Optimal designs for 2-color microarray experiments.

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.

Gene profiling for determining pluripotent genes in a time course microarray experiment.

In microarray experiments, it is often of interest to identify genes which have a prespecified gene expression profile with respect to time. Methods available in the literature are, however, typically not stringent enough in identifying such genes, particularly when the profile requires equivalence of gene expression levels at certain time points. In this paper, the authors introduce a new methodology, called gene profiling, that uses simultaneous differential and equivalent gene expression level testing to rank genes according to a prespecified gene expression profile. Gene profiling treats the vector of true gene expression levels as a linear combination of appropriate vectors, for example, vectors that give the required criteria for the profile. This gene profile model is fitted to the data, and the resulting parameter estimates are summarized in a single test statistic that is then used to rank the genes. The theoretical underpinnings of gene profiling (equivalence testing, intersection-union tests) are discussed in this paper, and the gene profiling methodology is applied to our motivating stem-cell experiment.

Factorial and time course designs for cDNA microarray experiments.

Microarrays are powerful tools for surveying the expression levels of many thousands of genes simultaneously. They belong to the new genomics technologies which have important applications in the biological, agricultural and pharmaceutical sciences. There are myriad sources of uncertainty in microarray experiments, and rigorous experimental design is essential for fully realizing the potential of these valuable resources. Two questions frequently asked by biologists on the brink of conducting cDNA or two-colour, spotted microarray experiments are 'Which mRNA samples should be competitively hybridized together on the same slide?' and 'How many times should each slide be replicated?' Early experience has shown that whilst the field of classical experimental design has much to offer this emerging multi-disciplinary area, new approaches which accommodate features specific to the microarray context are needed. In this paper, we propose optimal designs for factorial and time course experiments, which are special designs arising quite frequently in microarray experimentation. Our criterion for optimality is statistical efficiency based on a new notion of admissible designs; our approach enables efficient designs to be selected subject to the information available on the effects of most interest to biologists, the number of arrays available for the experiment, and other resource or practical constraints, including limitations on the amount of mRNA probe. We show that our designs are superior to both the popular reference designs, which are highly inefficient, and to designs incorporating all possible direct pairwise comparisons. Moreover, our proposed designs represent a substantial practical improvement over classical experimental designs which work in terms of standard interactions and main effects. The latter do not provide a basis for meaningful inference on the effects of most interest to biologists, nor make the most efficient use of valuable and limited resources.