Chapter Nonparametric methods for stratified C-sample designs: a case study

Several parametric and nonparametric methods have been proposed to deal with stratified C-sample problems where the main interest lies in evaluating the presence of a certain treatment effect, but the strata effects cannot be overlooked. Stratified scenarios can be found in several different fields. In this paper we focus on a particular case study from the field of education, addressing a typical stochastic ordering problem in the presence of stratification. We are interested in assessing how the performance of students from different degree programs at the University of Padova change, in terms of university credits and grades, when compared with their entry test results. To address this problem, we propose an extension of the Non-Parametric Combination (NPC) methodology, a permutation-based technique (see Pesarin and Salmaso, 2010), as a valuable tool to improve the data analytics for monitoring University students’ careers at the School of Engineering of the University of Padova. This new procedure indeed allows us to assess the efficacy of the University of Padova’s entry tests in evaluating and selecting future students

Approximation of Quantiles of Rank Test Statistics Using Almost Sure Limit Theorems

There are many problems in statistics where the analysis is based on asymptotic distributions. In some cases, the asymptotic distribution is in an open form or is intractable. One possible solution is the logarithmic quantile estimation (LQE) method introduced by Thangavelu (2005) for rank tests and Fridline (2010) for the correlation coefficient. LQE is derived from an almost sure version of the central limit theorem using the results of Berkes and Csaki (2001), and it estimates the quantiles of a test statistic using only the data. To date, LQE has been used in only a few applications. We extend the use of LQE to three widely analyzed problems. We investigate the LQE approach using fully nonparametric rank statistics to test for known trend and umbrella patterns in the main effects of three widely used factorial designs: a two-factor fixed effect model, a partial hierarchical repeated measures mixed effect model, and a mixed effect cross-classification repeated measures model. We also test for patterned alternatives in the interaction between the main effect and time in the partial hierarchical repeated measures model. We derive the almost sure central limit theorems for all of these problems and determine the level and power. The Pettitt (1979) test is a nonparametric test based on the Mann-Whitney statistic used to detect a change in distribution in a sequence of random variables. The proposed statistic has an asymptotic distribution that is the distribution of the supremum of the absolute value of the Brownian bridge, which has an open form. We propose an approximation of the quantiles for the test statistic based on LQE. We provide simulation results for Type I error and power of the logarithmic quantile estimates for the test statistic, and compare the LQE results with other methods for two real data examples. Thangavelu (2005) considered LQE for the nonparametric Behrens-Fisher problem with some success by introducing new numerically determined coefficients. We examine the nonparametric two-sample problem using an empirical process of U-statistic structure (Denker and Puri, 1992). Specifically, we investigate using LQE with a second order U-statistic for paired averages within each sample. We provide simulation results to show almost sure convergence of the new test statistic

Metabolomics analysis identifies sex-associated metabotypes of oxidative stress and the autotaxin-lysoPA axis in COPD.

Chronic obstructive pulmonary disease (COPD) is a heterogeneous disease and a leading cause of mortality and morbidity worldwide. The aim of this study was to investigate the sex dependency of circulating metabolic profiles in COPD.Serum from healthy never-smokers (healthy), smokers with normal lung function (smokers), and smokers with COPD (COPD; Global Initiative for Chronic Obstructive Lung Disease stages I-II/A-B) from the Karolinska COSMIC cohort (n=116) was analysed using our nontargeted liquid chromatography-high resolution mass spectrometry metabolomics platform.Pathway analyses revealed that several altered metabolites are involved in oxidative stress. Supervised multivariate modelling showed significant classification of smokers from COPD (p=2.8×10-7). Sex stratification indicated that the separation was driven by females (p=2.4×10-7) relative to males (p=4.0×10-4). Significantly altered metabolites were confirmed quantitatively using targeted metabolomics. Multivariate modelling of targeted metabolomics data confirmed enhanced metabolic dysregulation in females with COPD (p=3.0×10-3) relative to males (p=0.10). The autotaxin products lysoPA (16:0) and lysoPA (18:2) correlated with lung function (forced expiratory volume in 1 s) in males with COPD (r=0.86; p<0.0001), but not females (r=0.44; p=0.15), potentially related to observed dysregulation of the miR-29 family in the lung.These findings highlight the role of oxidative stress in COPD, and suggest that sex-enhanced dysregulation in oxidative stress, and potentially the autotaxin-lysoPA axis, are associated with disease mechanisms and/or prevalence

Statistical Theory and Methodology for the Analysis of Microbial Compositions, with Applications

Increasingly researchers are finding associations between the microbiome and human diseases such as obesity, inflammatory bowel diseases, HIV, and so on. Determining what microbes are significantly different between conditions, known as differential abundance (DA) analysis, and depicting the dependence structure among them, are two of the most challenging and critical problems that have received considerable interest. It is well documented in the literature that the observed microbiome data are relative abundances with excess zeros. These data are necessarily compositional; hence conventional DA methods are not appropriate as they significantly inflate the false discovery rate (FDR), and the standard notion of correlation often results in spurious correlation. To overcome such difficulties, in this dissertation, we develop a general statistical framework that can address a broad collection of problems encountered by researchers. This dissertation work is organized as follows. In Chapter 1, we conduct a brief review of the literature of a variety of parameters used to characterize microbial composition. Specifically, we shall describe various concepts of diversity and differential taxa abundance. In Chapter 2, an off-set based regression model, called the Analysis of Composition of Microbiomes with Bias Correction (ANCOM-BC), is introduced. The ANCOM-BC model not only successfully controls the FDR at the desired level but also maintains high power. Simulations and real data analysis were conducted to compare the performance of ANCOM-BC with other commonly used algorithms. In Chapter 3, we extend ANCOM-BC for performing DA analysis when there are more than two ecosystems. We tested the method for a variety of alternative hypotheses. Similar simulation settings and real data were used to evaluate its performance. Lastly, in Chapter 4, we introduce a distance correlation based methodology, called Distance Correlation for Microbiome (DICOM), to untangle dependence structure among microbes within an ecosystem or across ecosystems (e.g., gut and oral microbiomes). PUBLIC HEALTH SIGNIFICANCE: This dissertation proposes a general statistical framework for studying microbial compositions. The identified differentially abundant taxa and the constructed dependence network could provide medical experts more knowledge of changes in patients' microbiome. This information could contribute to developing precision medicine for better patient care

