Rank tests for clustered survival data

In a clinical trial, we may randomize subjects (called clusters) to different treatments (called groups), and make observations from multiple sites (called units) of each subject. In this case, the observations within each subject could be dependent, whereas those from different subjects are independent. If the outcome of interest is the time to an event, we may use the standard rank tests proposed for independent survival data, such as the logrank and Wilcoxon tests, to test the equality of marginal survival distributions, but their standard error should be modified to accommodate the possible intracluster correlation. In this paper we propose a method of calculating the standard error of the rank tests for two-sample clustered survival data. The method is naturally extended to that for K-sample tests under dependence.