Exact p-values for Simon's two-stage designs in clinical trials

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Inference

Background:

• The monotonic condition of tail probability functions is crucial for accurate Type I and II error rate determination in one-sided hypothesis testing.
• Limited research exists on this property within two-stage clinical trial designs, particularly Simon's two-stage design.
• Computational intensity for determining error rates increases without this monotonic property.

Purpose of the Study:

• To theoretically prove the monotonic property of the tail probability function in Simon's two-stage design.
• To provide justification for p-value occurrence at parameter space boundaries.
• To reduce computational burden in the design search for two-stage clinical trials.

Main Methods:

• Theoretical mathematical proof.
• Analysis of tail probability functions within the framework of Simon's two-stage design.

Main Results:

• The tail probability function in Simon's two-stage design is proven to be monotonically increasing with respect to the parameter.
• This establishes that error rates occur at the boundary of the parameter space.
• The proof simplifies the process of finding actual error rates.

Conclusions:

• The monotonic property is confirmed for Simon's two-stage design, offering theoretical rigor.
• This finding enhances the efficiency of clinical trial design by reducing computational requirements.
• The results are applicable to one-sided hypothesis testing in two-stage clinical trials.