A note on familywise error rate for a primary and secondary endpoint

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Inference

Background:

• Clinical trials often involve primary and secondary endpoints.
• Gatekeeping strategies are used to control error rates when testing multiple endpoints.
• Previous work by Hung et al. (2007) and Tamhane et al. (2010) highlighted issues with specific gatekeeping methods.

Purpose of the Study:

• To clarify why the naive approach to testing secondary endpoints in a two-look clinical trial fails to control the familywise error rate.
• To explain the misconception that the closure principle validates the naive approach.
• To demonstrate the extent of type I error rate inflation with the naive method.

Main Methods:

• Review and explanation of the gatekeeping approach in clinical trials.
• Analysis of a two-look trial scenario.
• Discussion of statistical principles, including the closure principle.
• Illustrative examples of alpha inflation.

Main Results:

• The naive method of testing a secondary endpoint at the full alpha level, even after the primary endpoint reaches significance, inflates the familywise error rate.
• The closure principle does not validate this naive procedure.
• Alpha inflation can be substantial, comparable to unadjusted monitoring of a single endpoint.

Conclusions:

• The naive approach for testing secondary endpoints in clinical trials is flawed and does not control the familywise error rate.
• Researchers must be cautious about applying the closure principle to justify this naive procedure.
• Accurate statistical methods are crucial for maintaining the integrity of clinical trial results.