Optimality of Matched-Pair Designs in Randomized Controlled Trials

TL;DR

This paper demonstrates that a specific matched-pair design in stratified RCTs maximizes statistical precision for estimating the average treatment effect, outperforming other schemes in simulations.

Contribution

It identifies the optimal stratified randomization scheme, pairing units based on baseline outcomes to improve estimator precision in RCTs.

Findings

Matched-pair design maximizes statistical precision.

Simulation shows 10% average reduction in standard error.

Up to 34% reduction in standard error in some cases.

Abstract

In randomized controlled trials (RCTs), treatment is often assigned by stratified randomization. I show that among all stratified randomization schemes which treat all units with probability one half, a certain matched-pair design achieves the maximum statistical precision for estimating the average treatment effect (ATE). In an important special case, the optimal design pairs units according to the baseline outcome. In a simulation study based on datasets from 10 RCTs, this design lowers the standard error for the estimator of the ATE by 10% on average, and by up to 34%, relative to the original designs.