Covariate-adaptive randomization using historical data and bootstrap-based inference
Abstract
Covariate-adaptive randomization (CAR) can improve the efficiency of average treatment effect (ATE) estimation by reducing chance imbalances in prognostic baseline covariates. A recently proposed CAR method that balances multiple covariates, including continuous ones, can achieve optimal precision when the conditional mean of the outcome can be expressed as a linear combination of the covariate features used for the CAR procedure. However, this condition may be difficult to satisfy when the relationship between covariates and the outcome is nonlinear. Furthermore, directly balancing multiple covariates may reduce estimation precision in finite samples. We propose three CAR methods that incorporate a prognostic score learned from individual-level historical data into their imbalance measures. The prognostic score reduces multiple covariates to one dimension while giving larger weights to covariates that are more strongly associated with the outcome. Another challenge with CAR is difficulty in inference due to dependence between subjects induced by the CAR procedure. Existing bootstrap-based inference methods emulate the CAR design by reassigning treatment within each bootstrap sample, which causes difficulty in interval estimation under CAR with continuous covariates. We propose a bootstrap method with unequal probability resampling corresponding to the CAR design, avoiding reassignment within each bootstrap sample. In simulations, the proposed CAR methods reduced prognostic imbalance, thereby improving estimation precision compared to existing assignment designs, and the proposed bootstrap method accurately assessed estimation uncertainty under our proposed CAR. An application to Clazosentan trials demonstrated that the proposed CAR methods similarly improved prognostic balance, and the proposed bootstrap method closely reproduced the distribution induced by the proposed CAR.
Related
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BibTeX
@misc{seya2026covariateadaptive,
title = {{Covariate-adaptive randomization using historical data and bootstrap-based inference}},
author = {Nodoka Seya and Masataka Taguri and Osamu Togo and Kengo Kamatani},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26254},
eprint = {2610.26254},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26254},
}
RIS
TY - UNPB
TI - Covariate-adaptive randomization using historical data and bootstrap-based inference
AU - Nodoka Seya
AU - Masataka Taguri
AU - Osamu Togo
AU - Kengo Kamatani
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26254
UR - https://arxiv.org/abs/2610.26254
AB - Covariate-adaptive randomization (CAR) can improve the efficiency of average treatment effect (ATE) estimation by reducing chance imbalances in prognostic baseline covariates. A recently proposed CAR method that balances multiple covariates, including continuous ones, can achieve optimal precision when the conditional mean of the outcome can be expressed as a linear combination of the covariate features used for the CAR procedure. However, this condition may be difficult to satisfy when the relationship between covariates and the outcome is nonlinear. Furthermore, directly balancing multiple covariates may reduce estimation precision in finite samples. We propose three CAR methods that incorporate a prognostic score learned from individual-level historical data into their imbalance measures. The prognostic score reduces multiple covariates to one dimension while giving larger weights to covariates that are more strongly associated with the outcome. Another challenge with CAR is difficulty in inference due to dependence between subjects induced by the CAR procedure. Existing bootstrap-based inference methods emulate the CAR design by reassigning treatment within each bootstrap sample, which causes difficulty in interval estimation under CAR with continuous covariates. We propose a bootstrap method with unequal probability resampling corresponding to the CAR design, avoiding reassignment within each bootstrap sample. In simulations, the proposed CAR methods reduced prognostic imbalance, thereby improving estimation precision compared to existing assignment designs, and the proposed bootstrap method accurately assessed estimation uncertainty under our proposed CAR. An application to Clazosentan trials demonstrated that the proposed CAR methods similarly improved prognostic balance, and the proposed bootstrap method closely reproduced the distribution induced by the proposed CAR.
ER -