arXiv 7 Mar 2026 · Statistics — Methodology
arXiv:2603.07055 · PDF · DOI · OpenAlex · Extracted main text
In modern randomized experiments, large-scale data collection increasingly yields rich baseline covariates and auxiliary information from multiple sources. Such information offers opportunities for more precise treatment effect estimation, but it also raises the challenge of integrating heterogeneous information coherently without compromising validity. Covariate-adaptive randomization (CAR) is widely used to improve covariate balance at the design stage, but it typically balances only a small set of covariates used to form strata, making covariate adjustment at the analysis stage essential for more efficient estimation of treatment effects. Beyond standard covariate adjustment, it is often desirable to incorporate auxiliary information, including cross-stratum information, predictions from various machine learning models, and external data from historical trials or real-world sources. While this auxiliary information is widely available, existing covariate adjustment methods under CAR primarily exploit within-stratum covariates and do not provide a coherent mechanism for integrating it. We propose a unified calibration framework that integrates such information through an information proxy vector and calibration weights defined by a convex optimization problem. The resulting estimator recovers many recent covariate adjustment procedures as special cases while providing a systematic mechanism for both internal and external information borrowing within a single framework. We establish large-sample validity and a no-harm efficiency guarantee, showing that incorporating additional information sources cannot increase asymptotic variance, and we extend the theory to settings in which both the number of strata and the number of information sources grow with the sample size.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Tu, Ma \ Liu (2024) `A unified framework for covariate adjustment under stratified randomisation', Stat 13(4), e70016 | 1.000 | 13 | 5 | 100% |
| 2 | Bannick, Shao, Liu, Du, Yi \ Ye (2025) `A general form of covariate adjustment in clinical trials under covariate-adaptive randomization', Biometrika 112(3), asaf029 | 1.000 | 10 | 4 | 100% |
| 3 | Bugni, Canay \ Shaikh (2019) `Inference under covariate-adaptive randomization with multiple treatments', Quantitative Economics 10(4), 1747–1785 | 1.000 | 6 | 3 | 100% |
| 4 | Liu, Tu \ Ma (2023) `Lasso-adjusted treatment effect estimation under covariate-adaptive randomization', Biometrika 110(2), 431–447 | 1.000 | 6 | 3 | 100% |
| 5 | Rafi (2023) `Efficient semiparametric estimation of average treatment effects under covariate adaptive randomization' | 0.969 | 11 | 6 | 91% |
| 6 | Ma, Tu \ Liu (2022) `Regression analysis for covariate-adaptive randomization: A robust and efficient inference perspective', Statistics in Medicine… | 0.956 | 8 | 4 | 88% |
| 7 | Pocock \ Simon (1975) `Sequential treatment assignment with balancing for prognostic factors in the controlled clinical trial', Biometrics 31(1), 103–… | 0.928 | 4 | 4 | 100% |
| 8 | Gu, Liu \ Ma (2024) `Incorporating external data for analyzing randomized clinical trials: A transfer learning approach' | 0.928 | 4 | 3 | 100% |
| 9 | Dupas, Karlan, Robinson \ Ubfal (2018) `Banking the unbanked? evidence from three countries', American Economic Journal: Applied Economics 10(2), 257–297 | 0.874 | 6 | 2 | 100% |
| 10 | Bugni, Canay \ Shaikh (2018) `Inference under covariate-adaptive randomization', Journal of the American Statistical Association 113(524), 1784–1796 | 0.843 | 4 | 3 | 75% |
Showing the top 10 of 62 scored citations.