Two-stage k-sample designs for the ordered alternative problem.

Area of Science:

• Biostatistics
• Clinical Trial Design
• Statistical Inference

Background:

• The Jonckheere-Terpstra test is standard for assessing dose-response relationships in preclinical and clinical studies.
• Existing two-stage analogs are limited, particularly for large sample sizes.

Purpose of the Study:

• To propose an exact two-stage test for dose-response assessment, adapting Simon's minimax and optimal design criteria.
• To evaluate the performance of the proposed test, including its convergence rates and behavior with ties.
• To demonstrate the practical application of the new design in clinical trial planning.

Main Methods:

• Development of an exact two-stage statistical test based on Simon's design criteria.
• Analysis of the joint distribution convergence rate for first and second stage statistics.
• Examination of test performance in the presence of tied data points.
• Application to a hypercholesterolemia clinical trial for design illustration.

Main Results:

• The proposed exact two-stage test demonstrates favorable convergence properties.
• Design parameters are provided for various alternative hypotheses.
• The test's behavior with ties is analyzed.
• Minimax and optimal two-stage designs reduce expected sample size compared to one-stage procedures for equivalent error constraints.

Conclusions:

• The proposed exact two-stage test offers an efficient alternative for dose-response assessment.
• Minimax and optimal two-stage designs provide statistical advantages, particularly in sample size reduction.
• This methodology enhances the planning and execution of clinical trials, such as those for hypercholesterolemia.