Ensuring balance with regard to optimality for known categorical covariates and multiple treatment groups

Ensuring balanced allocation by achieving optimality for known categorical covariates into two treatment groups has been analytically established with regard to D−, A−, Ds− and As−optimality in Hore et al. (2020) and for E− and Es−optimality hasbeen discussed by the authors earlier. However, the mathematical complexity of expression of the respective optimality function and mathematical computation increases with more number of treatments. In this work, the relationship between D-optimality and balancing criteria for known categorical covariates across three treatment groups is established through analytical derivation and simulation studies. It has been shown that D−optimality ensures a balanced allocation design, at least as a local optimal solution. Furthermore, simulation studies demonstrate that the balanced allocation design performs uniformly better than random allocation designs.