Robust group sequential designs for trials with survival endpoints and delayed response

Pranab Ghosh, Robin Ristl, Franz König, Martin Posch, Christopher Jennison, Heiko Götte, Armin Schüler, Cyrus Mehta

Research output: Contribution to journalArticlepeer-review

5 Citations (SciVal)
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Randomized clinical trials in oncology typically utilize time-to-event endpoints such as progression-free survival or overall survival as their primary efficacy endpoints, and the most commonly used statistical test to analyze these endpoints is the log-rank test. The power of the log-rank test depends on the behavior of the hazard ratio of the treatment arm to the control arm. Under the assumption of proportional hazards, the log-rank test is asymptotically fully efficient. However, this proportionality assumption does not hold true if there is a delayed treatment effect. Cancer immunology has evolved over time and several cancer vaccines are available in the market for treating existing cancers. This includes sipuleucel-T for metastatic hormone-refractory prostate cancer, nivolumab for metastatic melanoma, and pembrolizumab for advanced nonsmall-cell lung cancer. As cancer vaccines require some time to elicit an immune response, a delayed treatment effect is observed, resulting in a violation of the proportional hazards assumption. Thus, the traditional log-rank test may not be optimal for testing immuno-oncology drugs in randomized clinical trials. Moreover, the new immuno-oncology compounds have been shown to be very effective in prolonging overall survival. Therefore, it is desirable to implement a group sequential design with the possibility of early stopping for overwhelming efficacy. In this paper, we investigate the max-combo test, which utilizes the maximum of two weighted log-rank statistics, as a robust alternative to the log-rank test. The new test is implemented for two-stage designs with possible early stopping at the interim analysis time point. Two classes of weights are investigated for the max-combo test: the Fleming and Harrington (1981) (Formula presented.) weights and the Magirr and Burman (2019) modest (Formula presented.) weights.

Original languageEnglish
Pages (from-to)343-360
Number of pages18
JournalBiometrical Journal
Issue number2
Early online date21 Dec 2021
Publication statusPublished - 28 Feb 2022


  • cancer immunology
  • delayed response
  • Fleming–Harrington test
  • group sequential design
  • immuno-oncology
  • late separation of survival curves
  • log-rank test
  • max-combo test
  • modestly weighted log-rank test
  • nonproportional hazards

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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