Fast Power Evaluation under Biased-Coin Minimization: Sampling and Randomization Calibration

2026-08-05

AI Summary

This study addresses the high computational cost of power and sample size evaluation in biased coin designs by proposing the Stratified Imbalance Gaussian Approximation (SIGA) framework. By exactly decomposing the fixed-score statistic into between-stratum imbalance and within-stratum orthogonal components, SIGA establishes, for the first time, a reusable Gaussian approximation that explicitly distinguishes conditional variance from repeated-sampling variance. The framework further incorporates a calibration mechanism based on the covariance of paired allocation paths, yielding two specialized procedures: Sampling-based Calibration (SIGA-S) for marginal boundaries and Randomization-based Calibration (SIGA-R) for non-sharp boundaries. Empirical results demonstrate that both SIGA-S and SIGA-R achieve power estimates highly consistent with those from reference randomization tests while substantially reducing computational overhead.

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.

Problem

• biased-coin minimization
• power evaluation
• randomization test
• sample-size calculation
• computational efficiency

Innovation

• stratum-imbalance Gaussian approximation
• biased-coin minimization
• randomization calibration
• fixed-score statistic
• computational efficiency