In randomized trial studies, it is common to have hierarchical clustered survival data. In a multi-center randomized trial, for example, one might have access to infection records for patients who were treated in different hospitals. This design induces two levels of clustering: The patients’ infection records form the lower-level cluster while patients treated in the same hospital form the upper-level cluster. The analysis of such data should account for potential dependence between the infection records of a given patient, and between the patients from the same hospital.

This article proposes new statistical methodology for modeling the dependence in clustered survival data. The model is based on the so-called hierarchical Kendall copula with Archimedean clusters. Its key advantage is that it easily accommodates unequal cluster sizes without imposing restrictions on the parameter space. The construction also extends readily to multiple levels of clustering.

Given that the model is copula-based, marginal parameters can be estimated separately at the first stage. The hierarchical nature of the model further allows for the dependence parameters to be estimated sequentially, level by level. Because survival data are often subject to independent right censoring, the article develops a rigorous estimation procedure for such data based on imputation. It is shown that the estimators are well-behaved in large samples, and their good performance in small samples is documented via an extensive simulation study. Moreover, a test is proposed to validate the copula choice at each clustering level. The methodology is illustrated with data from a study of the chronic granulomatous disease.

The full article is available online here.