Modeling Microarray Data: Interpreting and communicating the biological results

Various statistical models have been proposed for detecting differential gene expression in data from microarray experiments. Given such detection, we are usually interested in describing the differential expression patterns. Due to the large number of genes that are typically analysed in microarray experiments, possibly more than ten thousand, the tasks of interpretation and communication of all the corresponding statistical models pose a considerable challenge, except perhaps in the simplest experiment involving only two groups. A further challenge is to find methods to summarize the resulting models. These challenges increase with experimental complexity. Biologists often wish to sort genes into ‘classes’ with similar response profiles/patterns. So, in this paper we describe a likelihood approach for assigning genes to these different class patterns for data from a replicated experimental design. The number of potential patterns increases very quickly as the number of combinations in the experimental design increases. In a two group experimental design there are only three patterns required to describe the mean response: up, down and no difference. For a factorial design with three treatments there are 13 different patterns, and with four levels there are 75 potential patterns to be considered, and so on. The approach is applied to the identification of differential response patterns in gene expression from a microarray experiment using RNA extracted from the leaves of Arabidopsis thaliana plants. We compare patterns of response found using additive and multiplicative models. A multiplicative model is more commonly used in the statistical analysis of microarray data because of the variance stabilizing properties of the logarithmic function. Then the error structure of the model is taken to be log-Normal. On the other hand, for the additive model the gene expression value is modeled directly as being from a gamma distribution which successfully accounts for the constant coefficient of variation often observed. Appropriate visualization displays for microarray data are important as a way of communicating the patterns of response amongst the genes. Here we use graphical ‘icons’ to represent the patterns of up/down and no response and two alternative displays, the Gene-plot and a grid layout to provide rapid overall summaries of the gene expression patterns.