The randomization design employed to gather the data is the basis for the exact distributions of the permutation tests. One of the designs that is frequently used in clinical trials to force balance and remove experimental bias is the truncated binomial design. The exact distribution of the weighted log-rank class of tests for censored cluster medical data under the truncated binomial design is examined in this paper. For p-values in this class, a double saddlepoint approximation is developed using the truncated binomial design. With the right censored cluster data, the saddlepoint approximation's speed and accuracy over the normal asymptotic make it easier to invert the weighted log-rank tests and find nominal 95 % confidence intervals for the treatment effect.