Repeated measures discriminant analysis using multivariate generalized estimation equations

Discriminant analysis procedures that assume parsimonious covariance and/or means structures have been proposed for distinguishing between two or more populations in multivariate repeated measures designs. However, these procedures rely on the assumptions of multivariate normality which is not tenable in multivariate repeated measures designs which are characterized by binary, ordinal, or mixed types of response distributions. This study investigates the accuracy of repeated measures discriminant analysis (RMDA) based on the multivariate generalized estimating equations (GEE) framework for classification in multivariate repeated measures designs with the same or different types of responses repeatedly measured over time. Monte Carlo methods were used to compare the accuracy of RMDA procedures based on GEE, and RMDA based on maximum likelihood estimators (MLE) under diverse simulation conditions, which included number of repeated measure occasions, number of responses, sample size, correlation structures, and type of response distribution. RMDA based on GEE exhibited higher average classification accuracy than RMDA based on MLE especially in multivariate non-normal distributions. Three repeatedly measured responses namely severity of epilepsy, current number of anti-epileptic drugs, and parent-reported quality of life in children with epilepsy were used to demonstrate the application of these procedures.

Analysis of Multiuser Cellular Systems Over Heterogeneous Channels

<p>This thesis considers the analysis of current and future cellular communication systems. The main focus is on multiuser multiple-input multiple-output (MU-MIMO) antenna systems. The goal of this work is to characterize the achievable spectral efficiency of MU-MIMO systems, as well as to analyze the performance of practical, linear MU-MIMO transceiver structures in heterogeneous propagation environments. The analytical derivations in this thesis are based on the mathematical theory of finite and large dimensional random matrices. A collection of new general random matrix theory results, which permit efficient numerical evaluation are derived. With downlink regularized zero-forcing (RZF) processing at a cellular base station (BS), a general framework for the analysis of the expected (average) signal-to-interference-plus-noise-ratio (SINR) and ergodic sum spectral efficiency is developed for uncorrelated and semi-correlated Rayleigh fading, as well as uncorrelated Ricean fading propagation channels. In contrast to existing results, the presented analyses are extremely general, applicable to single-cellular, multi-cellular, as well as distributed antenna systems. These systems could consist of arbitrary numbers of transmit and receive antennas, link signal-to-noise-ratios (SNRs), equal and unequal transmit correlation structures, and line-of-sight (LoS) levels, respectively. Numerical results are presented for single-cellular, as well as for two-tier multi-cellular systems demonstrating the impact of novel BS coordination strategies to suppress dominant inter-cellular interference. With dominant LoS directions in the propagation channel, the instantaneous downlink zero-forcing (ZF) SNR of a given terminal is analyzed. The ZF SNR is shown to be approximated by a gamma distribution for any number of transmit and receive antennas, link SNRs, and LoS levels. Furthermore, for moderately sized MU-MIMO systems, simplified instantaneous and ergodic sum spectral efficiency analyses are presented with RZF, ZF and matched-filter (MF) transmission on the downlink, and minimum-mean-squared-error, ZF and maximum-ratio combining (MRC) on the uplink, respectively. The simple nature of the derived expressions lead to the discovery of several valuable system level insights as a function of the contributing network parameters. Numerical results are presented for conventional and moderate MU-MIMO systems. Considering downlink semi-correlated Rayleigh fading channels with spatial correlation at the BS, it is mathematically proven that common correlation patterns for each terminal predicts lower ergodic sum spectral efficiencies in comparison to terminal specific correlation patterns. Closed-form approximations for the expected SINR and ergodic sum spectral efficiency are derived for both MF and ZF precoding, demonstrating the sensitivity of unequal correlation structures on the expected signal, interference and noise powers, respectively. The presented numerical results provide a cautionary tale of the impact of unequal correlation patterns on MU-MIMO performance and the importance of modeling this phenomenon. Finally, an approximate uplink performance analysis of large MU-MIMO systems with MRC and space-constrained uniform linear antenna arrays (ULA) is presented for semi-correlated Ricean fading channels. A space-constrained channel model is proposed, encapsulating the effects of unequal receive spatial correlation, unequal LoS levels, and unequal link gains for each terminal. The per-terminal and cell-wide ergodic sum spectral efficiencies are characterized and numerous practical special cases are presented. A limiting analysis of the ergodic per-terminal and cell-wide spectral efficiencies is also carried out, as the number of BS antennas grow without bound with a finite number of terminals and fixed physical dimensions of the ULA. Numerical results demonstrate the impact of space-constrained ULAs on the MU-MIMO system performance with variation in the LoS levels, correlation structures, physical array dimensions, and system size, respectively.</p>

