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Context Autoantibodies directed against the 65-kilodalton isoform of glutamic acid decarboxylase (GAD65Abs) are markers of autoimmune type 1 diabetes (T1D) but are also present in patients with Latent Autoimmune Diabetes of Adults and autoimmune neuromuscular diseases, and also in healthy individuals. Phenotypic differences between these conditions are reflected in epitope-specific GAD65Abs and anti-idiotypic antibodies (anti-Id) against GAD65Abs. We previously reported that 7.8% of T2D patients in the GRADE study have GAD65Abs but found that GAD65Ab positivity was not correlated with beta-cell function, glycated hemoglobin (HbA1c), or fasting glucose levels. Context In this study, we aimed to better characterize islet autoantibodies in this T2D cohort. This is an ancillary study to NCT01794143. Methods We stringently defined GAD65Ab positivity with a competition assay, analyzed GAD65Ab-specific epitopes, and measured GAD65Ab-specific anti-Id in serum. Results Competition assays confirmed that 5.9% of the patients were GAD65Ab positive, but beta-cell function was not associated with GAD65Ab positivity, GAD65Ab epitope specificity or GAD65Ab-specific anti-Id. GAD65-related autoantibody responses in GRADE T2D patients resemble profiles in healthy individuals (low GAD65Ab titers, presence of a single autoantibody, lack of a distinct epitope pattern, and presence of anti-Id to diabetes-associated GAD65Ab). In this T2D cohort, GAD65Ab positivity is likely unrelated to the pathogenesis of beta-cell dysfunction. Conclusion Evidence for islet autoimmunity in the pathophysiology of T2D beta-cell dysfunction is growing, but T1D-associated autoantibodies may not accurately reflect the nature of their autoimmune process. [ABSTRACT FROM AUTHOR]

Estimation of density functions supported on general domains arises when the data are naturally restricted to a proper subset of the real space. This problem is complicated by typically intractable normalizing constants. Score matching provides a powerful tool for estimating densities with such intractable normalizing constants but as originally proposed is limited to densities on |$\mathbb{R}^m$| and |$\mathbb{R}_+^m$|⁠. In this paper, we offer a natural generalization of score matching that accommodates densities supported on a very general class of domains. We apply the framework to truncated graphical and pairwise interaction models and provide theoretical guarantees for the resulting estimators. We also generalize a recently proposed method from bounded to unbounded domains and empirically demonstrate the advantages of our method. [ABSTRACT FROM AUTHOR]

We consider the problem of nonparametric regression with a potentially large number of covariates. We propose a convex, penalized estimation framework that is particularly well suited to high-dimensional sparse additive models and combines the appealing features of finite basis representation and smoothing penalties. In the case of additive models, a finite basis representation provides a parsimonious representation for fitted functions but is not adaptive when component functions possess different levels of complexity. In contrast, a smoothing spline-type penalty on the component functions is adaptive but does not provide a parsimonious representation. Our proposal simultaneously achieves parsimony and adaptivity in a computationally efficient way. We demonstrate these properties through empirical studies and show that our estimator converges at the minimax rate for functions within a hierarchical class. We further establish minimax rates for a large class of sparse additive models. We also develop an efficient algorithm that scales similarly to the lasso with the number of covariates and sample size. [ABSTRACT FROM AUTHOR]

Motivation: Pathway enrichment analysis has become a key tool for biomedical researchers to gain insight into the underlying biology of differentially expressed genes, proteins and metabolites. It reduces complexity and provides a system-level view of changes in cellular activity in response to treatments and/or in disease states. Methods that use existing pathway network information have been shown to outperform simpler methods that only take into account pathway membership. However, despite significant progress in understanding the association amongst members of biological pathways, and expansion of data bases containing information about interactions of biomolecules, the existing network information may be incomplete or inaccurate and is not cell-type or disease condition-specific. Results: We propose a constrained network estimation framework that combines network estimation based on cell- and condition-specific high-dimensional Omics data with interaction information from existing data bases. The resulting pathway topology information is subsequently used to provide a framework for simultaneous testing of differences in expression levels of pathway members, as well as their interactions. We study the asymptotic properties of the proposed network estimator and the test for pathway enrichment, and investigate its small sample performance in simulated and real data settings. [ABSTRACT FROM AUTHOR]

