The recent advancement of whole-transcriptome gene expression quantification technology - particularly at the single-cell level - has created a wealth of biological data. An increasingly popular unsupervised analysis is to find one dimensional manifolds or trajectories through such data that track the development of some biological process. Such methods may be necessary due to the lack of explicit time series measurements or due to asynchronicity of the biological process at a given time. This thesis aims to recast trajectory inference from high-dimensional "omics" data as a statistical latent variable problem. We begin by examining sources of uncertainty in current approaches and examine the consequences of propagating such uncertainty to downstream analyses. We also introduce a model of switch-like differentiation along trajectories. Next, we consider inferring such trajectories through parametric nonlinear factor analysis models and demonstrate that incorporating information about gene behaviour as informative Bayesian priors improves inference. We then consider the case of bifurcations in data and demonstrate the extent to which they may be modelled using a hierarchical mixture of factor analysers. Finally, we propose a novel type of latent variable model that performs inference of such trajectories in the presence of heterogeneous genetic and environmental backgrounds. We apply this to both single-cell and population-level cancer datasets and propose a nonparametric extension similar to Gaussian Process Latent Variable Models.

Thousands of risk variants underlying complex phenotypes (quantitative traits and diseases) have been identified in genome-wide association studies (GWAS). However, there are still several challenges towards deepening our understanding of the genetic architectures of complex phenotypes. First, the majority of GWAS hits are in non-coding region and their biological interpretation is still unclear. Second, most complex traits are suggested to be highly polygenic, i.e., they are affected by a vast number of risk variants with individually small or moderate effects, whereas a large proportion of risk variants with small effects remain unknown. Third, accumulating evidence from GWAS suggests the pervasiveness of pleiotropy, a phenomenon that some genetic variants can be associated with multiple traits, but there is a lack of unified framework which is scalable to reveal relationship among a large number of traits and prioritize genetic variants simultaneously with functional annotations integrated. In this thesis, we propose two statistical methods to address these challenges using integrative analysis of summary statistics from GWASs and functional annotations. In the first part, we propose a latent sparse mixed model (LSMM) to integrate functional annotations with GWAS data. Not only does it increase the statistical power of identifying risk variants, but also offers more biological insights by detecting relevant functional annotations. To allow LSMM scalable to millions of variants and hundreds of functional annotations, we developed an efficient variational expectation-maximization (EM) algorithm for model parameter estimation and statistical inference. We first conducted comprehensive simulation studies to evaluate the performance of LSMM. Then we applied it to analyze 30 GWASs of complex phenotypes integrated with nine genic category annotations and 127 cell-type specific functional annotations from the Roadmap project. The results demonstrate that our method possesses more statistical power than conventional methods, and can help researchers achieve deeper understanding of genetic architecture of these complex phenotypes. In the second part, we propose a latent probit model (LPM) which combines summary statistics from multiple GWASs and functional annotations, to characterize relationship and increase statistical power to identify risk variants. LPM can also perform hypothesis testing for pleiotropy and annotations enrichment. To enable the scalability of LPM as the number of GWASs increases, we developed an efficient parameter-expanded EM (PX-EM) algorithm which can execute parallelly. We first validated the performance of LPM through comprehensive simulations, then applied it to analyze 44 GWASs with nine genic category annotations. The results demonstrate the benefits of LPM and can offer new insights of disease etiology.

Existing methods to systematically characterize sequence-intrinsic activity of promoters are limited by relatively low throughput and the length of sequences that could be tested. Here we present Survey of Regulatory Elements (SuRE), a method to assay more than a billion DNA fragments in parallel for their ability to drive transcription autonomously. In SuRE, a plasmid library is constructed of random genomic fragments upstream of a barcode and decoded by paired-end sequencing. This library is transfected into cells and transcribed barcodes are quantified in the RNA by high-throughput sequencing. By computationally analyzing the resulting data using generalized linear models, we succeed in delineating subregions within promoters that are relevant for their activity on a genomic scale, and making accurate predictions of expression levels that can be used to inform minimal promoter reporter construct design. We also show how our approach can be extended to analyze the differential impact of single-nucleotide polymorphisms (SNPs) on gene expression.

published_or_final_version / Psychiatry / Doctoral / Doctor of Philosophy

Genome-wide association studies (GWAS) have identified thousands of genetic variants associated with hundreds of human traits. Yet the common variant model tested by traditional GWAS only provides an incomplete explanation for the known genetic heritability of many traits. Many divergent methods have been proposed to address the shortcomings of GWAS, including most notably the extension of association methods into rarer variants through whole exome and whole genome sequencing. GWAS methods feature numerous simplifications designed for feasibility and ease of use, as opposed to statistical rigor. Furthermore, no systematic quantification of the performance of GWAS across all traits exists. Beyond improving the utility of data that already exist, a more thorough understanding of the performance of GWAS on common variants may elucidate flaws not in the method but rather in its implementation, which may pose a continued or growing threat to the utility of rare variant association studies now underway. This thesis focuses on systematic evaluation and incremental improvement of GWAS modeling. We collect a rich dataset containing standardized association results from all GWAS conducted on quantitative human traits, finding that while the majority of published significant results in the field do not disclose sufficient information to determine whether the results are actually valid, those that do replicate precisely in concordance with their statistical power when conducted in samples of similar ancestry and reporting accurate per-locus sample sizes. We then look to the inability of effectively all existing association methods to handle missingness in genetic data, and show that adapting missingness theory from statistics can both increase power and provide a flexible framework for extending most existing tools with minimal effort. We finally undertake novel variant association in a schizophrenia cohort from a bottleneck population. We find that the study itself is confounded by nonrandom population sampling and identity-by-descent, manifesting as batch effects correlated with outcome that remain in novel variants after all sample-wide quality control. On the whole, these results emphasize both the past and present utility and reliability of the GWAS model, as well as the extent to which lessons from the GWAS era must inform genetic studies moving forward.