Regression Adjusted Target Effects Using Auxiliary Strata Under Design‐Based Inference

ABSTRACT

We propose a design‐based covariate adjustment that leverages information from auxiliary strata to improve the efficiency of average treatment effect estimation when target samples are sparse. The estimator borrows strength from related strata that may be correlated with the target, yielding gains for studies with limited observations or rare subpopulations. We present the estimator, develop a Neyman‐style conservative variance estimator for hypothesis testing and confidence interval construction, and establish its large‐sample properties. The procedure is straightforward to implement within standard randomization‐based workflows and does not require a correctly specified outcome model or stochastic error assumptions. In simulations, the method delivers lower variance and narrower confidence intervals than conventional design‐based or regression‐adjusted estimators across a range of sparsity and correlation patterns. Applications to a schooling experiment and the ACTG 175 randomized trial illustrate practical gains in precision.