The weighted log-rank class of permutation tests: P-values and confidence intervals using saddlepoint methods

Abstract

Test statistics from the weighted log-rank class are commonly used to compare treatment with control when there is right censoring. This paper uses saddlepoint methods to determine mid- p -values from the null permutation distributions of tests from the weighted log-rank class. Analytical saddlepoint computations replace the permutation simulations and provide mid- p -values that are virtually exact for all practical purposes. The speed of these saddlepoint computations makes it practicable to invert the weighted log-rank tests to determine nominal 95% confidence intervals for the treatment effect with right-censored data. Such analytical inversions lead to permutation confidence intervals that are easily computed and virtually identical to the exact intervals that would normally require massive amounts of simulation.