HARMONIZING FULLY OPTIMAL DESIGNS WITH CLASSIC RANDOMIZATION IN FIXED TRIAL EXPERIMENTS
ADAM KAPELNER – QUEENS COLLEGE
There is a movement in design of experiments away from the classic randomization put forward by Fisher, Cochran and others to one based on optimization. In fixed-sample trials comparing two groups, measurements of subjects are known in advance and subjects can be divided optimally into two groups based on a criterion of “imbalance” between the two groups. However, these designs are deterministic, and thus far from being random. We seek to understand the costs and benefits of optimizing imbalance over classic randomization. We do so for different performance criterions such as Efron’s sup criterion and a quantile criterion that we motivate. In our criterion, the optimal design is shown to lie between complete randomization and optimal imbalance. Much-needed further work will provide a procedure to find this optimal design in different scenarios in practice.