Browsing Department of Biostatistics and Epidemiology: Theses andDissertations by Title
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Mathematical and Stochastic Modeling of HIV Immunology and EpidemiologyIn HIV virus dynamics, controlling of viral load and maintaining of CD4 value at a higher level are always primary goals for the providers. In recent years, a new molecule was discovered, namely, eCD4Ig, which mimics CD4 if introduced into the human body and has potential to change existing HIV virus dynamics. Thus, to understand dynamics of viral load, eCD4Ig, CD4 cells, we have developed mathematical models by incorporating interactions between this new molecule and other known immunological, virological information. We further investigated model based speculations for management, and obtained the level of eCD4Ig required for elimination of virus. Next, we built epidemiological model for HIV spread and control among discordant couple through dynamics of PrEP (Preexposure prophylaxis). For this, an actuarial assumptions based stochastic model is used to obtain the mean remaining time of couple to stay as discordant. We generalized single hookup/marriage stochastic model to multiple hookup/marriage model.

A modified bump hunting approach with correlationadjusted kernel weight for detecting differentially methylated regions on the 450K arrayDNA methylation plays an important role in the regulation of gene expression, as hypermethylation is associated with gene silencing. The general purpose of this dissertation is the development of a statistical method, called DMR Detector, for detecting differentially methylated regions (DMRs) on the 450K array. DMR Detector makes three key modifications to an existing method called Bumphunter. The first is what statistic to collect from the initial fitting for further analysis. The second is to perform kernel smoothing under the assumption of correlated errors using a newly proposed correlationadjusted kernel weight. The third is how to define regions of interest. In simulation, the method was shown to have high power comparable to Bumphunter, with consistently lower familywise type I error rate, controlled well below the 0.1 FDR. DMR Detector was applied to real data and was able to detect one DMR that was not detected by Bumphunter.

A Modified Information Criterion in the 1d Fused Lasso for DNA Copy Number Variant Detection using Next Generation Sequencing DataDNA Copy Number Variations (CNVs) are associated with many human diseases. Recently, CNV studies have been carried out using Next Generation Sequencing (NGS) technology that produces millions of short reads. With NGS reads ratio data, we use the 1d fused lasso regression for CNV detection. Given the number of copy number changes, the corresponding genomic locations are estimated by fitting the 1d fused lasso. Estimation of the number of copy number changes depends on a tuning parameter in the 1d fused lasso. In this dissertation, we propose a new modified Bayesian information criterion, called JMIC, to estimate the optimal tuning parameter in the 1d fused lasso. In theoretical studies, we prove that the number of change points estimated by JMIC converges the true number of changes. Also, our simulation studies show that JMIC outperforms the other criteria considered. Finally, we apply our proposed method to the reads ratio data from the breast tumor cell HCC1954 and its matched cell line provided by Chiang et al. (2009).

Multivariate Poisson Abundance Models for Analyzing Antigen Receptor DataAntigen receptor data is an important source of information for immunologists that is highly statistically challenging to analyze due to the presence of a huge number of Tcell receptors in mammalian immune systems and the severe undersampling bias associated with the commonly used data collection procedures. Many important immunological questions can be stated in terms of richness and diversity of Tcell subsets under various experimental conditions. This dissertation presents a class of parametric models and uses a special case of them to compare the richness and diversity of antigen receptor populations in mammalian Tcells. The parametric models are based on a representation of the observed receptor counts as a multivariate Poisson abundance model (mPAM). A Bayesian model tting procedure is developed which allows tting of the mPAM parameters with the help of the complete likelihood as opposed to its conditional version which was used previously. The new procedure is shown to be often considerably more e cient (as measured by the amount of Fisher information) in the regions of the mPAM parameter space relevant to modeling Tcell data. A richness estimator based on the special case of the mPAM is shown to be superior to several existing richness estimators from the statistical ecology literature under the severe undersampling conditions encountered in antigen receptor data collection. The comparative diversity analyses based on the mPAM special case yield biologically meaningful results when applied to the Tcell receptor repertoires in mice. It is also shown that the amount of time to implement the Bayesian model tting procedure for the mPAM special case scales well as the dimension increases and that the amount of computational resources required to conduct complete statistical analyses for the mPAM special case can be drastically lower for our Bayesian model tting procedure than for code based on the conditional likelihood approach.

A New Method For Analyzing 1:N Matched Case Control Studies With Incomplete Data1:n matched casecontrol studies are commonly used to evaluate the association between the exposure to a risk factor and a disease, where one case is matched to up till n controls. The odds ratio is typically used to quantify such association. Difficulties in estimating the true odds ratio arise, when the exposure status is unknown for at least one individual in a group. In the case where the exposure status is known for all individuals in a group, the true odds ratio is estimated as the ratio of the counts in the discordant cells of the observed twobytwo table. In the case where all data are independent, the odds ratio is estimated using the crossproduct ratio from the observed table. Conditional logistic regression estimates are used for incomplete matching data. In this dissertation we suggest a simple method for estimating the odds ratio when the sample consists of a combination of paired and unpaired observations, with 1:n matching. This method uses a weighted average of the odds ratio calculations described above. This dissertation compares the new method to existing methods via simulation.

