Optimal and Efficient Sample Size Re-estimation: A Dynamic Cost Framework
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.