New techniques in clustering and microarray data analysis.

Abstract

In recent years, the use of gene expression data has expanded to many areas of medical research, drug discovery and development. Technological development will enable the entire human genome to be spotted onto one microarray in the near future. It is an exciting time for statisticians to deal with the explosive growth of this type of data. This thesis tackles two of the open questions regarding analysis of large scale gene expression data. Multiplicity issues arise when attempting to discern which of the ∼10,000 genes are differentially expressed. The Multiplicity-Adjusted Order Statistics Analysis (MAOSA) technique developed in the thesis is based on the normality of the middle portion of the distribution of the test statistics. After a transformation of the test statistics to the uniform scale, known features of the uniform order statistics are used to facilitate analysis. The multiplicity problem will be dealt with by performing a Bonferroni correction on a small number of hypothesis tests. Real data are used to illustrate the technique and compare it to existing methods. There is no tool to explore the relationship between groups of clustered genes at both the cluster level and the object level (i.e., gene-to-gene). The Inter-Cluster Investigator (ICI) is developed to address this need. It identifies positive and negative associations between clusters that have previously been overlooked. These cluster-level relationships may indicate repression or regulation in gene expression data. Once a significant cluster-level association is found, the ICI procedure will move to the object (gene)-level to identity associations that are driving the between-cluster relationship. The ICI method yields an alternative way of characterizing the between-object relationship that builds upon the existing structure obtained from clustering. Effectiveness of the ICI method is demonstrated in the analysis of gene expression data.