Methods for non-proportional hazards in clinical trials: A systematic review

For the analysis of time-to-event data, frequently used methods such as the log-rank test or the Cox proportional hazards model are based on the proportional hazards assumption, which is often debatable. Although a wide range of parametric and non-parametric methods for non-proportional hazards (NPH) has been proposed, there is no consensus on the best approaches. To close this gap, we conducted a systematic literature search to identify statistical methods and software appropriate under NPH. Our literature search identified 907 abstracts, out of which we included 211 articles, mostly methodological ones. Review articles and applications were less frequently identified. The articles discuss effect measures, effect estimation and regression approaches, hypothesis tests, and sample size calculation approaches, which are often tailored to specific NPH situations. Using a unified notation, we provide an overview of methods available. Furthermore, we derive some guidance from the identified articles. We summarized the contents from the literature review in a concise way in the main text and provide more detailed explanations in the supplement (page 29)

Multidimensional random sampling for Fourier transform estimation

This research considers the Fourier transform calculations of multidimensional signals. The calculations are based on random sampling, where the sampling points are nonuniformly distributed according to strategically selected probability functions, to provide new opportunities that are unavailable in the uniform sampling environment. The latter imposes the sampling density of at least the Nyquist density. Otherwise, alias frequencies occur in the processed bandwidth which can lead to irresolvable processing problems. Random sampling can mitigate Nyquist limit that classical uniform-sampling-based approaches endure, for the purpose of performing direct (with no prefiltering or downconverting) Fourier analysis of (high-frequency) signals with unknown spectrum support using low sampling density. Lowering the sampling density while achieving the same signal processing objective could be an efficient, if not essential, way of exploiting the system resources in terms of power, hardware complexity and the acquisition-processing time. In this research we investigate and devise novel random sampling estimation schemes for multidimensional Fourier transform. The main focus of the investigation and development is on the aspect of the quality of estimated Fourier transform in terms of the sampling density. The former aspect is crucial as it serves towards the heart objective of random sampling of lowering the sampling density. This research was motivated by the applicability of the random-sampling-based approaches in determining the Fourier transform in multidimensional Nuclear Magnetic Resonance (NMR) spectroscopy to resolve the critical issue of its long experimental time

Likelihood Asymptotics in Nonregular Settings: A Review with Emphasis on the Likelihood Ratio

This paper reviews the most common situations where one or more regularity conditions which underlie classical likelihood-based parametric inference fail. We identify three main classes of problems: boundary problems, indeterminate parameter problems -- which include non-identifiable parameters and singular information matrices -- and change-point problems. The review focuses on the large-sample properties of the likelihood ratio statistic. We emphasize analytical solutions and acknowledge software implementations where available. We furthermore give summary insight about the possible tools to derivate the key results. Other approaches to hypothesis testing and connections to estimation are listed in the annotated bibliography of the Supplementary Material

Psychological interventions to improve glycemic control in adults with type 2 diabetes: a systematic review and meta-analysis

The quality of evidence that psychological interventions are effective in improving glycemic control in adults with type 2 diabetes (T2D) is weak. We conducted a systematic review and meta-analysis of psychological interventions in T2D to assess whether their effectiveness in improving glycemic levels has improved over the past 30 years. We applied the protocol of a systematic review and aggregate meta-analysis conducted to January 2003. We added network meta-analysis (NMA) to compare intervention and control group type against usual care. MEDLINE, Cumulative Index to Nursing and Allied Health Literature, PsycINFO, EMBASE, Cochrane Controlled Trials Database, Web of Science, and Dissertation Abstracts International were searched from January 2003 to July 2018. Only randomized controlled trials (RCT) of psychological interventions for adults with T2D reported in any language were included. The primary outcome was change in glycemic control (glycated hemoglobin (HbA1c) in mmol/mol). Data were extracted from study reports and authors were contacted for missing data. 94 RCTs were eligible for inclusion in the systematic review since the last review. In 70 RCTs (n=14 796 participants) the pooled mean difference in HbA1c in those randomized to psychological intervention compared with control group was −0.19 (95% CI −0.25 to −0.12), equivalent to a reduction in HbA1c of 3.7 mmol/mol, with moderate heterogeneity across studies (I2=64.7%, p<0.001). NMA suggested the probability of intervention effectiveness is highest for self-help materials, cognitive–behavioral therapy, and counseling, compared with usual care. Limitations of this study include that there is a possibility that some studies may have been missed if diabetes did not appear in the title or abstract. The effectiveness of psychological interventions for adults with T2D have minimal clinical benefit in improving glycemic control. PROSPERO registration number CRD42016033619