On Optimal Allocation of Experimental Units with Known Covariates into Multiple Treatment Groups

Abstract

Finding the optimal design for allocating two or more treatments to a fixed group of experimental units with several known covariates is an important problem in many studies. With the objective of efficient estimation of the treatment effect or the covariate effects or both with regard to the well-known D- and or A- D _s - and A _s - optimalities, as well as some other robustness criteria, Hore et al.[1] considered this allocation problem in case of two treatments. In the present article, the method has been extended to r(≥2) treatments and the proposed design has been compared with several other allocation rules available in the literature including the most popular one, the randomized allocation rule. It is to be noted that finding the exact optimal allocation design with the above objective is computationally intractable in case of large number of experimental units having information on multiple covariates. By generalizing the algorithm of Hore et al.[1], a near-optimum allocation design may be obtained with less computational burden. Some simulation studies and real life data analysis have been undertaken to demonstrate the efficacy of the proposed algorithm in comparison with others for the case of multiple treatments.