Search

Continuous glucose monitoring (CGM) provides temporal data on glycemic variability, a predictor of outcomes related to type 2 diabetes mellitus. The current study sought to determine whether CGM-derived metrics in patients with type 2 diabetes are different in moderate-to-severe versus mild obstructive sleep apnea (OSA).In adults with type 2 diabetes, home testing was used of assess the presence of OSA. CGM data were collected for at least 7 days in those with an oxygen desaturation index (ODI) ≥ 5 events/hr. The study sample was divided into mild (ODI: 5.0-14.9 events/hr) and moderate-to-severe OSA (ODI ≥15 events/hr). Actigraphy was used to distinguish the wake and sleep periods. CGM-derived metrics were compared between the two groups using multivariable regression models.Compared to mild OSA, patients with moderate-to-severe OSA had higher mean glucose levels during sleep (adjusted difference 8.4 mg/dL; p-value: 0.03) and wakefulness (adjusted difference 7.1 mg/dL; p-value: 0.06). Moderate-to-severe OSA patients also had lower odds for having their glucose values within the acceptable range during wakefulness than those with mild OSA (adjusted odds ratio of 0.63; p-value: 0.02). The mean amplitude of glycemic excursion and standard deviation of the rate of change in glucose values (SD-ROC) were higher in moderate-to-severe than mild OSA, but only during wakefulness. Sex modified the association between OSA severity and SD-ROC, but not the other CGM-derived metrics.In patients with type 2 diabetes, moderate-to-severe OSA is associated with greater abnormalities in CGM-derived metrics than mild OSA with notable differences between sleep and wakefulness.

Methadone, a widely-prescribed medication for chronic pain and opioid addiction, is associated with respiratory depression and increased predisposition for torsades de pointes, a potentially fatal arrhythmia. Most methadone-related deaths occur during sleep. The objective of this study was to determine whether methadone’s arrhythmogenic effects increase during sleep, with a focus on cardiac repolarization instability using QT variability index (QTVI), a measure shown to predict arrhythmias and mortality. Sleep study data of 24 patients on chronic methadone therapy referred to a tertiary clinic for overnight polysomnography were compared with two matched groups not on methadone: 24 patients referred for overnight polysomnography to the same clinic (Clinic group), and 24 volunteers who had overnight polysomnography at home (Community group). Despite similar values for heart rate, heart rate variability, corrected QT interval, QTVI and oxygen saturation (SpO(2)) when awake, patients on methadone had larger QTVI (p=0.015 vs Clinic, p1000 premature beats per median sleep period), a precursor for torsades de pointes, was uncommon but more frequent in patients on methadone (p=0.039). This study demonstrates that chronic methadone use is associated with increased cardiac repolarization instability. Methadone’s pro-arrhythmic impact may be mediated by sleep-related hypoxemia which could explain the increased nocturnal mortality associated with this opioid.

Summary We introduce a multilevel functional Beta model to quantify the blood glucose levels measured by continuous glucose monitors for multiple days in study participants with type 2 diabetes mellitus. The model estimates the subject-specific marginal quantiles, quantifies the within- and between-subject variability, and produces interpretable parameters of blood glucose dynamics as a function of time from the actigraphy-estimated sleep onset. Results are validated via simulations and by studying the association between the estimated model parameters and hemoglobin A1c, the gold standard for assessing glucose control in diabetes.

Canonical correlation analysis investigates linear relationships between two sets of variables, but often works poorly on modern data sets due to high-dimensionality and mixed data types such as continuous, binary and zero-inflated. To overcome these challenges, we propose a semiparametric approach for sparse canonical correlation analysis based on Gaussian copula. Our main contribution is a truncated latent Gaussian copula model for data with excess zeros, which allows us to derive a rank-based estimator of the latent correlation matrix for mixed variable types without the estimation of marginal transformation functions. The resulting canonical correlation analysis method works well in high-dimensional settings as demonstrated via numerical studies, as well as in application to the analysis of association between gene expression and micro RNA data of breast cancer patients., Accepted to Biometrika. Main text: 19 pages and 3 figures. Supplementary material: 28 pages and 9 figures

