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How to conduct better time-to-event analysis with delayed treatment effects

The issue of delayed treatment effects in immuno-oncology was demonstrated during a FDA-Industry sponsored workshop over two years ago. This demonstration made it clear that traditional log-rank tests, often used for analyses of progression free survival and overall survival, would need to be replaced as essential assumptions of the test no longer held.

Cytel scientists along with colleagues at Pfizer, Merck, the Medical University of Vienna, Bath University and Harvard University, have recently proposed a new test in a study published in Biometrical Journal. The max-combo test enables analysis of PFS and OS when handling delayed treatment effects, while also adding the option for early stopping.


The log-rank test is the most common statistical test to analyze time-to-event endpoints like overall survival and progression free survival. In order to utilize the log-rank test, one must assume proportional hazard rates. These hazard rates measure the risk of death at a given time, during a time-to-event trial.

When studying a vaccine, the time it takes to see an immunological effect often means that the hazard rates between the standard of care versus the new intervention are no longer proportional. As a result, the log-rank test works less efficiently (i.e., loses power quickly).

The Vision

In order to solve for this critical problem affecting key immuno-oncology therapies, Pfizer’s Dr. Pranab Ghosh brought together leading academic and industry statisticians to find a solution. This included Dr. Robin Ristl (Vienna), Dr. Franz König (Vienna), Dr. Martin Posch (Vienna), Dr. Christopher Jennison (Bath), Dr. Heiko Götte (Merck), Dr. Armin Schüller (Merck) and Dr. Cyrus Mehta (Harvard) who is also one of Cytel’s founders.

Applying their combined statistical and industry knowledge to securing a new method for PFS and OFS, they were also able to find a test which allowed for industry needs like early stopping.

The Solution

Weights can be added to log-rank tests to handle such a delay. In this paper, Cytel statisticians and colleagues compare the balance of robustness and efficacy between Harrington-Fleming and Magirr-Burman weighted log-rank tests, and then apply them to a group sequential design.

One of the consequences of this approach has been a number of possibilities for early stopping, thanks to the group sequential design. This adds the benefit of detecting effective drugs earlier, and expediting their time to market.

Read Paper


About the Author of Blog: 


Dr. Esha Senchaudhuri is a research and communications specialist, committed to helping scholars and scientists translate their research findings to public and private sector executives. At Cytel Esha leads content strategy and content production across the company's five business units. She received a doctorate from the London School of Economics in philosophy, and is a former early-career policy fellow of the American Academy of Arts and Sciences. She has taught medical ethics at the Harvard School of Public Health (TH Chan School), and sits on the Steering Committee of the Society for Women in Philosophy's Eastern Division, which is responsible for awarding the Distinguished Woman in Philosophy Award. 


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