Matrix-Variate Regression with Measurement Error

Matrix-variate regression models are useful for featuring data with a matrix structure, such as brain imaging data. However, those methods do not apply to data with measurement error or misclassification. While mismeasurement is an inevitable issue in the data collecting process, little research has been available to handle matrix-variate regression with mismeasurement. In this thesis, we explore several important problems concerning matrix-variate regression with error-contaminated data. In Chapter 1, we provide a brief introduction for matrix-variate data and review relevant topics including logistic regression analysis, measurement error/misclassification mechanisms, regularization methods, and Bayesian inference procedures. In Chapter 2, we discuss matrix-variate logistic regression for handling error-contaminated data. Measurement error in covariates has been extensively studied in many conventional regression settings where covariate information is typically expressed in a vector form. However, there has been little work on error-prone matrix-variate data which commonly arise from studies with imaging, spatial-temporal structures. We particularly focus on matrix-variate logistic measurement error models. We examine the biases induced from the naive analysis which ignores measurement error. Two measurement error correction methods are developed to adjust for measurement error effects. The proposed methods are justified both theoretically and empirically. We analyze a data set arising from a study examining electroencephalography(EEG) correlates of genetic predisposition to alcoholism with the proposed methods. In Chapter 3, we consider a problem complement to that in Chapter 2. Instead of examining mismeasurement in covariates, here we study mismeasurement in binary responses. We particularly investigate the response misclassification effects on the matrix- variate logistic regression model. Matrix-variate logistic regression is useful in facilitating the relationship between the binary response and matrix-variates which arise commonly from medical imaging research. However, such a model is impaired by the presence of the response misclassification. It is imperative to account for misclassification effects when employing matrix-variate logistic regression to handle such data. In this chapter, we develop two inferential methods which account for misclassification effects. The first method is an imputation method which replaces the response variable with an observed and unbiased pseudo-response variable in the estimation procedure. The second method is derived from the likelihood function for the observed response surrogate. Our development is carried out for two settings where misclassification rates are either known or estimated from validation data. The proposed methods are justified both theoretically and empirically. We analyze the breast cancer Wisconsin prognostic data with the proposed methods. Chapter 4 is a continuation and extension of Chapter 3. We consider regularized matrix- variate logistic regression with response misclassification, where matrix-variate data may assume a sparsity structure. With a limited sample size, the presence of a large number of redundant parameters entails the difficulty of estimation. In this chapter, we develop inferential methods which account for misclassification effects in combination with the inclusion of penalty functions to deal with the sparsity of matrix-variate data. We examine the biases induced from the naive analysis which ignores the response misclassification. Our development is carried out for two settings where misclassification rates are either known or estimated from validation data. The proposed methods are justified both theoretically and empirically. We analyze the breast cancer Wisconsin prognostic data with the proposed methods. In Chapter 5, we shift our attention to the Bayesian framework. We consider applying Bayesian analysis to matrix-variate logistic regression. We propose a Bayesian algorithm to estimate the matrix-variate parameters element-wisely in combination with the use of horse-shore shrinkage prior. We investigate the influence on parameter estimation when ignoring the response misclassification and propose an algorithm to accommodate the effects of response misclassification. The performance of the proposed method is evaluated through numerical studies. We analyze the Lee Silverman voice treatment (LSVT) Companion data with the proposed method. Finally, Chapter 6 summarizes the thesis work and presents some future work

Design of egocentric network-based studies to estimate causal effects under interference

Many public health interventions are conducted in settings where individuals are connected to one another and the intervention assigned to randomly selected individuals may spill over to other individuals they are connected to. In these spillover settings, the effects of such interventions can be quantified in several ways. The average individual effect measures the intervention effect among those directly treated, while the spillover effect measures the effect among those connected to those directly treated. In addition, the overall effect measures the average intervention effect across the study population, over those directly treated along with those to whom the intervention spills over but who are not directly treated. Here, we develop methods for study design with the aim of estimating individual, spillover, and overall effects. In particular, we consider an egocentric network-based randomized design in which a set of index participants is recruited from the population and randomly assigned to treatment, while data are also collected from their untreated network members. We use the potential outcomes framework to define two clustered regression modeling approaches and clarify the underlying assumptions required to identify and estimate causal effects. We then develop sample size formulas for detecting individual, spillover, and overall effects. We investigate the roles of the intra-class correlation coefficient and the probability of treatment allocation on the required number of egocentric networks with a fixed number of network members for each egocentric network and vice-versa.Comment: 30 pages for main text including figures and tables, 5 figures and 3 table

Density fluctuations dispersion relationship for a polymer confined to a nanotube

DNA confined to rigid nanotubes shows density fluctuations around its stretched equilibrium conformation. We report an experimental investigation of the length-scale dependent dynamics of these density fluctuations. We find that for highly elongated molecules a Rouse description is consistent with observations at sufficiently large length scales. We further find that for strongly fluctuating molecules, or short length scales, such Rouse modes cannot be detected due to strong mixing of fluctuation modes