Efficiency of experimental designs for comparing two treatments with correlated binary responses

In this article, we consider the efficiency of three experimental designs for comparing two treatments with correlated binary outcomes. This work is motivated in large part by the use of toxicological bioassays with laboratory animals used to identify agents capable of causing adverse health effects in humans, but has much broader research design implications. From the toxicological perspective, the completely randomized (CR), litter-matched (LM) and nested (NE) designs correspond to the random assignment of individual animals, littermates, or entire litters to either a control or test group. The randomization schemes underlying these three designs provide a framework for the construction of exact randomization tests for comparing the two treatment groups, and for the development of the asymptotic properties of these tests. The computed Pitman asymptotic relative efficiencies demonstrate that the LM design is the most powerful in the presence of positive intra-litter correlation, followed by the CR and NE designs, respectively. The relevance of these asymptotic results for the finite sample case is confirmed by computer simulation. The more detailed results presented in this paper will be of value in informing the design of experiments with two treatment groups involving correlated binary outcomes.