Comparing Two Survival Time Distributions: An Investigation of Several Weight Functions for the Weighted Logrank Statistic

A weighted log-rank test and associated effect estimator for cancer trials with delayed treatment effect

The standard log-rank test has been extended by adopting various weight functions. Cancer vaccine or immunotherapy trials have shown a delayed onset of effect for the experimental therapy. This is manifested as a delayed separation of the survival curves. This work proposes new weighted log-rank tests to account for such delay. The weight function is motivated by the time-varying hazard ratio between the experimental and the control therapies. We implement a numerical evaluation of the Schoenfeld approximation (NESA) for the mean of the test statistic. The NESA enables us to assess the power and to calculate the sample size for detecting such delayed treatment effect and also for a more general specification of the non-proportional hazards in a trial. We further show a connection between our proposed test and the weighted Cox regression. Then the average hazard ratio using the same weight is obtained as an estimand of the treatment effect. Extensive simulation studies are conducted to compare the performance of the proposed tests with the standard log-rank test and to assess their robustness to model mis-specifications. Our tests outperform the G^ρ,γ class in general and have performance close to the optimal test. We demonstrate our methods on two cancer immunotherapy trials.

Nonparametric combination tests for comparing two survival curves with informative and non-informative censoring

This paper looks at permutation methods used to deal with hypothesis testing within the survival analysis framework. In the literature, several attempts have been made to deal with the comparison of survival curves and, depending on the survival and hazard functions of two groups, they can be more or less efficient in detecting differences. Furthermore, in some situations, censoring can be informative in that it depends on treatment effect. Our proposal is based on the nonparametric combination approach and has proven to be very effective under different configurations of survival and hazard functions. It allows the practitioner to test jointly on primary and censoring events and, by using multiple testing methods, to assess the significance of the treatment effect separately on the survival and the censoring process.