Latent Gaussian copula models provide a powerful means to perform multi-view data integration since these models can seamlessly express dependencies between mixed variable types (binary, continuous, zero-inflated) via latent Gaussian correlations. The estimation of these latent correlations, however, comes at considerable computational cost, having prevented the routine use of these models on high-dimensional data. Here, we propose a new computational approach for estimating latent correlations via a hybrid multi-linear interpolation and optimization scheme. Our approach speeds up the current state of the art computation by several orders of magnitude, thus allowing fast computation of latent Gaussian copula models even when the number of variables $p$ is large. We provide theoretical guarantees for the approximation error of our numerical scheme and support its excellent performance on simulated and real-world data. We illustrate the practical advantages of our method on high-dimensional sparse quantitative and relative abundance microbiome data as well as multi-view data from The Cancer Genome Atlas Project. Our method is implemented in the R package mixedCCA, available at https://github.com/irinagain/mixedCCA., Main text: 21 pages and 4 figures. Supplementary material: 24 pages and 5 figures

Multi-view data, which is matched sets of measurements on the same subjects, have become increasingly common with advances in multi-omics technology. Often, it is of interest to find associations between the views that are related to the intrinsic class memberships. Existing association methods cannot directly incorporate class information, while existing classification methods do not take into account between-views associations. In this work, we propose a framework for Joint Association and Classification Analysis of multi-view data (JACA). Our goal is not to merely improve the misclassification rates, but to provide a latent representation of high-dimensional data that is both relevant for the subtype discrimination and coherent across the views. We motivate the methodology by establishing a connection between canonical correlation analysis and discriminant analysis. We also establish the estimation consistency of JACA in high-dimensional settings. A distinct advantage of JACA is that it can be applied to the multi-view data with block-missing structure, that is to cases where a subset of views or class labels is missing for some subjects. The application of JACA to quantify the associations between RNAseq and miRNA views with respect to consensus molecular subtypes in colorectal cancer data from The Cancer Genome Atlas project leads to improved misclassification rates and stronger found associations compared to existing methods.

We consider the problem of extracting joint and individual signals from multi-view data, that is data collected from different sources on matched samples. While existing methods for multi-view data decomposition explore single matching of data by samples, we focus on double-matched multi-view data (matched by both samples and source features). Our motivating example is the miRNA data collected from both primary tumor and normal tissues of the same subjects; the measurements from two tissues are thus matched both by subjects and by miRNAs. Our proposed double-matched matrix decomposition allows to simultaneously extract joint and individual signals across subjects, as well as joint and individual signals across miRNAs. Our estimation approach takes advantage of double-matching by formulating a new type of optimization problem with explicit row space and column space constraints, for which we develop an efficient iterative algorithm. Numerical studies indicate that taking advantage of double-matching leads to superior signal estimation performance compared to existing multi-view data decomposition based on single-matching. We apply our method to miRNA data as well as data from the English Premier League soccer matches, and find joint and individual multi-view signals that align with domain specific knowledge., Comment: Accepted to Journal of Computational and Graphical Statistics

Continuous Glucose Monitoring (CGM) data play an increasing role in clinical practice as they provide detailed quantification of blood glucose levels during the entire 24-hour period. The R package iglu implements a wide range of CGM-derived metrics for measuring glucose control and glucose variability. The package also allows one to visualize CGM data using time-series and lasagna plots. A distinct advantage of iglu is that it comes with a point-and-click graphical user interface (GUI) which makes the package widely accessible to users regardless of their programming experience. Thus, the open-source and easy to use iglu package will help advance CGM research and CGM data analyses. R package iglu is publicly available on CRAN and at https://github.com/irinagain/iglu.

Sparse linear discriminant analysis via penalized optimal scoring is a successful tool for classification in high-dimensional settings. While the variable selection consistency of sparse optimal scoring has been established, the corresponding prediction and estimation consistency results have been lacking. We bridge this gap by providing probabilistic bounds on out-of-sample prediction error and estimation error of multi-class penalized optimal scoring allowing for diverging number of classes.

