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A weighted log‐rank test and associated effect estimator for cancer trials with delayed treatment effect
Author(s) -
Yu Chang,
Huang Xiang,
Nian Hui,
He Philip
Publication year - 2021
Publication title -
pharmaceutical statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 38
eISSN - 1539-1612
pISSN - 1539-1604
DOI - 10.1002/pst.2092
Subject(s) - mathematics , estimator , statistics , log rank test , test statistic , statistic , robustness (evolution) , hazard ratio , proportional hazards model , sample size determination , statistical hypothesis testing , confidence interval , biochemistry , chemistry , gene
Abstract 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.