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<p>In this research, we follow the late Professor Tze Lai’s inspiration to propose a new Kiefer–Weiss–Lorden–Lai (KWLL) framework that minimizes the expected number of samples to evaluate efficacy (rejecting the null hypothesis) or futility (accepting the null hypothesis) subject to the maximum sample size and Type I error probability constraints. Compared to the traditional sample size calculation, our proposed KWLL framework structures the parameter of the alternative hypothesis as a function of design decisions, instead of a pre-specified value, while making a quick and accurate decision whether to accept or reject the null hypothesis. Moreover, we use the so-called 2-Sequential Probability Ratio Test (2-SPRT) as the foundation to develop reasonable algorithms that might provide a useful approximate solution to the KWLL framework. Finally, a case study using correlation as the test statistic is presented to illustrate the usefulness of our proposed framework and algorithm.</p>

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The Kiefer–Weiss–Lorden–Lai Framework for Sequential Evaluation of Efficacy and Futility with Application to Correlation Study

  • 期刊论文

  • 发表日期：

    2026年7月2日

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  • Paul Horton,
  • Qunzhi Xu,
  • Yajun Mei

摘要

In this research, we follow the late Professor Tze Lai’s inspiration to propose a new Kiefer–Weiss–Lorden–Lai (KWLL) framework that minimizes the expected number of samples to evaluate efficacy (rejecting the null hypothesis) or futility (accepting the null hypothesis) subject to the maximum sample size and Type I error probability constraints. Compared to the traditional sample size calculation, our proposed KWLL framework structures the parameter of the alternative hypothesis as a function of design decisions, instead of a pre-specified value, while making a quick and accurate decision whether to accept or reject the null hypothesis. Moreover, we use the so-called 2-Sequential Probability Ratio Test (2-SPRT) as the foundation to develop reasonable algorithms that might provide a useful approximate solution to the KWLL framework. Finally, a case study using correlation as the test statistic is presented to illustrate the usefulness of our proposed framework and algorithm.