Adaptive sample size re-estimation (SSR) is a well-established strategy for improving the efficiency and flexibility of clinical trials. Its central challenge is determining whether, and by how much, to increase the sample size at an interim analysis. This decision requires a rational framework for balancing the potential gain in statistical power against the risk and cost of further investment. Prevailing optimization approaches, such as the Jennison and Turnbull (JT) method, address this by maximizing power for a fixed cost per additional participant. While statistically efficient, this paradigm assumes the cost of enrolling another patient is constant, regardless of whether the interim evidence is promising or weak. This can lead to impractical recommendations and inefficient resource allocation, particularly in weak-signal scenarios. We reframe SSR as a decision problem under dynamic costs, where the effective cost of additional enrollment reflects the interim strength of evidence. Within this framework, we derive two novel rules: (i) a likelihood-ratio based rule, shown to be Pareto optimal in achieving smaller average sample size under the null without loss of power under the alternative; and (ii) a return-on-investment (ROI) rule that directly incorporates economic considerations by linking SSR decisions to expected net benefit. To unify existing methods, we further establish a representation theorem demonstrating that a broad class of SSR rules can be expressed through implicit dynamic cost functions, providing a common analytical foundation for their comparison. Simulation studies calibrated to Phase III trial settings confirm that dynamic-cost approaches improve resource allocation relative to fixed-cost methods.

翻译：适应性样本量重估（SSR）是一种成熟的策略，用于提高临床试验的效率和灵活性。其核心挑战在于确定是否需要在期中分析时增加样本量，以及增加多少。这一决策需要一个合理的框架来平衡统计功效的潜在提升与进一步投入的风险和成本。现行的优化方法，如Jennison和Turnbull（JT）方法，通过最大化每增加一名参与者的固定成本下的功效来解决这一问题。尽管在统计上是高效的，但这种范式假设招募另一名患者的成本是恒定的，无论期中证据是有希望还是薄弱。这可能导致不切实际的建议和低效的资源分配，特别是在弱信号场景中。我们将SSR重新定义为动态成本下的决策问题，其中额外招募的有效成本反映了期中证据的强度。在此框架内，我们推导出两个新颖的规则：（i）基于似然比的规则，被证明在零假设下实现更小的平均样本量且在对立假设下不损失功效方面是帕累托最优的；以及（ii）投资回报率（ROI）规则，通过将SSR决策与预期净收益联系起来，直接纳入经济考量。为了统一现有方法，我们进一步建立了一个表示定理，证明一大类SSR规则可以通过隐式动态成本函数表达，为它们的比较提供了共同的分析基础。针对III期试验环境校准的模拟研究证实，动态成本方法相对于固定成本方法改善了资源分配。