Statistical Methods for Normalization and Analysis of High-Throughput Genomic Data

High-throughput genomic datasets obtained from microarray or sequencing studies have revolutionized the field of molecular biology over the last decade. The complexity of these new technologies also poses new challenges to statisticians to separate biological relevant information from technical noise. Two methods are introduced that address important issues with normalization of array comparative genomic hybridization (aCGH) microarrays and the analysis of RNA sequencing (RNA-Seq) studies. Many studies investigating copy number aberrations at the DNA level for cancer and genetic studies use comparative genomic hybridization (CGH) on oligo arrays. However, aCGH data often suffer from low signal to noise ratios resulting in poor resolution of fine features. Bilke et al. showed that the commonly used running average noise reduction strategy performs poorly when errors are dominated by systematic components. A method called pcaCGH is proposed that significantly reduces noise using a non-parametric regression on technical covariates of probes to estimate systematic bias. Then a robust principal components analysis (PCA) estimates any remaining systematic bias not explained by technical covariates used in the preceding regression. The proposed algorithm is demonstrated on two CGH datasets measuring the NCI-60 cell lines utilizing NimbleGen and Agilent microarrays. The method achieves a nominal error variance reduction of 60%-65% as well as an 2-fold increase in signal to noise ratio on average, resulting in more detailed copy number estimates. Furthermore, correlations of signal intensity ratios of NimbleGen and Agilent arrays are increased by 40% on average, indicating a significant improvement in agreement between the technologies. A second algorithm called gamSeq is introduced to test for differential gene expression in RNA sequencing studies. Limitations of existing methods are outlined and the proposed algorithm is compared to these existing algorithms. Simulation studies and real data are used to show that gamSeq improves upon existing methods with regards to type I error control while maintaining similar or better power for a range of sample sizes for RNA-Seq studies. Furthermore, the proposed method is applied to detect differential 3\u27 UTR usage