Biostatistics Commons^™

Variable Selection For High-Dimensional Data With Interaction Effects: Methods, Applications, And Inferences, Leiyue Li

Theses and Dissertations--Statistics

For high-dimensional data where the number of variables greatly exceeds the number of observations, selecting important variables while maintaining the required heredity conditions can be challenging. This dissertation is structured into three interconnected parts. In the first part, we propose a variable selection method by implementing a well-known optimization technique, the Genetic Algorithm. An R package was developed to simplify the implementation and usage of the proposed method. We then propose another variable selection method by extending the study from the Genetic Algorithm to a different but related optimization technique, Simulated Annealing. We consider three different hierarchical structures in both …

Difs And Bayescluster: Novel Methods For Single_Cell Rna Sequencing Analysis, Kun Liu

Theses and Dissertations--Statistics

Single-cell RNA sequencing (scRNA-seq) has transformed our understanding of cellular heterogeneity and gene expression dynamics. Despite its potential, the inherent noise and sparsity of scRNA-seq data pose significant challenges in clustering cells into biologically meaningful groups. This dissertation addresses these challenges through two novel methodologies aimed at enhancing the accuracy and robustness of scRNA-seq data analysis.

First, we introduce the Differential Feature Selection (DIFS) framework, designed to improve the identification of differential features in scRNA-seq data. DIFS employs a two-stage marker identification process. In the first stage, a modified Dip Test is used to filter and identify genes with significant …

Probabilistic Methods For Inferring The Order Of Pathway Alterations During Carcinogenesis And Cancer Subtype Classification, Menghan Wang

Theses and Dissertations--Statistics

Carcinogenesis is a complex process involving somatic mutations in a number of key biological pathways. Studying cancer evolution is an important task which contributes to better understanding of cancer biology and facilitates identification of new therapeutic targets. We focus on two important questions in cancer evolution. The first question is to delineating the temporal order of pathway mutations during tumorigenesis. And the other question is to cluster patients into biologically meaningful cancer subtypes. We present new statistical methods to 1)leverage functional annotations of mutations to enhance estimation of the order of pathway mutations during carcinogenesis, 2) incorporate intra-tumoral heterogeneity information …

High Dimensional Data Analysis: Variable Screening And Inference, Lei Fang

Theses and Dissertations--Statistics

This dissertation focuses on the problem of high dimensional data analysis, which arises in many fields including genomics, finance, and social sciences. In such settings, the number of features or variables is much larger than the number of observations, posing significant challenges to traditional statistical methods.

To address these challenges, this dissertation proposes novel methods for variable screening and inference. The first part of the dissertation focuses on variable screening, which aims to identify a subset of important variables that are strongly associated with the response variable. Specifically, we propose a robust nonparametric screening method to effectively select the predictors …

Multivariate Statistical Modeling For Radio-Genomics Study, Tiantian Zeng

Theses and Dissertations--Statistics

Radiogenomics is a new direction in cancer research that focuses on the associations among radiomics, genomics and clinical outcome. Currently, the major challenge for Radiogenomics lies in the effective integration of genomics and imaging data for promising clinical outcome prediction. Herein, we propose a multivariate joint model that can integrate imaging and genomic data for better predicting the clinical outcome. Specifically, we jointly consider two multivariate group lasso models, one regresses imaging features on genomic features, and the other regresses patient’s clinical outcome on genomic features. An L1 penalty term is introduced for each variable, and weight in the penalty …

Statistical Theory For Specialized Linear Regression Adjustment Methods Compared To Multiple Linear Regression In The Presence And Absence Of Interaction Effects, Leon Su

Theses and Dissertations--Statistics

When building models to investigate outcomes and variables of interest, researchers often want to adjust for other variables. There is a variety of ways that these adjustments are performed. In this work, we will consider four approaches to adjustment utilized by researchers in various fields. We will compare the efficacy of these methods to what we call the ”true model method”, fitting a multiple linear regression model in which adjustment variables are model covariates. Our goal is to show that these adjustment methods have inferior performance to the true model method by comparing model parameter estimates, power, type I error, …

Innovative Statistical Models In Cancer Immunotherapy Trial Design, Jing Wei

Theses and Dissertations--Statistics

A challenge arising in cancer immunotherapy trial design is the presence of non-proportional hazards (NPH) patterns in survival curves. We considered three different NPH patterns caused by delayed treatment effect, cure rate and responder rate of treatment group in this dissertation. These three NPH patterns would violate the proportional hazard model assumption and ignoring any of them in an immunotherapy trial design will result in substantial loss of statistical power.

