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

摘要

In many studies multivariate event time data are generated from clustershaving a possibly complex association pattern. Flexible models are needed tocapture this dependence. Vine copulas serve this purpose. Inference methods forvine copulas are available for complete data. Event time data, however, areoften subject to right-censoring. As a consequence, the existing inferentialtools, e.g. likelihood estimation, need to be adapted. A two-stage estimationapproach is proposed. First, the marginal distributions are modeled. Second,the dependence structure modeled by a vine copula is estimated via likelihoodmaximization. Due to the right-censoring single and double integrals show up inthe copula likelihood expression such that numerical integration is needed forits evaluation. For the dependence modeling a sequential estimation approachthat facilitates the computational challenges of the likelihood optimization isprovided. A three-dimensional simulation study provides evidence for the goodfinite sample performance of the proposed method. Using four-dimensionalmastitis data, it is shown how an appropriate vine copula model can be selectedfor data at hand.