Optimal factorial designs for cDNA microarray experiments

TL;DR

This paper develops optimal design strategies for cDNA microarray experiments with factorial structures, focusing on baseline parametrization and including dye-coloring effects, to improve experimental efficiency.

Contribution

It introduces analytical solutions for 2x2 factorial designs and extends to complex factorials and dye effects, offering practical design approaches.

Findings

Optimal designs for 2x2 factorials are analytically derived.

Saturated designs provide the most economical solutions.

Inclusion of dye effects and swapping impacts design efficiency.

Abstract

We consider cDNA microarray experiments when the cell populations have a factorial structure, and investigate the problem of their optimal designing under a baseline parametrization where the objects of interest differ from those under the more common orthogonal parametrization. First, analytical results are given for the $2\times 2$ factorial. Since practical applications often involve a more complex factorial structure, we next explore general factorials and obtain a collection of optimal designs in the saturated, that is, most economic, case. This, in turn, is seen to yield an approach for finding optimal or efficient designs in the practically more important nearly saturated cases. Thereafter, the findings are extended to the more intricate situation where the underlying model incorporates dye-coloring effects, and the role of dye-swapping is critically examined.