IDENTIFYING INTERESTING GENES WITH SIGGENES Identifying Interesting Genes with siggenes

A common and important task in microarray experiments is the identification of genes whose expression values differ substantially between groups or conditions. Finding such differentially expressed genes requires methods that can deal with multiple testing problems in which thousands or even tens of thousands of hypotheses are tested simultaneously. Usually, a statistic appropriate for testing if the expression levels are associated with a covariate of interest and the corresponding p-value are computed for each gene. Afterwards, these raw p-values are adjusted for multiplicity such that a Type I error rate is strongly controlled at a pre-specified level of significance. The classical example of such an error rate is the family-wise error rate (FWER), i.e. the probability of at least one false positive. This error rate, however, might be too conservative for a situation in which thousands of hypotheses are tested and several tens of genes should be identified. In the analysis of microarray data, another error rate has, hence, become very popular: The False Discovery Rate (FDR) which is loosely spoken the expected proportion of false positives among all rejected null hypotheses, i.e. identified genes. There are, however, other ways to adjust for multiplicity: For example, QQ plots or the Bayesian framework can be employed for this purpose. If the observed test statistics are plotted against the values of the test statistics that would be expected under the null hypothesis most of the points will approximately lie on the diagonal. Those points that differ substantially from this line correspond to genes that are most likely differentially expressed. The Significance Analysis of Microarrays (SAM) proposed by Tusher et al. (2001) can be used to specify what “differ substantially" means. While Tusher et al. (2001) base their analysis on a moderated t statistic, Schwender et al. (2003) compare this approach with a SAM version based on Wilcoxon rank sums. Efron et al. (2001) use an empirical Bayes analysis (EBAM) to model the distribution of the observed test statistics as a mixture of two components, one for the differentially expressed genes, and the other for the not differentially expressed genes. Following their analysis, a gene is called differentially expressed if the corresponding posterior probability is larger than 0.9. Both SAM and EBAM are implemented in the Bioconductor package siggenes. In this article, we, however, will concentrate on SAM. In the following, we briefly describe the SAM procedure, its implementation in siggenes (for more details, see Schwender et al. (2003)), and the test statistics already available in this package. Afterwards, we show how you can write your own function for other testing situations. Finally, we will give an example of how sam can be applied to gene expression data.