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

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.