Highly Efficient Factorial Designs for cDNA Microarray Experiments: Use of Approximate Theory Together with a Step-up Step-down Procedure

TL;DR

This paper introduces a novel method combining approximate theory and a step-up/down procedure to create highly efficient factorial designs for cDNA microarray experiments, accommodating unequal importance of effects and interactions.

Contribution

It develops a new approach that improves design efficiency and robustness in cDNA microarray experiments, addressing limitations of naive discretization.

Findings

Designs are nearly free from dye-color effects.

Designs are robust to heteroscedasticity.

Method works for various parametrizations.

Abstract

A general method for obtaining highly efficient factorial designs of relatively small sizes is developed for cDNA microarray experiments. The method allows the main effects and interactions of successive orders to be of possibly unequal importance. First, the approximate theory is em-ployed to get an optimal design measure which is then discretized. It is, however, observed that a na\"ive 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 highly efficient designs are found to remain almost free from possible dye-color effects under a suitable dye-color assignment. They are also seen to be quite robust to heteroscedasticity as may be caused by biological variability. 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.