Optimal snsn factorial designs when observations within-blocks are correlated

In this article, we characterize D-optimal designs for snsn symmetric factorial experiments when observations within blocks are correlated. The motivation to this problem lies in a pharmaceutical experiment where the experimenter needed to develop a once-daily tablet using a factorial design. These experiments are usually conducted in healthy human volunteers and the bioavailability is estimated. Since each subject is administered more than one formulation, the observations within subjects are correlated. We provide an explicit construction of DD-optimal designs for snsn factorial experiment with blocks of size s or multiples of s  , where observations within blocks are correlated. We discuss in detail the construction of optimal designs for 2n2n factorial experiments. We also provide an analytical proof of the DD-optimality when there exist a pair of blocks of odd size and remaining blocks are of even size.