Clustered survival data frequently occurs in biomedical research fields and clinical trials. The log-rank tests are used for two independent samples of clustered data tests. We use the block Efron’s biased-coin randomization (design) to assign patients to treatment groups in a clinical trial by forcing a sequential experiment to be balanced. In this article, the -values of the null permutation distribution of log-rank tests for clustered data are approximated via the double saddlepoint approximation method. Comprehensive numerical studies are carried out to assess the accuracy of the saddlepoint approximation. This approximation demonstrates great accuracy over the asymptotic normal approximation.
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