Distribution of the two-sample t-test statistic following blinded sample size re-estimation

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Methods

Background:

• Sample size re-estimation is critical for maintaining statistical power in clinical trials.
• Blinded sample size re-estimation offers an alternative to unblinded methods, potentially preserving trial integrity.
• Accurate control of type I error is paramount in non-inferiority trials.

Purpose of the Study:

• To characterize the exact distribution of the two-sample t-test statistic following blinded sample size re-estimation.
• To evaluate the performance of blinded sample size re-estimation against unblinded methods.
• To address type I error inflation in non-inferiority trials and propose adjustments.

Main Methods:

• Utilized a simple one-sample variance estimator for blinded sample size re-estimation at interim analysis.
• Derived the exact distribution of the two-sample t-test statistic for final analysis.
• Employed simulation algorithms to assess the probability of rejecting the null hypothesis.
• Compared blinded and unblinded re-estimation methods based on empirical type I error, power, and sample size distribution.

Main Results:

• Characterized the exact distribution of the t-test statistic under blinded sample size re-estimation.
• Demonstrated that the adjusted significance level increases with the internal pilot study sample size.
• Identified type I error inflation across various standardized non-inferiority margins.

Conclusions:

• Blinded sample size re-estimation provides a viable method for adjusting sample size while controlling statistical properties.
• An adjusted significance level is derived to ensure type I error control in non-inferiority trials with internal pilot studies.
• The findings offer guidance for optimizing clinical trial design and statistical analysis.