Modern biomedical studies generate high-dimensional data, meaning that the number of variables collected is equal to or larger than the number of observations. Examples are numerous, including single-cell transcriptome analyses and clinical trials. The dimensions of these data often prevent the use of traditional statistical methods: the theory motivating their application is no longer applicable. New procedures must be developed for express use in these contexts to ensure trustworthy inference. This dissertation delves into two topics in high-dimensional statistics, the first being covariance matrix estimator selection. Motivated by the need to nonparametrically identify an optimal estimator of the covariance matrix for a given dataset, we propose a cross-validated estimator selection procedure and investigate its finite-sample and high-dimensional asymptotic performance. Our theoretical results, supported by empirical evidence, demonstrate that this procedure selects the optimal estimator asymptotically. Here, optimality is defined in terms of a Frobenius-norm-based risk. Applications are myriad, though we focus on improving exploratory analyses in single-cell transcriptome analyses. The second topic, born of the need to reliably uncover biomarkers that predict clinical trial patients’ response to novel therapies, is treatment effect modifier discovery. Treatment effect modifiers are pre-treatment covariates that influence the effect of a treatment on an outcome. While many approaches exist for identifying these effect modifiers in traditional asymptotic settings, few developments have been made for high-dimensional data. We propose a nonparametric framework for defining parameters measuring treatment effect modification, deriving accompanying estimators, and establishing these estimators’ asymptotic properties. We derive several such parameters and estimators using our methodology, and assess these estimators’ empirical performance through comprehensive simulation studies and real clinical trial data analyses.

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I propose statistical methods and software for the analysis of single-cell transcriptome sequencing (scRNA-seq) and metagenomics data. Specifically, I present a general and flexible zero-inflated negative binomial-based wanted variation extraction (ZINB-WaVE) method, which extracts low-dimensional signal from scRNA-seq read counts, accounting for zero inflation (dropouts), over-dispersion, and the discrete nature of the data. Additionally, I introduce an application of the ZINB-WaVE method that identifies excess zero counts and generates gene and cell-specific weights to unlock bulk RNA-seq differential expression pipelines for zero-inflated data, boosting performance for scRNA-seq analysis. Finally, I present a method to estimate bacterial abundances in human metagenomes using full-length 16S sequencing reads.

It has become increasingly apparent that the set of exposures a person experiences can have profound ramifications for increasing their risks for various diseases. While genetics explains some portion of this risk, more complex diseases require understanding the interaction of genetics with this set of dynamic exposures, also referred to as the exposome. To address this, researchers have turned to various technologies focused on detecting indicators for these exposures. Due to the nature of the technologies used as well as the dynamic and continuous nature of the features measured, these exposomic datasets often suffer from a large amount of technical noise which must first be removed to allow for downstream detection of the biological signal of interest. In addition, it is important to consider the characteristics of these datasets and how they were generated when performing the analysis to answer the biological, and resulting statistical, questions at hand. In this dissertation we present analyses of three different types of exposomic datasets and associated questions of interest, in each case first discussing the necessary pre-processing. The first chapter applies a prediction framework to assess whether folate pathway disregulation is involved in increasing risk for pediatric ALL using a targeted metabolomics dataset. The second includes both hypothesis generation and a limited hypothesis testing analysis for transformed untargeted metabolomic features to reactomic features for paired mother-child data in a pediatric ALL case-control study. For hypothesis generation, marginal and joint analyses of the two datasets are performed using an ensemble feature selection method. Chapter three focuses on the previously mentioned ensemble feature selection method, using an untargeted adductomics lung cancer case-control dataset. Options for automating the method are proposed and evaluated using a simulation for bench-marking compared to standard hypothesis testing practices.

