Empirical bayes modelling of expression profiles and their associations

© 2013 Dr. Belinda PhipsonNew biotechnology developments such as the microarray, and more recently, next generation sequencing, have necessitated the need for new statistical methodologies to be developed. These methods are designed to combat unique issues present in the data generated by these technologies. They provide the perfect environment for information sharing strategies, such as empirical Bayes methods, due to the large numbers of simulataneous tests performed. We explore different estimators of the proportion of true null hypotheses and develop a fast and accurate estimator which is valid for any number of p-values. This estimator is based on local false discovery rates and is used in several of the proceeding sections. Another interest is in developing robust hyper-parameter estimators in an empirical Bayes hierarchical model setting. An estimator for the prior degrees of freedom which is robust to outliers is developed using two different approaches. This has the effect that highly variable genes are unlikely to be significantly differentially expressed, as well as increasing power to detect differential expression. The second half of the thesis focuses on gaining more information from the log fold changes obtained from microarray and sequencing experiments. More accurate log fold changes are developed for microarrays and RNA sequencing data, which provide additional information for ranking top differentially expressed genes. The new measure, called predictive log fold change, arises from the posterior distribution of the log fold changes. The relationship between two gene expression profiles is quantified when the p-values obtained from testing two hypotheses are not independent. This arises when two genotypes are compared to a common control group. The method is based on separating the true biological correlation from the technical correlation of the log fold changes. The hyperparameters of the prior distribution for the log fold changes need to be estimated in order to get an estimate of the biological correlation. This is possible since we show that the two dependent moderated t statistics have a scaled multivariate t distribution. The methods developed in this thesis are tested using simulations and applied to data sets collected in collaboration with biologists at The Walter and Eliza Hall Institute of Medical Research