Statistical methods in detecting differential expressed genes, analyzing insertion tolerance for genes and group selection for survival data

Abstract

The thesis is composed of three independent projects: (i) analyzing transposon-sequencing data to infer functions of genes on bacteria growth (chapter 2), (ii) developing semi-parametric Bayesian method method for differential gene expression analysis with RNA-sequencing data (chapter 3), (iii) solving group selection problem for survival data (chapter 4). All projects are motivated by statistical challenges raised in biological research. The first project is motivated by the need to develop statistical models to accommodate the transposon insertion sequencing (Tn-Seq) data, Tn-Seq data consist of sequence reads around each transposon insertion site. The detection of transposon insertion at a given site indicates that the disruption of genomic sequence at this site does not cause essential function loss and the bacteria can still grow. Hence, such measurements have been used to infer the functions of each gene on bacteria growth. We propose a zero-inflated Poisson regression method for analyzing the Tn-Seq count data, and derive an Expectation-Maximization (EM) algorithm to obtain parameter estimates. We also propose a multiple testing procedure that categorizes genes into each of the three states, hypo-tolerant, tolerant, and hyper-tolerant, while controlling false discovery rate. Simulation studies show our method provides good estimation of model parameters and inference on gene functions. In the second project, we model the count data from RNA-sequencing experiment for each gene using a Poisson-Gamma hierarchical model, or equivalently, a negative binomial (NB) model. We derive a full semi-parametric Bayesian approach with Dirichlet process as the prior for the fold changes between two treatment means. An inference strategy using Gibbs algorithm is developed for differential expression analysis. We evaluate our method with several simulation studies, and the results demonstrate that our method outperforms other methods including the popularly applied ones such as edgeR and DESeq. In the third project, we develop a new semi-parametric Bayesian method to address the