A General (Non-Markovian) Framework for Covariate Adaptive Randomization: Achieving Balance While Eliminating the Shift

2026-02-26

AI Summary

This work proposes a non-Markovian covariate-adaptive randomization framework to address the issue that existing methods often deviate from prespecified allocation targets, leading to unintended imbalances in additional covariates. By introducing a parameterized allocation function together with a dynamic parameter updating strategy, the proposed approach rigorously ensures that the long-run allocation proportions for all covariates converge to their target values while maintaining covariate balance. Theoretical analysis demonstrates that the method not only bounds the covariate imbalance in probability but also achieves, for the first time, a unified guarantee of both balance and allocation fidelity. This dual assurance yields asymptotic exactness and stability in the randomization process, thereby overcoming a fundamental limitation of current adaptive designs.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Fair Division
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Emerging applications increasingly demand flexible covariate adaptive randomization (CAR) methods that support unequal targeted allocation ratios. While existing procedures can achieve covariate balance, they often suffer from the shift problem. This occurs when the allocation ratios of some additional covariates deviate from the target. We show that this problem is equivalent to a mismatch between the conditional average allocation ratio and the target among units sharing specific covariate values, revealing a failure of existing procedures in the long run. To address it, we derive a new form of allocation function by requiring that balancing covariates ensures the ratio matches the target. Based on this form, we design a class of parameterized allocation functions. When the parameter roughly matches certain characteristics of the covariate distribution, the resulting procedure can balance covariates. Thus, we propose a feasible randomization procedure that updates the parameter based on collected covariate information, rendering the procedure non-Markovian. To accommodate this, we introduce a CAR framework that allows non-Markovian procedure. We then establish its key theoretical properties, including the boundedness of covariate imbalance in probability and the asymptotic distribution of the imbalance for additional covariates. Ultimately, we conclude that the feasible randomization procedure can achieve covariate balance and eliminate the shift.

Problem

• covariate adaptive randomization
• allocation ratio
• shift problem
• covariate balance
• non-Markovian

Innovation

• covariate adaptive randomization
• non-Markovian
• allocation ratio shift
• parameterized allocation function
• covariate balance