DNA microarrays are a widely used technology for genome-wide analysis of mRNA levels under different experimental conditions. Monitoring developmental changes of human and non-human organisms via changes in gene expression can provide us a way of unraveling
biological processes at the cellular level. However, determining true genomic differences between samples can be difficult due to the tremendous amount of noise. Analysis of microarray data includes the detection of differentially expressing genes among experimental groups, high dimensional variable selection, detection and stabilization of heterogeneity of variances and unraveling the inter-relationship between genes.
The focus of this thesis is development of statistical methodology for comprehensive analysis of microarray data. Our main focus here is GeneChip Affymetrix expression arrays, a widely used technology for studying mRNA abundance. However, our methodology is applicable to all types of microarrays. Chapter 1 gives a brief introduction. In Chapter 2 and 3, two popular preprocessing methods for constructing gene expression measurements, the robust multi-array average and MAS-5.0 Affymetrix algorithm, are studied and a new set of diagnostic tools for assessing the quality of microarray data is proposed. In Chapter 4, a classification and regression tree algorithm for variance stabilization and regularization of high throughput genomic data is developed. Chapter 5 considers cross-validation (CV) and multi-fold cross-validation (MCV) for model selection and prediction error estimation. Computationally efficient expressions of CV and MCV are derived and used for the analysis of multigroup time course data. In Chapter 6, a non-parametric, data-adaptive gene hunting filter for multigroup temporal microarray data is proposed for the identification of differentially expressing profiles. Finally, in Chapter 7, local and global orthogonal smoothing via a rescaled spike and slab model is introduced.
Microarrays are instrumental in answering important biological or genetical questions. Successful quantification of gene expression, identification of genetic markers, as well as measurement of gene expression changes over a variety of conditions is facilitated via
the usage of microarrays. Comparisons of distinct biological groups help unravel how phenotypes associate with certain genotypes. Therefore, microarrays can be utilized for improving disease diagnosis and prognosis, for providing therapeutic choice, as well as, for drug discovery.