As advances in technology allow the acquisition of complementary information, it is increasingly common for scientific studies to collect multiple datasets. Large-scale neuroimaging studies often include multiple modalities (e.g., task functional MRI, resting-state fMRI, diffusion MRI, and/or structural MRI), with the aim to understand the relationships between datasets. In this study, we seek to understand whether regions of the brain activated in a working memory task relate to resting-state correlations. In neuroimaging, a popular approach uses principal component analysis for dimension reduction prior to canonical correlation analysis with joint independent component analysis, but this may discard biological features with low variance and/or spuriously associate structure unique to a dataset with joint structure. We introduce Simultaneous Non-Gaussian component analysis (SING) in which dimension reduction and feature extraction are achieved simultaneously, and shared information is captured via subject scores. We apply our method to a working memory task and resting-state correlations from the Human Connectome Project. We find joint structure as evident from joint scores whose loadings highlight resting-state correlations involving regions associated with working memory. Moreover, some of the subject scores are related to fluid intelligence.

BackgroundMelanoma causes the vast majority of deaths attributable to skin cancer, largely due to its propensity for metastasis. To date, few studies have examined molecular changes between primary cutaneous melanoma and adjacent putatively normal skin. To broaden temporal inferences related to initiation of disease, we performed a metabolomics investigation of primary melanoma and matched extratumoral microenvironment (EM) tissues; and, to make inferences about progressive disease, we also compared unmatched metastatic melanoma tissues to EM tissues.MethodsUltra-high performance liquid chromatography-mass spectrometry-based metabolic profiling was performed on frozen human tissues.ResultsWe observed 824 metabolites as differentially abundant among 33 matched tissue samples, and 1,118 metabolites as differentially abundant between metastatic melanoma (n = 46) and EM (n = 34) after false discovery rate (FDR) adjustment (pConclusionsOverall, pathway-based results significantly distinguished melanoma tissues from EM in the metabolism of: ascorbate and aldarate, propanoate, tryptophan, histidine, and pyrimidine. Within pathways, the majority of individual metabolite abundances observed in comparisons of primary melanoma vs. EM and metastatic melanoma vs. EM were directionally consistent. This observed concordance suggests most identified compounds are implicated in the initiation or maintenance of melanoma.

Background Urine protein loss is common in dogs with chronic kidney disease (CKD). Currently available noninvasive means of evaluating CKD in dogs cannot accurately predict the severity of glomerular and tubulointerstitial damage. Electrophoretic analysis of urine proteins can indicate the compromised renal compartment (glomerular vs tubular), but extensive evaluation of protein banding pattern associations with histologic damage severity has not been performed in dogs. Objectives We aimed to evaluate electrophoretic banding patterns as indicators of the presence and severity of glomerular and tubulointerstitial damage in dogs with naturally occurring, predominantly proteinuric CKD. Methods We performed a retrospective study using urine and renal tissue from 207 dogs with CKD. Urine protein banding patterns were correlated with histologic severity of renal damage. Sensitivity and specificity of banding patterns for the detection of glomerular and tubulointerstitial damage were determined. Results Banding patterns were 97% sensitive and 100% specific for the detection of glomerular damage and 90% sensitive and 100% specific for the detection of tubulointerstitial damage. Correlations between composite banding patterns and the severity of renal damage were strong, while glomerular banding patterns correlated moderately with glomerular damage severity, and tubular gel scores correlated weakly to moderately with the severity of tubulointerstitial damage. Conclusions and clinical importance Urine protein banding patterns are useful for the detection of glomerular and tubulointerstitial damage in dogs with proteinuric CKD.

The TREX is a recently introduced approach to sparse linear regression. In contrast to most well-known approaches to penalized regression, the TREX can be formulated without the use of tuning parameters. In this paper, we establish the first known prediction error bounds for the TREX. Additionally, we introduce extensions of the TREX to a more general class of penalties, and we provide a bound on the prediction error in this generalized setting. These results deepen the understanding of the TREX from a theoretical perspective and provide new insights into penalized regression in general.

