WHOMP: Optimizing Randomized Controlled Trials via Wasserstein Homogeneity

TL;DR

This paper introduces WHOMP, a novel partitioning method using Wasserstein homogeneity to improve subgroup diversity and reduce errors in controlled trials, outperforming existing techniques.

Contribution

The paper presents the WHOMP method, a new optimal partitioning approach that minimizes errors and balances subgroup stability, with algorithms and theoretical analysis.

Findings

WHOMP outperforms traditional partitioning methods in numerical experiments.

Theoretical analysis reveals a trade-off between subgroup mean stability and variance.

Algorithms effectively find optimal solutions balancing this trade-off.

Abstract

We investigate methods for partitioning datasets into subgroups that maximize diversity within each subgroup while minimizing dissimilarity across subgroups. We introduce a novel partitioning method called the $\textit{Wasserstein Homogeneity Partition}$ (WHOMP), which optimally minimizes type I and type II errors that often result from imbalanced group splitting or partitioning, commonly referred to as accidental bias, in comparative and controlled trials. We conduct an analytical comparison of WHOMP against existing partitioning methods, such as random subsampling, covariate-adaptive randomization, rerandomization, and anti-clustering, demonstrating its advantages. Moreover, we characterize the optimal solutions to the WHOMP problem and reveal an inherent trade-off between the stability of subgroup means and variances among these solutions. Based on our theoretical insights, we design algorithms that not only obtain these optimal solutions but also equip practitioners with tools to select the desired trade-off. Finally, we validate the effectiveness of WHOMP through numerical experiments, highlighting its superiority over traditional methods.