challenges.

Findings

Good finite sample performance demonstrated in simulations

Effective model selection shown on mastitis data

Likelihood estimation adapts to right-censored multivariate data

Abstract

In many studies multivariate event time data are generated from clusters having a possibly complex association pattern. Flexible models are needed to capture this dependence. Vine copulas serve this purpose. Inference methods for vine copulas are available for complete data. Event time data, however, are often subject to right-censoring. As a consequence, the existing inferential tools, e.g. likelihood estimation, need to be adapted. A two-stage estimation approach is proposed. First, the marginal distributions are modeled. Second, the dependence structure modeled by a vine copula is estimated via likelihood maximization. Due to the right-censoring single and double integrals show up in the copula likelihood expression such that numerical integration is needed for its evaluation. For the dependence modeling a sequential estimation approach that facilitates the computational challenges of the likelihood optimization is provided. A three-dimensional simulation study provides evidence for the good finite sample performance of the proposed method. Using four-dimensional mastitis data, it is shown how an appropriate vine copula model can be selected for data at hand.