Rank tests for clustered survival data when dependent subunits are randomized.
In clustered survival data, subunits within each cluster share similar characteristics, so that observations made from them tend to be positively correlated. In clinical trials, the correlated subunits from the same cluster are often randomized to different treatment groups. In this case, the variance formulas of the standard rank tests such as the logrank, Gehan-Wilcoxon or Prentice-Wilcoxon, proposed for independent samples, need to be adjusted for intracluster correlations both within and between treatment groups for testing equality of marginal survival distributions. In this paper we derive a general form of simple variance formulas of the rank tests when subunits from the same cluster are randomized into different treatment groups. Extensive simulation studies are conducted to investigate small sample performance of the variance formulas. We compare our non-parametric rank tests based on the adjusted variances with one from a shared frailty model, which is an optimal semi-parametric testing procedure when the intracluster correlations within and between groups are the same.
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