Fast Power Evaluation under Biased-Coin Minimization: Sampling and Randomization Calibration
Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Kojima, Masahiro
Institution: Chuo University
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7201840960
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