Robust Design and Analysis of Clinical Trials With Nonproportional Hazards: A Straw Man Guidance From a Cross-Pharma Working Group

Abstract

Loss of power and clear description of treatment differences are key issues in designing and analyzing a clinical trial where nonproportional hazard (NPH) is a possibility. A log-rank test may be inefficient and interpretation of the hazard ratio estimated using Cox regression is potentially problematic. In this case, the current ICH E9 (R1) addendum would suggest designing a trial with a clinically relevant estimand, for example, expected life gain. This approach considers appropriate analysis methods for supporting the chosen estimand. However, such an approach is case specific and may suffer from lack of power for important choices of the underlying alternate hypothesis distribution. On the other hand, there may be a desire to have robust power under different deviations from proportional hazards. We would contend that no single number adequately describes treatment effect under NPH scenarios. The cross-pharma working group has proposed a combination test to provide robust power under a variety of alternative hypotheses. These can be specified for primary analysis at the design stage and methods appropriately accounting for combination test correlations are efficient for a variety of scenarios. We have provided design and analysis considerations based on a combination test under different NPH types and present a straw man proposal for practitioners. The proposals are illustrated with real life example and simulation.

Keywords:

• Clinical trial design
• Combination test
• Log-rank test
• Nonproportional hazards
• Weighted log-rank test

Supplementary Materials

In the online appendix, we provide the R programs associated with the examples discussed in this article along with a detailed literature review. These may help practitioners while implementing the MaxCombo test in real life clinical trials.

Acknowledgments

We would like to thank all the members of the cross-pharma nonproportional hazards working group for their input. Special thanks to Renee B Iacona (Astrazeneca Pharmaceuticals), Tai-Tsang Chen (Bristol-Myers Squibb Company), Ray Lin (Roche), Ji Lin (Eli Lilly & Co.), Tianle Hu (Eli Lilly & Co.) for their contributions and constant support. We would also like to thank Dr. Susan Halabi from Duke University for her valuable suggestion and encouragements. A special thanks goes to the referees and associate editor (AE) and editors of Statistics in Biopharmaceutical Research. The comments from referee and AE helped significantly in improving the contents of this article. Finally, we would also thank the industry and the FDA participants in the Duke-Margolis workshop for their valuable input and discussions. All materials of the Duke-Margolis workshop are available at https://healthpolicy.duke.edu/events/public-workshop-oncology-clinical-trials-presence-non-proportional-hazards.