偏币最小化下的快速功效评估：抽样与随机化校准
Fast Power Evaluation under Biased-Coin Minimization: Sampling and Randomization Calibration
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中文总结 AI 辅助
针对偏币最小化下设计阶段功效评估计算量大的问题，开发SIGA框架及SIGA-S、SIGA-R程序，可高效近似参考随机化检验的结果并显著降低计算量。
中文摘要 AI 辅助
在偏币最小化下的设计阶段功效与样本量评估中，若在每个模拟试验内重复预先指定的随机化检验，计算量会很大。我们开发了可复用的层不平衡高斯近似（SIGA）框架，通过将固定得分统计量精确分解为联合层不平衡与正交层内分量实现。在相同绝对不平衡规则的显式分配复制极限条件下，经抽样校准的SIGA-S程序可一致估计边际均值或风险差边界处的重复抽样方差；在非尖锐边界处，固定得分随机化检验的条件方差可能存在差异，因得分包含观测分配路径。为刻画该差异，我们将一阶方差 gap 表示为含配对路径协方差的二次型，并引入基于可复用仅配对分配校准的随机化校准程序SIGA-R，以近似条件参考分布。独立综合基准测试显示，各SIGA程序与对应参考随机化检验的结果高度一致；基于已发表汇总规划特征的试验启发式模拟也表明，SIGA-S、SIGA-R与参考随机化检验的功效相近，且两种可复用校准程序相较嵌套重随机化大幅降低了计算量。
英文摘要
Design-stage power and sample-size evaluation under biased-coin minimization can be computationally intensive when a prespecified randomization test is reproduced within every simulated trial. We develop a reusable stratum-imbalance Gaussian approximation (SIGA) framework by exactly decomposing a fixed-score statistic into joint-stratum imbalance and orthogonal within-stratum components. Under explicit allocation-copy limit conditions for the same absolute-imbalance rule, the sampling-calibrated procedure, SIGA-S, consistently estimates the repeated-sampling variance at a marginal mean- or risk-difference boundary. At a nonsharp boundary, the conditional variance of a fixed-score randomization test can differ because the score contains the observed allocation path. To characterize this distinction, we express the first-order variance gap as a quadratic form involving pair-path covariance and introduce the randomization-calibrated procedure, SIGA-R, based on a reusable paired allocation-only calibration to approximate the conditional reference distribution. Separate comprehensive benchmarks showed close agreement between each SIGA procedure and the corresponding reference randomization test. A trial-inspired simulation based on published aggregate planning characteristics likewise produced similar power for SIGA-S, SIGA-R and the reference randomization test, while both reusable calibration procedures substantially reduced computation relative to nested rerandomization.
