Screening for Differential Gene Expressions from Microarray Data

Living organisms need proteins to provide structure, such as skin and bone, and to provide function to the organism through, for example, hormones and enzymes. Genes are translated to proteins after first being transcribed to messenger RNA. Even though every cell of an organism contains the full set of genes for that organism, only a small set of the genes is functional in each cell. The levels at which the different genes are functional in various cell types (their expression levels) can all be screened simultaneously using microarrays. The design of two-channel microarray experiments is discussed and ideas are illustrated through the analysis of data from a designed microarray experiment on gene expression using liver and muscle tissue. The number of genes screened in a microarray experiment can be in the thousands or tens of thousands. So it is important to adjust for the multiplicity of comparisons of gene expression levels because, otherwise, the more genes that are screened, the more likely incorrect statistical inferences are to occur. Different purposes of gene expression experiments may call for different control of multiple comparison error rates. We illustrate how control of the statistical error rate translates into control of the rate of incorrect biological decisions. We discuss the pros and cons of two forms of multiple comparisons inference: testing for significant difference and providing confidence bounds. Two multiple testing principles are described: closed testing and partitioning. Stepdown testing, a popular form of gene expression analysis, is shown to be a shortcut to closed and partitioning testing. We give a set of conditions for such a shortcut to be valid.