Conditional copula models for right-censored clustered event time data.

Abstract

We outline an estimation and a testing strategy to infer the impact of a continuous cluster-level covariate on the within-cluster association of right-censored event time data, as modeled through a conditional copula. We propose a local likelihood approach to estimate the copula parameter and we describe a generalized likelihood ratio test to formally assess its constancy. The test decision is based on an approximate p-value obtained via a parametric bootstrap. We evaluate the finite sample performance of the estimation and the testing strategy in a simulation study, under different rates of right-censoring and for various parametric copula families, considering both parametrically and nonparametrically estimated margins. Moreover, the selection of a suitable bandwidth and the impact of a misspecified copula are investigated. Results indicate that the local likelihood approach leads to on target estimation and that the testing strategy has reasonable to high power. Finally, the methods are illustrated on data from the field of medicine.