Log-rank permutation tests for trend: saddlepointp-values and survival rate confidence intervals

Abstract

Suppose p + 1 experimental groups correspond to increasing dose levels of a treatment and all groups are subject to right censoring. In such instances, permutation tests for trend can be performed based on statistics derived from the weighted log-rank class. This article uses saddlepoint methods to determine the mid-P-values for such permutation tests for any test statistic in the weighted log-rank class. Permutation simulations are replaced by analytical saddlepoint computations which provide extremely accurate mid-P-values that are exact for most practical purposes and almost always more accurate than normal approximations. The speed of mid-P-value computation allows for the inversion of such tests to determine confidence intervals for the percentage increase in mean (or median) survival time per unit increase in dosage. © 2009 Statistical Society of Canada.