Mixture-Regression Cluster Model applied to Longitudinal Microarray Experiments
Emma Holian · 2007
The aim of this work is to explore various statistical techniques to identify genes which contribute to some change in phenotype level. For example, the response of fish kept under stressful conditions for various lengths of time. We aim to assess the level of dierential expression of each gene in the tissue samples and also attempt to model the expression patterns of genes over time, not only to classify genes by similarities in expression patterns, but also to model these patterns as specified functions. The proposed Mixture-Regression Cluster Model is developed to model and cluster the genes into groups according to their expressions measured over time. This model is similar to that of the multivariate normal mixture model in that clusters are identified by the EM algorithm but is adapted to incorporate the flexibility of regression curves to fit the trends. In this way, additional features such as covariates, random eects and correlation structures can be incorporated into the model while potentially oering a considerable saving on the number of parameters required to model the trends. 1. Introduction and Background Microarray technology measures genetic expression in the cells of a tissue sample and is implemented to identify the function of genes in an organism. A cDNA microarray can measure the genetic expression exhibited in two tissue samples. The animal sources from which these tissue samples are taken are often chosen because they dier in phenotype for some particular trait, for example, trout fish displaying symptoms of stress versus unstressed trout. The source with the phenotype trait is often labelled as the treatment and the source not displaying the trait labelled the control. Of course the genetic makeup of any one phenotype consists of many thousands of genes and so detecting which genes are relevant to that particular trait is no menial task. The microarray facilitates detection of the presence and abundance of the expression exhibited in the tissue samples of thousands of genes simultaneously since an array consists of thousands of probes of dierent genetic material spotted at key locations on a glass slide. The level of expression of a gene at a spot is measured by recording the levels of intensity of two fluorescent dye molecules, Cyan 5 and Cyan 3, when the array is excited by