High-throughput microbial sequencing techniques, such as targeted amplicon-based and metagenomic profiling, provide low-cost genomic survey data of microbial communities in their natural environment, ranging from marine ecosystems to host-associated habitats. While standard microbiome profiling data can provide sparse relative abundances of operational taxonomic units or genes, recent advances in experimental protocols give a more quantitative picture of microbial communities by pairing sequencing-based techniques with orthogonal measurements of microbial cell counts from the same sample. These tandem measurements provide absolute microbial count data albeit with a large excess of zeros due to limited sequencing depth. In this contribution we consider the fundamental statistical problem of estimating correlations and partial correlations from such quantitative microbiome data. To this end, we propose a semi-parametric rank-based approach to correlation estimation that can naturally deal with the excess zeros in the data. Combining this estimator with sparse graphical modeling techniques leads to the Semi-Parametric Rank-based approach for INference in Graphical model (SPRING). SPRING enables inference of statistical microbial association networks from quantitative microbiome data which can serve as high-level statistical summary of the underlying microbial ecosystem and can provide testable hypotheses for functional species-species interactions. Due to the absence of verified microbial associations we also introduce a novel quantitative microbiome data generation mechanism which mimics empirical marginal distributions of measured count data while simultaneously allowing user-specified dependencies among the variables. SPRING shows superior network recovery performance on a wide range of realistic benchmark problems with varying network topologies and is robust to misspecifications of the total cell count estimate. To highlight SPRING’s broad applicability we infer taxon-taxon associations from the American Gut Project data and genus-genus associations from a recent quantitative gut microbiome dataset. We believe that, as quantitative microbiome profiling data will become increasingly available, the semi-parametric estimators for correlation and partial correlation estimation introduced here provide an important tool for reliable statistical analysis of quantitative microbiome data.

This article considers the problem of sparse estimation of canonical vectors in linear discriminant analysis when $p\gg N$. Several methods have been proposed in the literature that estimate one canonical vector in the two-group case. However, $G-1$ canonical vectors can be considered if the number of groups is $G$. In the multi-group context, it is common to estimate canonical vectors in a sequential fashion. Moreover, separate prior estimation of the covariance structure is often required. We propose a novel methodology for direct estimation of canonical vectors. In contrast to existing techniques, the proposed method estimates all canonical vectors at once, performs variable selection across all the vectors and comes with theoretical guarantees on the variable selection and classification consistency. First, we highlight the fact that in the $N>p$ setting the canonical vectors can be expressed in a closed form up to an orthogonal transformation. Secondly, we propose an extension of this form to the $p\gg N$ setting and achieve feature selection by using a group penalty. The resulting optimization problem is convex and can be solved using a block-coordinate descent algorithm. The practical performance of the method is evaluated through simulation studies as well as real data applications., Comment: Accepted to JASA, 2015

The increased availability of multi-view data (data on the same samples from multiple sources) has led to strong interest in models based on low-rank matrix factorizations. These models represent each data view via shared and individual components, and have been successfully applied for exploratory dimension reduction, association analysis between the views, and consensus clustering. Despite these advances, there remain challenges in modeling partially-shared components and identifying the number of components of each type (shared/partially-shared/individual). We formulate a novel linked component model that directly incorporates partially-shared structures. We call this model SLIDE for Structural Learning and Integrative DEcomposition of multi-view data. The proposed model-fitting and selection techniques allow for joint identification of the number of components of each type, in contrast to existing sequential approaches. In our empirical studies, SLIDE demonstrates excellent performance in both signal estimation and component selection. We further illustrate the methodology on the breast cancer data from The Cancer Genome Atlas repository.

