Estimation and expected sample size in Simon's two-stage designs that stop as early as possible

Area of Science:

• Clinical Trials Methodology
• Biostatistics
• Oncology Research

Background:

• Simon's two-stage designs are standard for early-phase oncology trials.
• Early stopping rules, including non-stochastic curtailment, can improve trial efficiency but complicate response rate estimation.

Purpose of the Study:

• To develop an accurate and efficient method for estimating response rates in Simon's two-stage designs with non-stochastic curtailment.
• To provide a uniformly minimum-variance unbiased estimator (UMVUE) for response rates under these specific trial conditions.

Main Methods:

• Proposed a novel uniformly minimum-variance unbiased estimator (UMVUE) for the response rate.
• Utilized the Rao-Blackwell theorem for theoretical proof of the estimator's properties.
• Conducted analytical and simulation-based evaluations of bias, mean squared error, and confidence interval coverage.

Main Results:

• The proposed estimator is proven to be UMVUE.
• Evaluations demonstrate good performance in terms of bias and mean squared error.
• Derived confidence intervals show appropriate coverage properties.

Conclusions:

• The developed UMVUE offers a statistically sound solution for estimating response rates in Simon's two-stage designs with non-stochastic curtailment.
• This method enhances the reliability of statistical inference in efficient early-phase oncology trials.