Balanced and Robust Multi-Treatment Experimental Designs via Randomized Differencing

Qing Chen, Jing Jia, Peng Zhang

TL;DR: We propose the first multi-arm RCT design that achieves exponential covariate balance improvements, preserves robustness, and runs in near-linear time.

Abstract: We introduce GKK+, a new design for multi-arm randomized controlled trials. Standard Bernoulli randomization is robust but often yields poor covariate balance, while existing restricted-randomness designs mainly address two-arm settings. GKK+ extends the Karmarkar–Karp (KK) differencing method to multiple arms. When covariates are smooth and well-behaved, GKK+ achieves an exponentially better covariate balance than the standard Bernoulli design while preserving sufficient randomness. GKK+ improves efficiency in treatment effect estimation while supporting standard asymptotic inference. Simulations on synthetic and real datasets demonstrate improved balance and lower estimator variance compared to existing methods.

Submission Number: 634