Nearly optimal truncated group sequential test on binomial proportions

ABSTRACT

In this article, we systematically study the optimal truncated group sequential test on binomial proportions. Through analysis of the cost structure, average test cost is introduced as a new optimality criterion. According to the new criterion, the optimal tests on different design parameters including the boundaries, success discriminant value, stage sample vector, stage size, and the maximum sample size are defined. Since the computation time in finding optimal designs by exhaustive search is intolerably long, group sequential sample space sorting method and procedures are developed to find the near-optimal ones. In comparison with the international standard ISO2859-1, the truncated group sequential designs proposed in this article can reduce the average test costs around 20%.

KEYWORDS:

• Binomial distribution
• Cost structure of experiment
• Group sequential test
• Optimal design
• Sequential analysis

MATHEMATICS SUBJECT CLASSIFICATION:

• 62L05
• 62K05

Acknowledgments

The authors wish to thank the editor and the anonymous referee for helpful suggestions and comments concerning this article.

funding

This study was supported by the National Natural Science Foundation of China(11561011).