Statistical equivalence in gene expression studies.

Abstract

The goal of this thesis is to develop methods that enable researchers to identify genes with a pre-specified profile in gene expression studies. The motivation for these methods is a gene expression study performed at the University of Adelaide to identify the genes associated with pluripotency in mouse embryonic stem cells. The method developed, gene profiling, utilises intersection-union tests that combine tests both for equivalent and differential expression. The theoretical basis of gene profiling and its application to the stem cell data are discussed in the thesis, as well as a comparison of gene profiling to alternative methods described in the literature for identifying genes corresponding to a pre-specified profile. In the second part of this thesis, `strength of evidence' measures for equivalence and gene profiling are developed. A P-value for equivalence is shown to have undesirable properties and a posterior probability of equivalence is proposed. The calculation of the posterior probabilities for equivalence using a hierarchical model is described and extended to gene profiling. A method to calculate q-values from the posterior probabilities is described. The resultant q-values are compared to the posterior probabilities.