Modelling hierarchical clustered censored data with the hierarchical Kendall copula

Abstract

This article proposes a new model for right-censored survival data with multi-level clustering based on the hierarchical Kendall copula model of Brechmann (2014) with Archimedean clusters. This model accommodates clusters of unequal size and multiple clustering levels, without imposing any structural conditions on the parameters or on the copulas used at various levels of the hierarchy. A step-wise estimation procedure is proposed and shown to yield consistent and asymptotically Gaussian estimates under mild regularity conditions. The model fitting is based on multiple imputation, given that the censoring rate increases with the level of the hierarchy. To check the model assumption of Archimedean dependence, a goodness-of test is developed. The finite-sample performance of the proposed estimators and of the goodness-of-fit test is investigated through simulations. The new model is applied to data from the study of chronic granulomatous disease. The Canadian Journal of Statistics 47: 182-203; 2019 (c) 2019 Statistical Society of Canada