A New Sequential Randomization Procedure for Comparative Experiments

For comparative experiments with several treatments, balancing the arms optimizes inference about the treatment effects under homoscedasticity. Moreover, ensuring that treatment groups are comparable in terms of key covariates is another critical aspect. Often, this translates into the equality of the covariate distributions in the treatment arms; while in the presence of heteroscedasticity the optimal design may induce a more complex structure that generally depends on the unknown model parameters. In all these cases, the optimal designs are characterized by a set of equality constraints involving, for instance, the percentage of allocations to each treatment and the empirical moments of the covariates in the different arms. We propose a new sequential randomization procedure for implementing optimal designs based on equality constraints across the treatment groups; the suggested sequential design is aimed at minimizing the variances of the group-specific elements involved in the optimal design. A simulation study shows the validity of the approach, which guarantees a significant improvement in the convergence to the optimum.