Sample Size Determination Under Non-proportional Hazards

  • Miao Yang
  • Zhaowei HuaEmail author
  • Saran Vardhanabhuti
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 218)


The proportional hazards assumption rarely holds in clinical trials of cancer immunotherapy. Specifically, delayed separation of the Kaplan-Meier survival curves and long-term survival have been observed. Routine practice in designing a randomized controlled two-arm clinical trial with a time-to-event endpoint assumes proportional hazards. If this assumption is violated, traditional methods could inaccurately estimate statistical power and study duration. This article addresses how to determine the sample size in the presence of nonproportional hazards (NPH) due to delayed separation, diminishing effects, etc. Simulations were performed to illustrate the relationship between power and the number of patients/events for different types of nonproportional hazards. Novel efficient algorithms are proposed to optimize the selection of a cost-effective sample size.


Non-proportional hazards Sample size Time-to-event endpoint Log-rank test Cancer immunotherapy Power analysis 


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of StatisticsOregon State UniversityCorvallisUSA
  2. 2.Alnylam Pharmaceuticals, Inc.CambridgeUSA
  3. 3.Takeda PharmaceuticalsCambridgeUSA

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