Analysis of Multiuser Cellular Systems Over Heterogeneous Channels

<p>This thesis considers the analysis of current and future cellular communication systems. The main focus is on multiuser multiple-input multiple-output (MU-MIMO) antenna systems. The goal of this work is to characterize the achievable spectral efficiency of MU-MIMO systems, as well as to analyze the performance of practical, linear MU-MIMO transceiver structures in heterogeneous propagation environments. The analytical derivations in this thesis are based on the mathematical theory of finite and large dimensional random matrices. A collection of new general random matrix theory results, which permit efficient numerical evaluation are derived. With downlink regularized zero-forcing (RZF) processing at a cellular base station (BS), a general framework for the analysis of the expected (average) signal-to-interference-plus-noise-ratio (SINR) and ergodic sum spectral efficiency is developed for uncorrelated and semi-correlated Rayleigh fading, as well as uncorrelated Ricean fading propagation channels. In contrast to existing results, the presented analyses are extremely general, applicable to single-cellular, multi-cellular, as well as distributed antenna systems. These systems could consist of arbitrary numbers of transmit and receive antennas, link signal-to-noise-ratios (SNRs), equal and unequal transmit correlation structures, and line-of-sight (LoS) levels, respectively. Numerical results are presented for single-cellular, as well as for two-tier multi-cellular systems demonstrating the impact of novel BS coordination strategies to suppress dominant inter-cellular interference. With dominant LoS directions in the propagation channel, the instantaneous downlink zero-forcing (ZF) SNR of a given terminal is analyzed. The ZF SNR is shown to be approximated by a gamma distribution for any number of transmit and receive antennas, link SNRs, and LoS levels. Furthermore, for moderately sized MU-MIMO systems, simplified instantaneous and ergodic sum spectral efficiency analyses are presented with RZF, ZF and matched-filter (MF) transmission on the downlink, and minimum-mean-squared-error, ZF and maximum-ratio combining (MRC) on the uplink, respectively. The simple nature of the derived expressions lead to the discovery of several valuable system level insights as a function of the contributing network parameters. Numerical results are presented for conventional and moderate MU-MIMO systems. Considering downlink semi-correlated Rayleigh fading channels with spatial correlation at the BS, it is mathematically proven that common correlation patterns for each terminal predicts lower ergodic sum spectral efficiencies in comparison to terminal specific correlation patterns. Closed-form approximations for the expected SINR and ergodic sum spectral efficiency are derived for both MF and ZF precoding, demonstrating the sensitivity of unequal correlation structures on the expected signal, interference and noise powers, respectively. The presented numerical results provide a cautionary tale of the impact of unequal correlation patterns on MU-MIMO performance and the importance of modeling this phenomenon. Finally, an approximate uplink performance analysis of large MU-MIMO systems with MRC and space-constrained uniform linear antenna arrays (ULA) is presented for semi-correlated Ricean fading channels. A space-constrained channel model is proposed, encapsulating the effects of unequal receive spatial correlation, unequal LoS levels, and unequal link gains for each terminal. The per-terminal and cell-wide ergodic sum spectral efficiencies are characterized and numerous practical special cases are presented. A limiting analysis of the ergodic per-terminal and cell-wide spectral efficiencies is also carried out, as the number of BS antennas grow without bound with a finite number of terminals and fixed physical dimensions of the ULA. Numerical results demonstrate the impact of space-constrained ULAs on the MU-MIMO system performance with variation in the LoS levels, correlation structures, physical array dimensions, and system size, respectively.</p>

