The Role of Pairwise Matching in Experimental Design for an Incidence Outcome

TL;DR

This paper demonstrates that pairwise matching in experimental design optimally reduces mean squared error for binary outcomes, outperforming other block designs and providing robustness against adversarial responses.

Contribution

It proves the optimality and minimax properties of pairwise matching designs for binary outcome experiments under a nonparametric model.

Findings

Pairwise matching minimizes mean squared error compared to other designs.

The design is robust under adversarial response models.

Simulation and clinical data support theoretical results.

Abstract

We consider the problem of evaluating designs for a two-arm randomized experiment with an incidence (binary) outcome under a nonparametric general response model. Our two main results are that the priori pair matching design of Greevy et al. (2004) is (1) the optimal design as measured by mean squared error among all block designs which includes complete randomization. And (2), this pair-matching design is minimax, i.e. it provides the lowest mean squared error under an adversarial response model. Theoretical results are supported by simulations and clinical trial data.