Weighted log-rank tests for clustered censored data: Saddlepoint p-values and confidence intervals

Abstract

Clustered data with censored failure times frequently arise in clinical trials and tumorigenicity studies. For such data, the common and extensively used class of two-sample tests is the weighted log-rank tests. In this article, a double saddlepoint approximation is used to calculate the p-values of the null permutation distribution of these tests. This technique is demonstrated using three real clustered data sets. Comprehensive simulation studies are conducted to appraise the efficiency of the saddlepoint approximation. This approximation is far superior to the asymptotic normal approximation. This precision allows us to determine almost exact confidence intervals for the treatment impact.