Problem
Research questions and friction points this paper is trying to address.
Covariate Adjustment
Monotonicity
Empirical Likelihood
Randomized Experiment
Distribution Function
Shape-Preserving Covariate Adjustment via Empirical Likelihood in Randomized Experiment
๐ค AI Summary
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๐ Abstract
Covariate adjustment improves estimation efficiency in randomized experiments, but standard calibration and augmentation methods, when applied to distribution or survival functions, do not preserve monotonicity---a fundamental property of the estimand. We propose using empirical likelihood with covariate-balancing constraints to construct a covariate-adjusted empirical measure for each treatment arm. Estimators of a broad class of distributional functionals, including cumulative distribution functions, survival functions, quantiles, and restricted mean survival times, are then derived as plug-in functionals of this measure, automatically inheriting proper shape constraints. We establish asymptotic normality with an explicit, guaranteed efficiency gain over unadjusted estimators. The asymptotic distributions are invariant to the randomization scheme, providing a unified inference procedure under simple randomization and all commonly used covariate-adaptive designs satisfying a mild balancing condition. This unified construction, adjusting the empirical measure once and deriving all estimators from it, offers a principled reconciliation of covariate adjustment with shape preservation. Simulations and an application to the SURPASS-4 trial confirm the theoretical gains.
Innovation
Methods, ideas, or system contributions that make the work stand out.
empirical likelihood
covariate adjustment
shape preservation
randomized experiments
asymptotic normality
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