Covariate Adjustment in Randomized Experiments: A Unified Framework for Decision and Practice
Abstract
Should researchers adjust for covariates in randomized experiments, and if so, how? The literature offers three distinct prescriptions: do not adjust because randomization guarantees unbiasedness; adjust for outcome-prognostic covariates to improve precision; or adjust for covariates imbalanced between treatment arms. These competing prescriptions create confusion and uncertainty. We develop a unified framework for decision and practice. Given available information, we show that the optimal correction is what we call ex-post bias. The only relevant criterion for adjustment is prognosticity for ex-post bias; neither raw covariate imbalance nor outcome prognosticity is sufficient by itself. We also show that correcting imbalance and improving precision are two sides of the same decision problem. We develop two estimation approaches, one of which recovers familiar adjustment estimators and provides a new theoretical justification for them. Simulations compare alternative covariate-selection and adjustment strategies. Overall, our framework provides a unified foundation for covariate adjustment in randomized experiments.
Related
- Automated, Efficient, and Model-Free Inference for Randomized Clinical Trials via Data-Driven Covariate Adjustment
- Regression adjustment in completely randomized experiments with many covariates
- Covariate Adjustment for Time-Restricted Marginal Win Statistics in Randomized Trials: Assumption-Lean Inference and Guaranteed Efficiency Gain
- Regression Adjustment for Ratios of Treatment Effects in Randomized Experiments
- Simple Covariate Adjustment for Many Estimands Using Stable Balancing Weights
BibTeX
@misc{fu2026covariate,
title = {{Covariate Adjustment in Randomized Experiments: A Unified Framework for Decision and Practice}},
author = {Jiawei Fu and Donald P. Green},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.09039},
eprint = {2609.09039},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.09039},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Covariate Adjustment in Randomized Experiments: A Unified Framework for Decision and Practice
AU - Jiawei Fu
AU - Donald P. Green
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2609.09039
UR - https://arxiv.org/abs/2609.09039
AB - Should researchers adjust for covariates in randomized experiments, and if so, how? The literature offers three distinct prescriptions: do not adjust because randomization guarantees unbiasedness; adjust for outcome-prognostic covariates to improve precision; or adjust for covariates imbalanced between treatment arms. These competing prescriptions create confusion and uncertainty. We develop a unified framework for decision and practice. Given available information, we show that the optimal correction is what we call ex-post bias. The only relevant criterion for adjustment is prognosticity for ex-post bias; neither raw covariate imbalance nor outcome prognosticity is sufficient by itself. We also show that correcting imbalance and improving precision are two sides of the same decision problem. We develop two estimation approaches, one of which recovers familiar adjustment estimators and provides a new theoretical justification for them. Simulations compare alternative covariate-selection and adjustment strategies. Overall, our framework provides a unified foundation for covariate adjustment in randomized experiments.
ER -