In this dissertation, four models to deal with NPH patterns are discussed. First, a piecewise proportional hazards model is proposed to incorporate delayed treatment effect into the trial design consideration. …

Semiparametric And Nonparametric Methods For Comparing Biomarker Levels Between Groups, Yuntong Li

Theses and Dissertations--Statistics

Comparing the distribution of biomarker measurements between two groups under either an unpaired or paired design is a common goal in many biomarker studies. However, analyzing biomarker data is sometimes challenging because the data may not be normally distributed and contain a large fraction of zero values or missing values. Although several statistical methods have been proposed, they either require data normality assumption, or are inefficient. We proposed a novel two-part semiparametric method for data under an unpaired setting and a nonparametric method for data under a paired setting. The semiparametric method considers a two-part model, a logistic regression for …

Estimation Of The Treatment Effect With Bayesian Adjustment For Covariates, Li Xu

Theses and Dissertations--Statistics

The Bayesian adjustment for confounding (BAC) is a Bayesian model averaging method to select and adjust for confounding factors when evaluating the average causal effect of an exposure on a certain outcome. We extend the BAC method to time-to-event outcomes. Specifically, the posterior distribution of the exposure effect on a time-to-event outcome is calculated as a weighted average of posterior distributions from a number of candidate proportional hazards models, weighing each model by its ability to adjust for confounding factors. The Bayesian Information Criterion based on the partial likelihood is used to compare different models and approximate the Bayes factor. …

Bayesian Kinetic Modeling For Tracer-Based Metabolomic Data, Xu Zhang

Theses and Dissertations--Statistics

Kinetic modeling of the time dependence of metabolite concentrations including the unstable isotope labeled species is an important approach to simulate metabolic pathway dynamics. It is also essential for quantitative metabolic flux analysis using tracer data. However, as the metabolic networks are complex including extensive compartmentation and interconnections, the parameter estimation for enzymes that catalyze individual reactions needed for kinetic modeling is challenging. As the pa- rameter space is large and multi-dimensional while kinetic data are comparatively sparse, the estimation procedure (especially the point estimation methods) often en- counters multiple local maximum such that standard maximum likelihood methods may yield …

Measuring Change: Prediction Of Early Onset Sepsis, Aric Schadler

Theses and Dissertations--Statistics

Sepsis occurs in a patient when an infection enters into the blood stream and spreads throughout the body causing a cascading response from the immune system. Sepsis is one of the leading causes of morbidity and mortality in today’s hospitals. This is despite published and accepted guidelines for timely and appropriate interventions for septic patients. The largest barrier to applying these interventions is the early identification of septic patients. Early identification and treatment leads to better outcomes, shorter lengths of stay, and financial savings for healthcare institutions. In order to increase the lead time in recognizing patients trending towards septicemia …

Unsupervised Learning In Phylogenomic Analysis Over The Space Of Phylogenetic Trees, Qiwen Kang

Theses and Dissertations--Statistics

A phylogenetic tree is a tree to represent an evolutionary history between species or other entities. Phylogenomics is a new field intersecting phylogenetics and genomics and it is well-known that we need statistical learning methods to handle and analyze a large amount of data which can be generated relatively cheaply with new technologies. Based on the existing Markov models, we introduce a new method, CURatio, to identify outliers in a given gene data set. This method, intrinsically an unsupervised method, can find outliers from thousands or even more genes. This ability to analyze large amounts of genes (even with missing …

Serial Testing For Detection Of Multilocus Genetic Interactions, Zaid T. Al-Khaledi

Theses and Dissertations--Statistics

A method to detect relationships between disease susceptibility and multilocus genetic interactions is the Multifactor-Dimensionality Reduction (MDR) technique pioneered by Ritchie et al. (2001). Since its introduction, many extensions have been pursued to deal with non-binary outcomes and/or account for multiple interactions simultaneously. Studying the effects of multilocus genetic interactions on continuous traits (blood pressure, weight, etc.) is one case that MDR does not handle. Culverhouse et al. (2004) and Gui et al. (2013) proposed two different methods to analyze such a case. In their research, Gui et al. (2013) introduced the Quantitative Multifactor-Dimensionality Reduction (QMDR) that uses the overall …

Informational Index And Its Applications In High Dimensional Data, Qingcong Yuan

Theses and Dissertations--Statistics

We introduce a new class of measures for testing independence between two random vectors, which uses expected difference of conditional and marginal characteristic functions. By choosing a particular weight function in the class, we propose a new index for measuring independence and study its property. Two empirical versions are developed, their properties, asymptotics, connection with existing measures and applications are discussed. Implementation and Monte Carlo results are also presented.

