• Penalized Least Squares and the Algebraic Statistical Model for Biochemical Reaction Networks

      Linder, Daniel F. II; Department of Biostatistics and Epidemiology (2013-07)
      Systems 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.
    • Ranking analysis of F-statistics for microarray data.

      Tan, Yuan-De; Fornage, Myriam; Xu, Hongyan; Department of Biostatistics and Epidemiology (2008-04-15)
      BACKGROUND: Microarray technology provides an efficient means for globally exploring physiological processes governed by the coordinated expression of multiple genes. However, identification of genes differentially expressed in microarray experiments is challenging because of their potentially high type I error rate. Methods for large-scale statistical analyses have been developed but most of them are applicable to two-sample or two-condition data. RESULTS: We developed a large-scale multiple-group F-test based method, named ranking analysis of F-statistics (RAF), which is an extension of ranking analysis of microarray data (RAM) for two-sample t-test. In this method, we proposed a novel random splitting approach to generate the null distribution instead of using permutation, which may not be appropriate for microarray data. We also implemented a two-simulation strategy to estimate the false discovery rate. Simulation results suggested that it has higher efficiency in finding differentially expressed genes among multiple classes at a lower false discovery rate than some commonly used methods. By applying our method to the experimental data, we found 107 genes having significantly differential expressions among 4 treatments at <0.7% FDR, of which 31 belong to the expressed sequence tags (ESTs), 76 are unique genes who have known functions in the brain or central nervous system and belong to six major functional groups. CONCLUSION: Our method is suitable to identify differentially expressed genes among multiple groups, in particular, when sample size is small.
    • A resampling method of time course gene expression data for gene network inference

      Garren, Jeonifer Margaret; Department of Biostatistics (2015)
      Manipulation 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 time-course 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 time-course 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.
    • Simultaneous analysis of all single-nucleotide polymorphisms in genome-wide association study of rheumatoid arthritis.

      Mathew, George; Xu, Hongyan; George, Varghese; Department of Biostatistics and Epidemiology (2009-12-18)
      ABSTRACT : The availability of very large number of markers by modern technology makes genome-wide association studies very popular. The usual approach is to test single-nucleotide polymorphisms (SNPs) one at a time for association with disease status. However, it may not be possible to detect marginally significant effects by single-SNP analysis. Simultaneous analysis of SNPs enables detection of even those SNPs with small effect by evaluating the collective impact of several neighboring SNPs. Also, false-positive signals may be weakened by the presence of other neighboring SNPs included in the analysis. We analyzed the North American Rheumatoid Arthritis Consortium data of Genetic Analysis Workshop 16 using HLasso, a new method for simultaneous analysis of SNPs. The simultaneous analysis approach has excellent control of type I error, and many of the previously reported results of single-SNP analyses were confirmed by this approach.
    • SoTL Scholars Speak

      Schwind, Jessica Smith; Weeks, Thomas; Reich, Nickie; Johnson, Melissa; Armstrong, Rhonda; Hartmann, Quentin; Department of Biostatistics and Epidemiology; University Libraries; Department of Mathematics; University Libraries; Department of English and Foreign Languages; Department of English and Foreign Languages; Department of Psychological Sciences (2016-09)
      Jessica Smith Schwind, Learning is Contagious: Lessons in Online Course Design: Online learning environments are a key platform for teaching and learning in the 21st century, but they often try to simply recreate the classical in-person classroom. Our goal was to develop, implement and evaluate an immersive, online course where students are key players in a captivating epidemiologic outbreak investigation using a multidisciplinary team approach.; Thomas Weeks, Using threshold concepts in information literacy instruction: While "threshold concept" is a buzzword in information literacy instruction, can it be useful for single-session information literacy instruction? This project evaluated students who received instruction based in threshold concepts to see if they did better than their peers who received traditional skills-based instruction.; Nickie Reich, Lessons Learned From My First Son Project Traditional vs. Discovery Learning in College Algebra: Ms. Reich will step the audience through the planning, implementation, and analysis of her first So TL project. Knowledge gained from the experience and from the project data will be shared.; Melissa Johnson and Rhonda Armstrong, Using Freely Available Texts in a Literature Classroom: Rhonda Armstrong and Melissa Johnson will present their So TL project and discuss the challenges of creating an American Literature survey (pre-colonial to present) using freely-available texts. They will also discuss the students' attitude toward and level of engagement with digital texts.; Quentin Hartmann, Can peers improve performance? An investigation of the Think-Pair-Share teaching strategy: The Think-Pair-Share teaching strategy was tested with a class of psychology majors in a Senior Capstone course. All students did the same assignment alone, then one half of the students provided feedback to each other; the other half worked alone and all were given the option to revise their work. Performance between groups was compared.
    • Statistical Methods for reaction Networks

      Odubote, Oluseyi Samuel; Department of Biostatistics and Epidemiology
      Stochastic 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 so-called 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 Fokker-Planck 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 1665-1666 and the COVID-19 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 Next-Generation Sequencing Data

      Hu, Fengjiao (2016-07-07)
      Researchers 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 likelihood-based 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.

      Hellebuyck, Rafael Adriel; Department of Biostatistics and Epidemiology (2019-01-08)
      Within the medical field, the demand to store and analyze small sample, large variable data has become ever-abundant. Several two-sample 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 Type-I error.