Split-Plot Microarray Experiments
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METHODOLOGY
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Split-Plot Microarray Experiments Issues of Design, Power and Sample Size Pi-Wen Tsai1 and Mei-Ling Ting Lee2 1 2
Division of Biostatistics and Bioinformatics, National Health Research Institutes, Taipei, Taiwan, Republic of China Division of Biostatistics, School of Public Health, The Ohio State University, Columbus, Ohio, USA
Abstract
This article focuses on microarray experiments with two or more factors in which treatment combinations of the factors corresponding to the samples paired together onto arrays are not completely random. A main effect of one (or more) factor(s) is confounded with arrays (the experimental blocks). This is called a split-plot microarray experiment. We utilise an analysis of variance (ANOVA) model to assess differentially expressed genes for between-array and within-array comparisons that are generic under a split-plot microarray experiment. Instead of standard t- or F-test statistics that rely on mean square errors of the ANOVA model, we use a robust method, referred to as ‘a pooled percentile estimator’, to identify genes that are differentially expressed across different treatment conditions. We illustrate the design and analysis of split-plot microarray experiments based on a case application described by Jin et al. A brief discussion of power and sample size for split-plot microarray experiments is also presented.
Microarrays have been used to study the relative quantities of specific mRNAs from two or more biological samples for thousands of genes simultaneously. The primary aim is to discover genes that are differentially expressed across different treatment conditions. The word ‘treatment’ is used in its widest possible sense and includes not only applied treatments, such as different concentrations of an applied chemical, but also inherent treatments, such as the sex or age of an animal. As an example, suppose that in a factorial experiment with two factors (A and B), each factor has two levels: thus, the treatment conditions included 22 = 4 combinations of the levels of the two factors. In a two-colour spotted microarray experiment, two samples derived from cells under these four different treatment conditions are paired together onto an array. As Kerr and Churchill[1] have pointed out, a two-colour spotted microarray can be considered an experimental block with a block size of two. When there are more than two experimental conditions of interest, all sample conditions cannot appear on the same array. In this article, we focus on microarry experiments with two or more factors in which a main effect of one (or more) factor(s) is confounded with arrays (the experimental blocks), and we call this a split-plot microarray experiment.
The early development of split-plot designs occurred in agricultural research in response to a very common problem in field experiments, that of two different sizes of experimental units. The levels of a factor are randomly assigned to the larger size experimental units, called wh
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