🤖 AI Summary
This paper addresses the ethical and statistical trade-off between patient safety and statistical efficiency in sequential hypothesis testing, specifically concerning excessive exposure to inferior treatments. We propose a likelihood-ratio-driven adaptive sequential testing framework that integrates the Sequential Probability Ratio Test (SPRT) with a dynamic treatment allocation mechanism. Crucially, we derive, for the first time, an explicit closed-form upper bound on the number of assignments to the inferior treatment, thereby rigorously guaranteeing its finite exposure. Theoretical analysis establishes asymptotic statistical efficiency—achieving the optimal sample size growth rate under both hypotheses. Numerical simulations demonstrate that, compared to classical SPRT, our method maintains high correct-decision probability while reducing inferior-treatment allocations by 30–60%. Our core contribution lies in unifying statistical power, patient safety, and ethical constraints into a single coherent framework—offering a theoretically rigorous yet practically implementable paradigm for sensitive applications such as clinical trials.
📝 Abstract
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.