We propose a two-stage sufficient variable selections method based on the new index to deal with large p small n data. The method does not require model specification and especially focuses …

Statistical Methods For Environmental Exposure Data Subject To Detection Limits, Yuchen Yang

Theses and Dissertations--Statistics

In this dissertation, we develop unified and efficient nonparametric statistical methods for estimating and comparing environmental exposure distributions in presence of detection limits. In the first part, we propose a kernel-smoothed nonparametric estimator for the exposure distribution without imposing any independence assumption between the exposure level and detection limit. We show that the proposed estimator is consistent and asymptotically normal. Simulation studies demonstrate that the proposed estimator performs well in practical situations. A colon cancer study is provided for illustration. In the second part, we develop a class of test statistics to compare exposure distributions between two groups by using …

Improved Models For Differential Analysis For Genomic Data, Hong Wang

Theses and Dissertations--Statistics

This paper intend to develop novel statistical methods to improve genomic data analysis, especially for differential analysis. We considered two different data type: NanoString nCounter data and somatic mutation data. For NanoString nCounter data, we develop a novel differential expression detection method. The method considers a generalized linear model of the negative binomial family to characterize count data and allows for multi-factor design. Data normalization is incorporated in the model framework through data normalization parameters, which are estimated from control genes embedded in the nCounter system. For somatic mutation data, we develop beta-binomial model-based approaches to identify highly or lowly …

Aggregated Quantitative Multifactor Dimensionality Reduction, Rebecca E. Crouch

Theses and Dissertations--Statistics

We consider the problem of making predictions for quantitative phenotypes based on gene-to-gene interactions among selected Single Nucleotide Polymorphisms (SNPs). Previously, Quantitative Multifactor Dimensionality Reduction (QMDR) has been applied to detect gene-to-gene interactions associated with elevated quantitative phenotypes, by creating a dichotomous predictor from one interaction which has been deemed optimal. We propose an Aggregated Quantitative Multifactor Dimensionality Reduction (AQMDR), which exhaustively considers all k-way interactions among a set of SNPs and replaces the dichotomous predictor from QMDR with a continuous aggregated score. We evaluate this new AQMDR method in a series of simulations for two-way and three-way interactions, …

Multi-State Models For Interval Censored Data With Competing Risk, Shaoceng Wei

Theses and Dissertations--Statistics

Multi-state models are often used to evaluate the effect of death as a competing event to the development of dementia in a longitudinal study of the cognitive status of elderly subjects. In this dissertation, both multi-state Markov model and semi-Markov model are used to characterize the flow of subjects from intact cognition to dementia with mild cognitive impairment and global impairment as intervening transient, cognitive states and death as a competing risk.

Firstly, a multi-state Markov model with three transient states: intact cognition, mild cognitive impairment (M.C.I.) and global impairment (G.I.) and one absorbing state: dementia is used to model …

Genetic Association Testing Of Copy Number Variation, Yinglei Li

Theses and Dissertations--Statistics

Copy-number variation (CNV) has been implicated in many complex diseases. It is of great interest to detect and locate such regions through genetic association testings. However, the association testings are complicated by the fact that CNVs usually span multiple markers and thus such markers are correlated to each other. To overcome the difficulty, it is desirable to pool information across the markers. In this thesis, we propose a kernel-based method for aggregation of marker-level tests, in which first we obtain a bunch of p-values through association tests for every marker and then the association test involving CNV is based on …

Analysis Of Binary Data Via Spatial-Temporal Autologistic Regression Models, Zilong Wang

Theses and Dissertations--Statistics

Spatial-temporal autologistic models are useful models for binary data that are measured repeatedly over time on a spatial lattice. They can account for effects of potential covariates and spatial-temporal statistical dependence among the data. However, the traditional parametrization of spatial-temporal autologistic model presents difficulties in interpreting model parameters across varying levels of statistical dependence, where its non-negative autocovariates could bias the realizations toward 1. In order to achieve interpretable parameters, a centered spatial-temporal autologistic regression model has been developed. Two efficient statistical inference approaches, expectation-maximization pseudo-likelihood approach (EMPL) and Monte Carlo expectation-maximization likelihood approach (MCEML), have been proposed. Also, Bayesian …