YASMA - Yet Another Statistical Microarray Analysis

One problem arising in the analysis of gene expression data from microarrays is the identification of differentially expressed genes. There exist some popular rules, for example, to accept two-fold over or under-expression as significant. Though such rules might be quite useful in providing a quick overview, statistics has to offer a more thorough approach. By considering the amount of variability between replicates of the same experiments, a statistical significance in form of p-values can be assigned to differential gene expression levels.

YASMA is an add-on library for the R statistical package and can be used to analyse simple replicated experiments. For example, we are interested in bacterial genes over- or under-expressed in mutants as compared to the wild type. For this purpose, multiple mRNA preparations are hybridized on several arrays. As long as the same number of arrays is used for each preparation a straightforward ANOVA analysis and analysis of variance components can be applied to the series of experiments (a balanced factorial design).

At the moment the package contains

• Routines for inspecting the correlation between array replicates and for removing low expression genes that cause low correlation.
• A method for interpolating missing data using estimates from an ANOVA analysis.
• Routines for fast ANOVA analysis of data typical for microarrays experiments (balanced factorial designs with nested factors). The design matrix for such analysis is usually very large (due to the effects involving genes) and cannot be dealt with efficiently by standard ANOVA routines based on design matrix evaluations.
• Routines for an analysis of variance components: cultures, arrays, etc are random representatives of possible experiments and need to be analyzed in a slightly different way than by simple ANOVA.
• A routine to caculate the optimal design of an experiment based on relative costs of cultures, arrays, etc, and on estimates of variability from a prior experiment.
• Calculation of p-values derived from the results of the analysis of variance components. If residuals show different amounts of variance (which is often the case), hierarchical bootstrapping of residuals is a more reliable way to derive p-values.
• Implementations of additional standard tests (t-statistic) and of Newton's et. al hierarchical model methods (see below the Statistics Notes) for multiple experiments.

As the name suggests YASMA is intendended as a complement to the SMA microarray analysis package. High on my list of future extensions are the incorporation of regression analysis for time series data and extensions to more general designs (eg, latin square design).

Downloads

• yasma_0.20.tar.gz (17/02/03), an R library for the ANOVA analysis of replicated microarray experiments (balanced factorial designs only)
• YASMA tutorial (v0.19,14/05/02) , which provides a quick tour through a typical ANOVA analysis of microarray experiments (A4 version for printing).
• replicates.pdf (14/05/02), a manuscript explaining our approach to normalization, filtering, ANOVA analysis, analysis of variance components, and significance analysis for differential expression in detail.
• Statistics notes, which are primarily for my own reference, but other people may find them useful as well. I will update them continuously. At the moment the notes contain some background and additional explanations of the hierarchical models approach by M.A. Newton et. al., On differential variability of expression ratios: Improving statistical inference about gene expression changes from microarray data, Journal of Computational Biology 8:37-52, 2001 (abstract, paper) and how to extend it to a multiple slide analysis.

This is joint work with Sharon Kendall, Neil Stoker, Shamit Soneji, and the Bugs group