Browsing by Author "Vsevolozhskaya, Olga"

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Follow-up testing in functional analysis of variance
(Montana State University - Bozeman, College of Letters & Science, 2013) Vsevolozhskaya, Olga; Chairperson, Graduate Committee: Mark Greenwood; Mark C. Greenwood, Gabriel J. Bellante, Scott L. Powell, Rick L. Lawrence and Kevin S. Repasky were co-authors of the article, 'Combining functions and the closure principle for performing follow-up tests in functional analysis of variance.' in the journal 'Journal of computational statistics and data analysis' which is contained within this thesis.; Mark C. Greenwood and Dmitri Holodov were co-authors of the article, 'Pairswise comparison of treatment levels in functional analysis of variance with application to erythrocyte hemolysis' submitted to the journal 'Journal of annals of applied statistics' which is contained within this thesis.; Mark C. Greenwood, Scott L. Powell, and Dmitri V. Zaykin were co-authors of the article, 'Resampling-based multiple comparison procedure with application to point-wise testing with functional data' submitted to the journal 'Environmental and ecological statistic' which is contained within this thesis.
Sampling responses at a high time resolution is gaining popularity in pharmaceutical, epidemiological, environmental and biomedical studies. For example, investigators might expose subjects continuously to a certain treatment and make measurements throughout the entire duration of each exposure. An important goal of statistical analysis for a resulting longitudinal sequence is to evaluate the effect of the covariates, which may or may not be time dependent, on the outcomes of interest. Traditional parametric models, such as generalized linear models, nonlinear models, and mixed effects models, are all subject to potential model misspecification and may lead to erroneous conclusions in practice. In semiparametric models, a time-varying exposure might be represented by an arbitrary smooth function (the nonparametric part) and the remainder of the covariates are assumed to be fixed (the parametric part). The potential drawbacks of the semiparametric approach are uncertainty in the smoothing function interpretation, and ambiguity in the parametric test (a particular regression coefficient being zero in the presence of the other terms in the model). Functional linear models (FLM), or the so called structural nonparametric models, are used to model continuous responses per subject as a function of time-variant coefficients and a time-fixed covariate matrix. In recent years, extensive work has been done in the area of nonparametric estimation methods, however methods for hypothesis testing in the functional data setting are still undeveloped and greatly in demand. In this research we develop methods that address hypotheses testing problem in a special class of FLMs, namely the Functional Analysis of Variance (FANOVA). In the development of our methodology, we pay a special attention to the problem of multiplicity and correlation among tests. We discuss an application of the closure principle to the follow-up testing of the FANOVA hypotheses as well as computationally efficient shortcut arising from a combination of test statistics or p-values. We further develop our methods for pair-wise comparison of treatment levels with functional data and apply them to simulated as well as real data sets.
Functional Analysis of Variance for Association Studies
(Public Library of Science, 2014) Greenwood, Mark C.; Vsevolozhskaya, Olga; Zaykin, Dmitri; Wei, Changshuai; Lu, Qing
While progress has been made in identifying common genetic variants associated with human diseases, for most of common complex diseases, the identified genetic variants only account for a small proportion of heritability. Challenges remain in finding additional unknown genetic variants predisposing to complex diseases. With the advance in next-generation sequencing technologies, sequencing studies have become commonplace in genetic research. The ongoing exome-sequencing and whole-genome-sequencing studies generate a massive amount of sequencing variants and allow researchers to comprehensively investigate their role in human diseases. The discovery of new disease-associated variants can be enhanced by utilizing powerful and computationally efficient statistical methods. In this paper, we propose a functional analysis of variance (FANOVA) method for testing an association of sequence variants in a genomic region with a qualitative trait. The FANOVA has a number of advantages: (1) it tests for a joint effect of gene variants, including both common and rare; (2) it fully utilizes linkage disequilibrium and genetic position information; and (3) allows for either protective or risk-increasing causal variants. Through simulations, we show that FANOVA outperform two popularly used methods – SKAT and a previously proposed method based on functional linear models (FLM), – especially if a sample size of a study is small and/or sequence variants have low to moderate effects. We conduct an empirical study by applying three methods (FANOVA, SKAT and FLM) to sequencing data from Dallas Heart Study. While SKAT and FLM respectively detected ANGPTL 4 and ANGPTL 3 associated with obesity, FANOVA was able to identify both genes associated with obesity.