Saddlepoint approximation for weighted log-rank tests based on block truncated binomial design.

Clustered data frequently occur in biomedical research fields and clinical trials. The log-rank tests are widely used for two-independent samples of clustered data tests. The randomized block design and truncated binomial design are used for forcing balance in clinical trials and reducing selection bias. In this paper, survival clustered data are randomized by generalized randomized block, and subsequently clustered data in each block are randomized by truncated binomial design. Consequently, the p-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 has a great accuracy over the asymptotic normal approximation.