Saddle-point p-values and confidence intervals based on log-rank tests when dependent subunits of clustered survival data are randomized by random allocation design

In clinical trials, Clustered data with censored failure times often arise from a litter-matched tumorigenesis experiment. Based on such data, the mutual and widely used class of two-sample tests is the weighted log-rank tests. A double saddle-point approximation is used to calculate the p-values of the null permutation distribution of these tests. This approximation is superior to the asymptotic normal approximation. This precision allows us to determine exact confidence intervals for the treatment impact. The findings reveal the efficiency of saddle-point approximation using two real clustered data sets. Extensive simulation studies are carried out to assess the performance of the saddle-point approximation.