We propose an adaptive sequential framework for testing two simple hypotheses that analytically ensures finite exposure to the less effective treatment. Our proposed procedure employs a likelihood ratio-driven adaptive allocation rule, dynamically concentrating sampling effort on the superior population while preserving asymptotic efficiency (in terms of average sample number) comparable to the Sequential Probability Ratio Test (SPRT). The foremost contribution of this work is the derivation of an explicit closed-form expression for the expected number of applications to the inferior treatment. This approach achieves a balanced method between statistical precision and ethical responsibility, aligning inferential reliability with patient safety. Extensive simulation studies substantiate the theoretical results, confirming stability in allocation and consistently high probability of correct selection (PCS) across different settings. In addition, we demonstrate how the adaptive procedure markedly reduces inferior allocations compared with the classical SPRT, highlighting its practical advantage in ethically sensitive sequential testing scenarios. The proposed design thus offers an ethically efficient and computationally tractable framework for adaptive sequential decision-making.

翻译：我们提出了一种用于检验两个简单假设的自适应序贯框架，该框架通过解析方法确保对次优治疗的有限暴露。所提出的程序采用基于似然比的自适应分配规则，动态地将抽样努力集中在优势群体上，同时保持与序贯概率比检验（SPRT）相当的渐近效率（以平均样本数衡量）。本工作的首要贡献是推导出了应用于次优治疗的期望次数的显式闭式表达式。该方法实现了统计精度与伦理责任之间的平衡，将推断可靠性与患者安全相统一。广泛的仿真研究验证了理论结果，证实了分配稳定性以及在不同设置下持续较高的正确选择概率（PCS）。此外，我们展示了与经典SPRT相比，该自适应程序显著减少了次优分配，突出了其在伦理敏感的序贯检验场景中的实际优势。因此，所提出的设计为自适应序贯决策提供了一个伦理高效且计算可行的框架。