Highly efficient factorial designs for cDNA microarray experiments: use of approximate theory together with a step-up step-down procedure

A general method for obtaining highly efficient factorial designs of relatively small sizes is developed for cDNA microarray experiments. It allows the main effects and interactions to be of possibly unequal importance. First, the approximate theory is employed to get an optimal design measure which is then discretized. It is, however, observed that a naïve discretization may fail to yield an exact design of the stipulated size and, even when it yields such an exact design, there is often scope for improvement in efficiency. To address these issues, we propose a step-up/down procedure which is seen to work very well. The resulting designs turn out to be quite robust to possible dye-color effects and heteroscedasticity. We focus on the baseline and all-to-next parametrizations but our method works equally well also for hybrids of the two and other parametrizations.