Statistical Methods for Single-Cell RNA Data

Recent advancements in single-cell RNA sequencing (scRNA-seq) have revolutionized transcriptomic research by enabling the study of gene expression at unprecedented resolution, revealing intricate cellular heterogeneity and dynamics. Despite these advancements, analyzing scRNA-seq data poses significant challenges, including normalization biases, excessive zeros, and donor effects, which can confound differential expression (DE) analysis. This thesis addresses these challenges through innovative methodologies. Chapter 2 critically evaluates existing DE analysis methods, highlighting limitations such as normalization biases and the impact of excessive zeros on statistical models. To overcome these issues, we introduce a novel paradigm using a generalized linear mixed model (GLMM) that leverages raw unique molecular identifier (UMI) counts for robust DE analysis. In Chapter 3, we adopt the HIPPO framework, a clustering algorithm that prioritizes zero proportion as a primary indicator. We examine the potential of higher order counts (proportions) to extract additional information beyond zero proportion, aiming to enhance the HIPPO algorithm. To achieve this, we introduce the k-inflation test for identifying k-inflated genes and develop a Poisson proportion t-test for further analysis. Chapter 4 shifts focus to cell-type specific differential methylation analysis, recognizing RNA methylation, particularly N6-methyladenosine (m6A), as pivotal in RNA regulation. Building on the RADAR framework, a novel methodology is proposed using a mixture Poisson GLMM to analyze methylation data integrated with scRNA-seq. This approach utilizes cellular composition estimates to uncover differential methylation patterns across cell types without direct measurement of cell-type specific methylation. This dissertation proposes novel frameworks for DE and methylation analysis in scRNA-seq data, enhancing our understanding of cellular diversity and gene regulation. These methodologies contribute to advance biological research and pave the way for new discoveries in precision medicine and therapeutic development.