Detecting Sparse Microbial Association Signals Adaptively From Longitudinal Microbiome Data Based on Generalized Estimating Equations

Background: The relationship between the compositions of microbial communities and various host phenotypes is an important research topic. Microbiome association research addresses multiple domains, such as human disease, diet and medicine. Statistical methods for testing microbiome-phenotype associations have been studied recently to determine their ability to assess longitudinal microbiome data. However, existing methods fail to detect sparse association signals in longitudinal microbiome data. Methods: In this paper, we developed a novel method, namely, aGEEMiHC, which is a data-driven adaptive microbiome higher criticism analysis based on generalized estimating equations, to detect sparse microbial association signals from longitudinal microbiome data. aGEEMiHC adopts a generalized estimating equations framework that fully considers the correlation among different observations from the same cluster (individuals) in longitudinal data, and it integrates multiple microbiome higher criticism analyses based on generalized estimating equations by setting different working correlation structures. Thus, the proposed method is robust to diverse correlation structures for longitudinal data.Results: The proposed method shows a stable performance for diverse association patterns in both sparsity levels and phylogenetic relevance. Extensive simulation experiments demonstrate that it can control the type I error correctly and achieve superior performance according to a statistical power comparison. In our simulation, we applied aGEEMiHC to longitudinal microbiome data with various types of host phenotypes to demonstrate the stability of our method. aGEEMiHC is also utilized for real longitudinal microbiome data, and we found a significant association between the gut microbiome and Crohn's disease. Conclusions: aGEEMiHC is a statistical method that facilitates association testing for sparse microbial association signals from longitudinal microbiome data, and it can be applied to situations in which the true underlying correlations among different observations from the same cluster in longitudinal data are unknown. It is worth noting that our method also ranks the significant factors associated with the host phenotype to provide potential biomarkers. The R package GEEMiHC is available at https://github.com/xpjiang-ccnu/GEEMiHC.

Correction to: Correlation Structures between Satellite All-Sky Infrared Brightness Temperatures and the Atmospheric State at Storm Scales

The article “Correlation Structures between Satellite All-Sky Infrared Brightness Temperatures and the Atmospheric State at Storm Scales”, written by Yunji ZHANG, Eugene E. CLOTHIAUX, and David J. STENSRUD was originally published electronically on the publisher’s internet portal on 30 of April 2021 without open access. With the author(s)’ decision to opt for Open Choice, the copyright of the article changed on 26 of October 2021 to © The Author(s), 2021 and the article is forthwith distributed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0.The original article has been corrected.

DNA methylation signature of chronic low-grade inflammation and its role in cardio-respiratory diseases

We performed a trans-ethnic Epigenome Wide Association study on 22,774 individuals to describe the DNA methylation signature of chronic low-grade inflammation as measured by C-Reactive protein (CRP). We found 1,511 independent differentially methylated loci associated with CRP. These CpG sites showed correlation structures across chromosomes, and were primarily situated in euchromatin, depleted in CpG islands and enriched in transcription factor binding sites and genomic enhancer regions. Mendelian randomisation analysis suggests altered CpG methylation is a consequence of increased blood CRP levels. Mediation analysis revealed obesity and smoking as important underlying driving factors for changed CpG methylation. Finally, we found that a fully activated CpG signature, meaning that if all novel discovered CpGs would either be fully methylated or unmethylated depending on their CRP associated direction of effect, the risk of myocardial infarction would be increased by 20.3%, risk of T2D by 11.3% and the risk of COPD by 5.6%.