I present a biological study of differentiating stem cells along with statistical and computational methods for the analysis of data from such studies. The motivating biological example comes from a study of steady-state tissue maintenance in the mouse olfactory epithelium, where we are interested in characterizing the transcriptional changes that drive cell fate decisions. This study uses single-cell RNA sequencing (scRNA-Seq) to quantify the transcriptional activity of hundreds of cells across thousands of genes. Analysis of such data requires an intensive computational pipeline. I present two novel tools designed to fit into such a pipeline: first, I present Slingshot, a method for modeling the developmental process and ordering cellular profiles along it; second, I present tradeR, a method for analyzing patterns of gene expression along such a developmental process and testing for meaningful differences. Together with existing tools, these methods can help us understand the molecular mechanics underlying such fundamental biological processes as organism development, tissue maintenance, and regeneration.

Beginning with microarray data in the 90's, omics technologies have exploded in the last three decades. Proteomic, metabolomic, genomic and epigenomic data are used to understand disease etiology, to detect diseases early on and to identify novel disease therapies. Almost every omics dataset is the result of a complicated experiment and data collection process. The unwanted variation introduced during the experimental process, along with biological complexity and heterogeneity, requires extensive exploratory data analysis and pre-processing to understand the variability within the data.

The goal throughout this dissertation is to demonstrate the need for appropriate exploratory data analysis and pre-processing in various omics data types, and to provide examples of such. Exploratory data analysis refers to extensive visualization and summarization of omics data in order to understand distributional properties of samples and features, to identify unwanted variation, to determine biological patterns, etc. Work done during exploratory data analysis informs subsequent data pre-processing, or a series of steps taken to filter samples and features, to impute missing values, to normalize or transform the data, etc., prior to performing formal statistical analyses.

Here, we first demonstrate exploratory data analysis and pre-processing within the context of single-cell RNA-sequencing data. One goal of single cell RNA-sequencing (scRNA-seq) is to expose possible heterogeneity within cell populations due to meaningful, biological variation. Examining cell-to-cell heterogeneity, and further, identifying subpopulations of cells based on scRNA-seq data has been of common interest in life science research. A key component to successfully identifying cell subpopulations (or clustering cells) is the (dis)similarity measure used to group the cells. We introduce a novel measure, named SIDEseq, to assess cell-to-cell similarity using scRNA-seq data. SIDEseq first identifies a list of putative differentially expressed (DE) genes for each pair of cells. SIDEseq then integrates the information from all the DE gene lists (corresponding to all pairs of cells) to build a similarity measure between two cells. SIDEseq can be implemented in any clustering algorithm that requires a (dis)similarity matrix. This new measure incorporates information from all cells when evaluating the similarity between any two cells, a characteristic not commonly found in existing (dis)similarity measures. This property is advantageous for two reasons: (a) borrowing information from cells of different subpopulations allows for the investigation of pair-wise cell relationships from a global perspective, and (b) information from other cells of the same subpopulation could help to ensure a robust relationship assessment. We applied SIDEseq to a newly generated human ovarian cancer scRNA-seq dataset, a public human embryo scRNA-seq dataset and several simulated data sets. The clustering results suggest that the SIDEseq measure is capable of uncovering important relationships between cells, and outperforms or at least does as well as several popular (dis)similarity measures when used on these datasets.

We then focus on exploratory data analysis and pre-processing in the context of adductomics data. Metabolism of chemicals from the diet, exposures to xenobiotics, the microbiome, and lifestyle factors (e.g., smoking, alcohol intake) produce reactive electrophiles that react with nucleophilic sites in DNA and proteins. Since many of these reactive intermediates are unknown, we reported an untargeted adductomics method to detect Cys34 modifications of human serum albumin (HSA) in human serum and plasma. Here, we extended that assay to investigate HSA-Cys34 adducts in archived newborn dried blood spots (DBS). As proof-of-principle, we applied the method to 49 archived DBS collected from newborns whose mothers either actively smoked during pregnancy or were nonsmokers. Twenty-six HSA-Cys34 adducts were detected, including Cys34 oxidation products, mixed disulfides with low-molecular-weight thiols (e.g., cysteine, homocysteine, glutathione, cysteinylglycine, etc.), and other modifications. We used careful exploratory data analysis and data pre-processing methods to uncover biological signal in this relatively new omics data type. With an ensemble of statistical approaches, the Cys34 adduct of cyanide was found to consistently discriminate between newborns with smoking versus nonsmoking mothers with a mean fold change (smoking/nonsmoking) of 1.31. Our DBS-based adductomics method is currently being applied to discover in utero exposures to reactive chemicals and metabolites that may influence disease risks later in life.

