Linear rank tests for left-truncated data using randomized block design: saddlepoint p-values and confidence intervals

Survival analysis is most typically characterized by left truncation; left -truncated data are composed of two recorded times, the time of occurrence of an event before the event of interest, and the time of the interested event. In this study, p-values of the permutation distribution of the linear rank tests are computed using saddlepoint approximation method for left -truncated data using a randomized block design. Simulation studies demonstrate the saddlepoint approximation method's accuracy in approximating p-value of the linear rank tests. Due to the efficiency of the proposed method over the normal approximation, 95% confidence intervals for the treatment impact are performed.