Multivariate association analysis is of primary interest in many applications. Despite the prevalence of high-dimensional and non-Gaussian data (such as count-valued or binary), most existing methods only apply to low-dimensional data with continuous measurements. Motivated by the Computer Audition Lab 500-song (CAL500) music annotation study, we develop a new framework for the association analysis of two sets of high-dimensional and heterogeneous (continuous/binary/count) data. We model heterogeneous random variables using exponential family distributions, and exploit a structured decomposition of the underlying natural parameter matrices to identify shared and individual patterns for two data sets. We also introduce a new measure of the strength of association, and a permutation-based procedure to test its significance. An alternating iteratively reweighted least squares algorithm is devised for model fitting, and several variants are developed to expedite computation and achieve variable selection. The application to the CAL500 data sheds light on the relationship between acoustic features and semantic annotations, and provides effective means for automatic music annotation and retrieval.

The TREX is a recently introduced method for performing sparse high-dimensional regression. Despite its statistical promise as an alternative to the lasso, square-root lasso, and scaled lasso, the TREX is computationally challenging in that it requires solving a non-convex optimization problem. This paper shows a remarkable result: despite the non-convexity of the TREX problem, there exists a polynomial-time algorithm that is guaranteed to find the global minimum. This result adds the TREX to a very short list of non-convex optimization problems that can be globally optimized (principal components analysis being a famous example). After deriving and developing this new approach, we demonstrate that (i) the ability of the preexisting TREX heuristic to reach the global minimum is strongly dependent on the difficulty of the underlying statistical problem, (ii) the new polynomial-time algorithm for TREX permits a novel variable ranking and selection scheme, (iii) this scheme can be incorporated into a rule that controls the false discovery rate (FDR) of included features in the model. To achieve this last aim, we provide an extension of the results of Barber and Candes (2015) to establish that the knockoff filter framework can be applied to the TREX. This investigation thus provides both a rare case study of a heuristic for non-convex optimization and a novel way of exploiting non-convexity for statistical inference.

We consider the problem of high-dimensional classification between two groups with unequal covariance matrices. Rather than estimating the full quadratic discriminant rule, we propose to perform simultaneous variable selection and linear dimension reduction on the original data, with the subsequent application of quadratic discriminant analysis on the reduced space. In contrast to quadratic discriminant analysis, the proposed framework does not require the estimation of precision matrices; it scales linearly with the number of measurements, making it especially attractive for the use on high-dimensional datasets. We support the methodology with theoretical guarantees on variable selection consistency, and empirical comparisons with competing approaches. We apply the method to gene expression data of breast cancer patients, and confirm the crucial importance of the ESR1 gene in differentiating estrogen receptor status.

The abundance of high-dimensional data in the modern sciences has generated tremendous interest in penalized estimators such as the lasso, scaled lasso, square-root lasso, elastic net, and many others. In this paper, we establish a general oracle inequality for prediction in high-dimensional linear regression with such methods. Since the proof relies only on convexity and continuity arguments, the result holds irrespective of the design matrix and applies to a wide range of penalized estimators. Overall, the bound demonstrates that generic estimators can provide consistent prediction with any design matrix. From a practical point of view, the bound can help to identify the potential of specific estimators, and they can help to get a sense of the prediction accuracy in a given application.

This article considers the problem of multi-group classification in the setting where the number of variables $p$ is larger than the number of observations $n$. Several methods have been proposed in the literature that address this problem, however their variable selection performance is either unknown or suboptimal to the results known in the two-group case. In this work we provide sharp conditions for the consistent recovery of relevant variables in the multi-group case using the discriminant analysis proposal of Gaynanova et al., 2014. We achieve the rates of convergence that attain the optimal scaling of the sample size $n$, number of variables $p$ and the sparsity level $s$. These rates are significantly faster than the best known results in the multi-group case. Moreover, they coincide with the optimal minimax rates for the two-group case. We validate our theoretical results with numerical analysis., 22 pages, 2 figures

We investigate the difference between using an $\ell_1$ penalty versus an $\ell_1$ constraint in generalized eigenvalue problems, such as principal component analysis and discriminant analysis. Our main finding is that an $\ell_1$ penalty may fail to provide very sparse solutions; a severe disadvantage for variable selection that can be remedied by using an $\ell_1$ constraint. Our claims are supported both by empirical evidence and theoretical analysis. Finally, we illustrate the advantages of an $\ell_1$ constraint in the context of discriminant analysis and principal component analysis., 18 pages, 8 figures