Group sequential hypothesis tests with variable group sizes: Optimal design and performance evaluation

Abstract

In this article, we propose a computer-oriented method of construction of optimal group sequential hypothesis tests with variable group sizes. In particular, for independent and identically distributed observations, we obtain the form of optimal group sequential tests which turn to be a particular case of sequentially planned probability ratio tests (SPPRTs, see Schmitz 1993). Formulas are given for computing the numerical characteristics of general SPPRTs, like error probabilities, average sampling cost, etc. A numerical method of designing the optimal tests and evaluation of the performance characteristics is proposed, and computer algorithms of its implementation are developed. For a particular case of sampling from a Bernoulli population, the proposed method is implemented in R programming language, the code is available in a public GitHub repository. The proposed method is compared numerically with other known sampling plans.

KEYWORDS:

• sequential analysis
• sequentially planned procedure
• hypothesis test
• optimal sampling
• optimal stopping

Subject Classifications:

• 62L10
• 62L15
• 62F03
• 60G40

Acknowledgments

The author thanks the anonymous Reviewers and the Associate Editor for valuable comments and useful suggestions.

Notes

1 https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/loess

Additional information

Funding

The author gratefully acknowledges a partial support of SNI by CONACyT (Mexico) for this work.