Finally, we show how exploratory data analysis and pre-processing is essential for the successful analysis of untargeted metabolomics data. Untargeted metabolomics datasets contain large proportions of uninformative features that can impede subsequent statistical analysis such as biomarker discovery and metabolic pathway analysis. Thus, there is a need for versatile and data-adaptive methods for filtering data prior to investigating the underlying biological phenomena. Here, we propose a data-adaptive pipeline for filtering metabolomics data that are generated by liquid chromatography-mass spectrometry (LC-MS) platforms. Our data-adaptive pipeline includes novel methods for filtering features based on blank samples, proportions of missing values, and estimated intra-class correlation coefficients. Using metabolomics datasets that were generated in our laboratory from samples of human blood serum, as well as two public LC-MS datasets, we compared our data-adaptive filtering method with traditional methods that rely on non-method specific thresholds. The data-adaptive approach outperformed traditional approaches in terms of removing noisy features and retaining high quality, biologically informative ones. Our proposed data-adaptive filtering pipeline is intuitive and effectively removes uninformative features from untargeted metabolomics datasets. It is particularly relevant for interrogation of biological phenomena in data derived from complex matrices associated with biospecimens.

Over the last two decades, technological improvements have led to a tremendous reduction in the cost and speed of DNA sequencing. This has opened the door to many new applications, including the quantification of transcriptomes at the resolution of single cells (scRNA-Seq), and the discovery of genetic features associated with phenotypes of interest, also known as genome-wide association study (GWAS).

scRNA-Seq has emerged in just 10 years as a major tool to investigate biological diversity. The ability to assess gene expression for individual cells enables the study of a range of biological processes at new levels of resolution. This can have many interesting applications, including the identification of novel cell types, defined by their unique transcriptomic signatures. Drawing from the clustering literature, many methods have been developed to group cells together based on their gene expression characteristics. However, all those algorithms require the tuning of hyper-parameters based on typically ad hoc recommendations. Moreover, the direct validation of the discovered cell types is generally difficult, if not impossible. The grouping of cells is also not unique for a given biological system, and there often exists a hierarchy of cell types, with ever-finer levels of resolutions. Because of all this, the discovery of reliable, replicable cell types remains a major challenge. In Chapter 2, we will delve deeper into this issue and introduce a new method called Dune that tackles the resolution-replicability trade-off in clustering.

scRNA-Seq data also enable the tracking of continuous developmental changes, without the need for arbitrary discretization that stemmed purely from the data collection protocol. This allows to investigate processes such as the cell cycle, the differentiation of stem cells into different cell types, or the cellular response to a drug over time. In Chapter 3, we will investigate how to characterize patterns of gene expression along such developmental trajectories, to identify dynamic genes and drivers of differentiation, using the tradeSeq method. In Chapter 4, we will provide a general workflow called condiments for analyzing such dynamic systems in the presence of multiple conditions, such as treatment/control.

GWAS represent another field that has gained major attention following the emergence of cheaper high-throughput sequencing technologies. In human populations, the problem has been extensively studied, mainly in the context of diseases such as diabetes. However, GWAS can also be applied to bacterial genomes, especially in the context of antibiotic resistance. Some concepts from the human GWAS literature are applicable in bacteria. However, characteristics of bacterial genome mean that other concepts, such as that of a reference genome, are inappropriate and irrelevant. New methods need to be developed for this specific problem. In Chapter 5, we present a new subgraph enumeration method named CALDERA that leverages the structure of the data to provides more robust analyses and facilitate the interpretation of bacterial GWAS data.