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

TL;DR

This paper introduces a computer-based method for designing optimal group sequential hypothesis tests with variable group sizes, applicable to i.i.d. data, and provides algorithms and implementation details.

Contribution

It develops a numerical approach for constructing and evaluating optimal group sequential tests, extending the framework of SPPRTs with practical algorithms and software implementation.

Findings

The method accurately computes error probabilities and average sampling costs.

It outperforms existing sampling plans in numerical comparisons.

The R implementation is publicly available for practical use.

Abstract

In this paper, 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, 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.