Graph-constrained estimation methods encourage similarities among neighboring covariates presented as nodes of a graph, and can result in more accurate estimates, especially in high-dimensional settings. Variable selection approaches can then be utilized to select a subset of variables that are associated with the response. However, existing procedures do not provide measures of uncertainty of estimates. Further, the vast majority of existing approaches assume that available graph accurately captures the association among covariates; violations to this assumption could severely hurt the reliability of the resulting estimates. In this article, we present a new inference framework, called the Grace test, which produces coefficient estimates and corresponding p-values by incorporating the external graph information. We show, both theoretically and via numerical studies, that the proposed method asymptotically controls the type-I error rate regardless of the choice of the graph. We also show that when the underlying graph is informative, the Grace test is asymptotically more powerful than similar tests that ignore the external information. We study the power properties of the proposed test when the graph is not fully informative and develop a more powerful Grace-ridge test for such settings. Our numerical studies show that as long as the graph is reasonably informative, the proposed inference procedures deliver improved statistical power over existing methods that ignore external information. [ABSTRACT FROM AUTHOR]

We consider the problem of estimating the parameters in a pairwise graphical model in which the distribution of each node, conditioned on the others, may have a different exponential family form. We identify restrictions on the parameter space required for the existence of a well-defined joint density, and establish the consistency of the neighbourhood selection approach for graph reconstruction in high dimensions when the true underlying graph is sparse. Motivated by our theoretical results, we investigate the selection of edges between nodes whose conditional distributions take different parametric forms, and show that efficiency can be gained if edge estimates obtained from the regressions of particular nodes are used to reconstruct the graph. These results are illustrated with examples of Gaussian, Bernoulli, Poisson and exponential distributions. Our theoretical findings are corroborated by evidence from simulation studies. [ABSTRACT FROM PUBLISHER]

In recent years, there has been considerable interest in estimating conditional independence graphs in high dimensions. Most previous work assumed that the variables are multivariate Gaussian or that the conditional means of the variables are linearly related. Unfortunately, if these assumptions are violated, the resulting conditional independence estimates can be inaccurate. We propose a semiparametric method, graph estimation with joint additive models, which allows the conditional means of the features to take an arbitrary additive form. We present an efficient algorithm for computation of our estimator, and prove that it is consistent. We extend our method to estimation of directed graphs with known causal ordering. Using simulated data, we show that our method performs better than existing methods when there are nonlinear relationships among the features, and is comparable to methods that assume multivariate normality when the conditional means are linear. We illustrate our method on a cell signalling dataset. [ABSTRACT FROM AUTHOR]

Directed acyclic graphs are commonly used to represent causal relationships among random variables in graphical models. Applications of these models arise in the study of physical and biological systems where directed edges between nodes represent the influence of components of the system on each other. Estimation of directed graphs from observational data is computationally NP-hard. In addition, directed graphs with the same structure may be indistinguishable based on observations alone. When the nodes exhibit a natural ordering, the problem of estimating directed graphs reduces to the problem of estimating the structure of the network. In this paper, we propose an efficient penalized likelihood method for estimation of the adjacency matrix of directed acyclic graphs, when variables inherit a natural ordering. We study variable selection consistency of lasso and adaptive lasso penalties in high-dimensional sparse settings, and propose an error-based choice for selecting the tuning parameter. We show that although the lasso is only variable selection consistent under stringent conditions, the adaptive lasso can consistently estimate the true graph under the usual regularity assumptions. [ABSTRACT FROM PUBLISHER]

Motivation: Components of biological systems interact with each other in order to carry out vital cell functions. Such information can be used to improve estimation and inference, and to obtain better insights into the underlying cellular mechanisms. Discovering regulatory interactions among genes is therefore an important problem in systems biology. Whole-genome expression data over time provides an opportunity to determine how the expression levels of genes are affected by changes in transcription levels of other genes, and can therefore be used to discover regulatory interactions among genes. Results: In this article, we propose a novel penalization method, called truncating lasso, for estimation of causal relationships from time-course gene expression data. The proposed penalty can correctly determine the order of the underlying time series, and improves the performance of the lasso-type estimators. Moreover, the resulting estimate provides information on the time lag between activation of transcription factors and their effects on regulated genes. We provide an efficient algorithm for estimation of model parameters, and show that the proposed method can consistently discover causal relationships in the large p, small n setting. The performance of the proposed model is evaluated favorably in simulated, as well as real, data examples. [ABSTRACT FROM AUTHOR]