Beyond biased coin minimization: eliminating shift in covariate-adaptive randomization for unequal allocation
Authors
Research Topics
Paper Information
-
Journal:
Biometrika -
DOI:
10.1093/biomet/asag073 -
Published:
November 10, 2026 -
Added to Tracker:
Nov 13, 2026
Abstract
Summary The biased coin has long been a central device in covariate-adaptive randomization: an imbalance measure is defined, and the next assignment is biased toward the treatment that improves balance. Although this biased coin minimization paradigm is highly effective under equal allocation, its natural extensions to unequal allocation can cause a shift problem, where additional covariate imbalances are not centered at zero. We propose a new covariate-adaptive randomization procedure that moves beyond this paradigm by designing the allocation function directly. The resulting procedure achieves strong marginal balance for covariates used in allocation and eliminates the shift asymptotically for additional covariates. The allocation form is derived from a mechanism analysis of the shift problem and its elimination. An explicit variance formula further reveals favorable variability in additional covariate imbalance.
Author Details
Hengjia Fang
AuthorWei Ma
AuthorResearch Topics & Keywords
Experimental Design
Research AreaCitation Information
APA Format
Hengjia Fang
&
Wei Ma
(2026)
.
Beyond biased coin minimization: eliminating shift in covariate-adaptive randomization for unequal allocation.
Biometrika
, 10.1093/biomet/asag073.
BibTeX Format
@article{paper1910,
title = { Beyond biased coin minimization: eliminating shift in covariate-adaptive randomization for unequal allocation },
author = {
Hengjia Fang
and Wei Ma
},
journal = { Biometrika },
year = { 2026 },
doi = { 10.1093/biomet/asag073 },
url = { https://doi.org/10.1093/biomet/asag073 }
}