An additive boundary for group sequential designs with connection to conditional error.

Area of Science:

• Clinical Trials
• Biostatistics
• Statistical Methods

Background:

• Group sequential designs allow early clinical trial termination based on interim data analysis.
• Existing error spending functions often lack interpretable parameters, leading to arbitrary boundary selection.
• The Lan and DeMets spending function provides a natural approximation to O'Brien-Fleming boundaries.

Purpose of the Study:

• To extend the Lan and DeMets spending function approach to a general family of group sequential boundaries.
• To introduce a common parameter for regulating error spending rate and group sequential boundary behavior.
• To develop interpretable spending functions, particularly those incorporating conditional error rates.

Main Methods:

• Development of a general family of error spending functions based on Brownian motion with additive terms.
• Introduction of a shared parameter controlling error spending and boundary characteristics.
• Exploration of three subfamilies, including one with a conditional error rate interpretation.

Main Results:

• The proposed spending functions offer enhanced flexibility and interpretability compared to generic functions.
• The conditional error rate parameter provides a link between group sequential and adaptive trial designs.
• Numerical results demonstrate the practical utility and adaptability of the new procedures.

Conclusions:

• The extended error spending functions provide a more principled and interpretable approach to group sequential trial design.
• The conditional error rate offers a valuable tool for designing adaptive and flexible clinical trials.
• These methods enhance the ability to make timely decisions in clinical trials based on accumulating evidence.