Abstract: We investigate optimal factorial designs for cDNA microarray experiments, where the parameters of interest differ from traditional factorials. We apply approximate theory to obtain analytical results for 22 factorial. More general, including asymmetric factorials are considered next and tools of Kronecker representation and unimodularity are employed to derive strong exact result on optimal saturated designs. Its impact on the study of optimal or efficient nearly saturated designs is also investigated. These results are then extended to more intricate situation where the underlying model incorporates dye-colouring effects, and finally the role of dye-swapping is critically examined.

(A joint work with Rahul Mukerjee, Indian Institute of Management, Calcutta)