The Efficient Covariate-Adaptive Design for high-order balancing of quantitative and qualitative covariates

In the context of sequential treatment comparisons, the acquisition of covariate information about the statistical units is crucial for the validity of the trial. Furthermore, balancing the assignments among covariates is of primary importance, since the potential imbalance of the covariate distributions across the groups can severely undermine the statistical analysis. For this reason, several covariate-adaptive randomization procedures have been suggested in the literature, but most of them only apply to categorical factors. In this paper we propose a new class of rules, called the Efficient Covariate-Adaptive Design, which is high-order balanced regardless of the number of factors and their nature (qualitative and/or quantitative), also accounting for every order covariate effects and interactions. The suggested procedure performs very well, is flexible and simple to implement. The advantages of our proposal are also analyzed via simulations and its finite sample properties are compared with those of other well-known rules, by also including the redesign of a real clinical trial.