Optimal designs for 2-color microarray experiments

Abstract

Statisticians can play a crucial role in the design of gene expression studies to ensure the most effective allocation of available resources. This paper considers Pareto optimal designs for gene expression studies involving 2-color microarrays. Pareto optimality enables the recommendation of designs that are particularly efficient for the effects of most interest to biologists. This is relevant in the microarray context where analysis is typically carried out separately for those effects. Our approach will allow for effects of interest that correspond to contrasts rather than solely considering parameters of the linear model. We further develop the approach to cater for additional experimental considerations such as contrasts that are of equal scientific interest. This amounts to partitioning all relevant contrasts into subsets of effects that are of equal importance. Based on the partitions, a penalty is employed in order to recommend designs for complex and varied microarray experiments. Finally, we address the issue of gene-specific dye bias. We illustrate using studies of leukemia and breast cancer.

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

“…The design problem in this situation becomes rather complex. As noted in Sanchez and Glonek (2009), this happens on three counts:…”

“…Yang and Speed (2002) introduced this parametrization for factorial designs, while Glonek and Solomon (2004) reported illuminating admissibility results through complete enumeration, primarily for the factorial and also touching upon the 2 factorial. The idea of admissibility was followed up by Sanchez and Glonek (2009) and Sanchez (2010), who termed it Pareto optimality and studied Pareto optimal designs for linear functions of the main effects and interactions in and factorials under the baseline parametrization, by complete enumeration for smaller designs, and simulated annealing for larger designs. Banerjee and Mukerjee (2008) derived theoretical results on optimal factorial designs under the baseline parametrization.…”

Optimality Criteria for the Design of 2-Color Microarray Studies

“…There is broad agreement that a design criterion should match, as closely as possible, the scientific objectives of a study (Sanchez and Glonek, 2009; Wit et al, 2005). In a microarray study there are scientific questions of interest that correspond to contrasts of interest.…”

“…For two-color microarrays, an immediate question in the early stages of planning a microarray study is how to choose the arrangement of samples onto the microarrays. Multiple papers have taken up this question, including Kerr and Churchill (2001); Dobbin and Simon (2002); Yang and Speed (2002); Kerr (2003a); Wit et al (2005); Kerr (2006); Bailey (2007); Sanchez and Glonek (2009). Some of these papers have utilized the so-called ”alphabet” design criteria such as A - and D -optimality to evaluate microarray designs.…”

Qualification des dispositifs expérimentaux par deux algorithmes de blocage <em>a posteriori</em>

“…En somme, il ressort de cette étude que les blocs dans les essais en champs en région tropicale ne répondent pas aux conditions théoriques de la planification expérimentale et de l'analyse de la variance. Comme dans le cas des études d'expression des gènes, les statisticiens peuvent jouer un rôle crucial en assurant une meilleure allocation des unités expérimentales (Sanchez et Glonek, 2009). En effet¸ l'utilisation des blocs aléatoires complets en région tropicale est parfois nuisible à l'expérimentation et les résultats obtenus mettent en évidence 50% d'essais en randomisation totale meilleurs que le bloc aléatoire complet.…”