Sequential rerandomization

TL;DR

This paper develops a mathematical framework for sequential rerandomization in experiments where units are enrolled in groups, demonstrating it can achieve better covariate balance than traditional rerandomization.

Contribution

It introduces a novel sequential rerandomization method with theoretical guarantees, extending the classic rerandomization approach to sequential enrollment scenarios.

Findings

Sequential rerandomization achieves better covariate balance than one-time rerandomization.

The method is effective for balancing covariates over continuous or binary variables.

Theoretical proof supports improved performance under mild assumptions.

Abstract

The seminal work of Morgan and Rubin (2012) considers rerandomization for all the units at one time. In practice, however, experimenters may have to rerandomize units sequentially. For example, a clinician studying a rare disease may be unable to wait to perform an experiment until all the experimental units are recruited. Our work offers a mathematical framework for sequential rerandomization designs, where the experimental units are enrolled in groups. We formulate an adaptive rerandomization procedure for balancing treatment/control assignments over some continuous or binary covariates, using Mahalanobis distance as the imbalance measure. We prove in our key result, Theorem 3, that given the same number of rerandomizations (in expected value), under certain mild assumptions, sequential rerandomization achieves better covariate balance than rerandomization at one time.