Penalized Least Squares and the Algebraic Statistical Model for Biochemical Reaction NetworksSystems biology seeks to understand the formation of macro structures such as cellular processes and higher level cellular phenomena by investigating the interactions of systems’ individual components. For cellular biology, this goal is to understand the dynamic behavior of biological materials within the cell, a container consisting of smaller materials such as mRNA, proteins, enzymes and other intermediates necessary for regulating intracellular functions and chemical species levels. Understanding these cellular dynamics is needed to help develop new drug therapies, which can be targeted to specific molecules or specific genes, in order to perturb the system for a desired result. In this work we develop inferential procedures to estimate reaction rate coefficients in cellular systems of ordinary differential equations (ODEs) from noisy data arising from realizations of molecular trajectories. It is assumed that these systems obey the so called chemical mass action law of kinetics, with corresponding deterministic mass action limit as the system size becomes infinite. The estimation and inference is based on the penalized least squares estimates, where the covariance structure of these estimates corresponds to the solution of a system of coupled nonautonomuous ODEs. Another topic discussed here is that of network topology estimation. The algebraic statistical model (ASM) offers a means of performing this topological inference for the special class of conic networks. We prove that the ASM recovers the true network topology as the number of samples grows without bound, a property known in the literature as sparsistency. We propose a method to extend the ASM to a wider class of networks that are decomposable into multiple cones.

A resampling method of time course gene expression data for gene network inferenceManipulation of cellular functions may aid in treatment and/or cure of a disease. Thus, identifying the topology of a gene regulatory network (GRN) and the molecular role of each gene is essential. Discovering GRNs from gene expression data is hampered by intrinsic attributes of the data: small sample size n, large number of variables (genes) p, and unknown error structure. Numerous theoretical approaches for GRN inference attempt to overcome these difficulties; however, most solutions utilized in these methods are to provide either point estimators such as coefficient estimators or make numerous assumptions which are often incompatible with the data. Furthermore, the different solutions cause GRN inference methods to provide inconsistent results. This dissertation proposes a resampling method for timecourse gene expression data which can provide interval estimators for existing GRN inference methods without any distributional assumptions via bootstrapping and a statistical model that considers the various components of the data structure such as trend of gene expressions, errors of timecourse data, and correlation between genes, etc. This method will produce more precise GRNs that are consistent with observed gene expression data. Furthermore, by applying our method to multiple existing GRN inference methods, the resulting networks obtained from different inference methods could be combined using the joint confidence region for their parameters. Thus, this method can be used for the validation of identified networks and GRN inference methods.

Statistical Methods for reaction NetworksStochastic reaction networks are important tools for modeling many biological phenomena, and understanding these networks is important in a wide variety of applied research, such as in disease treatment and in drug development. Statistical inference about the structure and parameters of reaction networks, sometimes referred to in this setting as model calibration, is often challenging due to intractable likelihoods. Here we utilize an idea similar to that of generalized estimating equations (GEE), which in this context are the socalled martingale estimating equations, for estimation of reaction rates of the network. The variance component is estimated using the approximate variance under the linear noise approximation, which is based on partial dierential equation, or FokkerPlanck equations, which provides an approximation to the exact chemical master equation. The method is applied to data from the plague outbreak at Eyam, England from 16651666 and the COVID19 pandemic data. We show empirically that the proposed method gives good estimates of the parameters in a large volume setting and works well in small volume settings.

Statistical Methods to Detect Deferentially Methyleated Regions with NextGeneration Sequencing DataResearchers in genomics are increasingly interested in epigenetic factors such as DNA methylation because they play an important role in regulating gene expression without changes in the sequence of DNA. Abnormal DNA methylation is associated with many human diseases, including various types of cancer. We propose three different approaches to test for differentially methylated regions (DMRs) associated with complex traits, while accounting for correlations within and among CpG sites in the DMRs. One approach is a nonparametric method using a kernel distance statistic and the second one is a likelihoodbased method using a binomial spatial scan statistic. Both of these approaches detect differential methylation regions between cases and controls along the genome. The kernel distance method uses the kernel function, while the binomial scan statistic approach uses a mixed effect model to incorporate correlations among CpG sites. Extensive simulations show that both approaches have excellent control of type I error, and both have reasonable statistical power. The binomial scan statistic approach appears to have higher power, while the kernel distance method is computationally faster. We also propose a third method under the Bayesian framework for comparing methylation rates when disease status is classified into ordinal multinomial categories (e.g., stages of cancer). The DMRs are detected using moving windows along the genome. Within each window, the Bayes factor is calculated to compare the two models corresponding to constant vs. monotonic methylation rates among the groups. As in the case of the scan statistic approach, the correlations between the sites are incorporated using a mixed effect model. Results from extensive simulation indicate that the Bayesian method is statistically valid and reasonably powerful to detect DMRs associated with disease severity. The proposed methods are demonstrated using data from a chronic lymphocytic leukemia (CLL) study.

TWOSAMPLE TESTS FOR HIGH DIMEMSIONAL MEANS WITH PREPIVOTING and DATA TRANSFORMATIONWithin the medical field, the demand to store and analyze small sample, large variable data has become everabundant. Several twosample tests for equality of means, including the revered Hotelling’s T2 test, have already been established when the combined sample size of both populations exceeds the dimension of the variables. However, tests such as Hotelling’s T2 become either unusable or output small power when the number of variables is greater than the combined sample size. We propose a test using both prepivoting and Edgeworth expansion that maintains high power in this higher dimensional scenario, known as the “large p small n ” problem. Our test’s finite sample performance is compared with other recently proposed tests designed to also handle the “large p small n ” situation. We apply our test to a microarray gene expression data set and report competitive rates for both power and TypeI error.