The weighted log-rank class under truncated binomial design: saddlepoint p-values and confidence intervals

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Inference

Background:

• Randomization designs are crucial for valid statistical testing in clinical trials.
• Truncated binomial designs are frequently employed to balance groups and minimize bias.
• Analyzing censored data requires specialized statistical methods.

Purpose of the Study:

• To derive the exact distribution of weighted log-rank tests for censored data under a truncated binomial design.
• To develop and evaluate a double saddlepoint approximation for p-values within this framework.
• To enhance the precision and efficiency of confidence interval estimation for treatment effects.

Main Methods:

• Utilizing exact distributions derived from randomization designs.
• Applying the truncated binomial design to force group balance.
• Deriving a double saddlepoint approximation for p-values of weighted log-rank tests.
• Inverting weighted log-rank tests for confidence interval calculation.

Main Results:

• The study provides the exact distribution for permutation tests based on the randomization design.
• A novel double saddlepoint approximation for p-values is successfully derived.
• The approximation demonstrates superior speed and accuracy compared to normal asymptotic methods.
• This facilitates the accurate determination of 95% confidence intervals for treatment effects.

Conclusions:

• The double saddlepoint approximation offers a computationally efficient and accurate method for analyzing censored data.
• This approach is particularly valuable for weighted log-rank tests under truncated binomial designs in clinical trials.
• The findings contribute to more reliable estimation of treatment effects and improved clinical trial analysis.