Degrees of Randomness in Rerandomization Procedures

TL;DR

This paper investigates the spectrum of rerandomization procedures in experimental design, proposing a method to optimize the balance between randomness and covariate balance, supported by new tools like the fastrerandomize R package.

Contribution

It introduces a framework linking rerandomization and deterministic assignment, and provides tools for optimal threshold selection in rerandomization procedures.

Findings

Deterministic assignment is an extreme case of rerandomization.

Optimal rerandomization thresholds improve covariate balance.

New R package fastrerandomize facilitates implementation.

Abstract

Randomized controlled trials are susceptible to imbalance on covariates predictive of the outcome. Rerandomization and deterministic treatment assignment are two proposed solutions. This paper explores the relationship between rerandomization and deterministic assignment, showing how deterministic assignment is an extreme case of rerandomization. The paper argues that in small experiments, both fully randomized and fully deterministic assignment have limitations. Instead, the researcher should consider setting the rerandomization acceptance probability based on an analysis of covariates and assumptions about the data structure to achieve an optimal alignment between randomness and balance. This allows for the calculation of minimum p-values along with valid permutation tests and fiducial intervals. The paper also introduces tools, including a new, open-source R package named fastrerandomize, to implement rerandomization and explore options for optimal rerandomization acceptance thresholds.