High dimensional semiparametric latent graphical model for mixed data

Relating stability of individual dynamical networks to change in psychopathology

One hypothesis flowing from the network theory of psychopathology is that symptom network structure is associated with psychopathology severity and in turn, one may expect that individual network structure changes with the level of psychopathology severity. However, this expectation has rarely been addressed directly. This study aims to examine (1) the stability of individual contemporaneous symptom networks over a one-year period and (2) whether network stability is associated with a change in psychopathology. We used daily diary data of n = 66 individuals, located along the psychosis severity continuum, from two separate 90-day periods, one year apart (t = 180). Based on the newly developed Individual Network Invariance Test (INIT) to assess symptom-network stability, participants were divided into two groups with stable and unstable networks and we tested whether these groups differed in their absolute change in psychopathology severity. The majority of the sample (n = 51, 77.3%) showed a stable network over time while most individuals showed a decrease in psychopathological severity. We found no significant association between a change in psychopathology severity and individual network stability. Our results call for further critical evaluation of the association between networks and psychopathology to optimize the implementation of clinical applications based on current methods.

Decomposition of variation of mixed variables by a latent mixed Gaussian copula model

Many biomedical studies collect data of mixed types of variables from multiple groups of subjects. Some of these studies aim to find the group-specific and the common variation among all these variables. Even though similar problems have been studied by some previous works, their methods mainly rely on the Pearson correlation, which cannot handle mixed data. To address this issue, we propose a latent mixed Gaussian copula (LMGC) model that can quantify the correlations among binary, ordinal, continuous, and truncated variables in a unified framework. We also provide a tool to decompose the variation into the group-specific and the common variation over multiple groups via solving a regularized M-estimation problem. We conduct extensive simulation studies to show the advantage of our proposed method over the Pearson correlation-based methods. We also demonstrate that by jointly solving the M-estimation problem over multiple groups, our method is better than decomposing the variation group by group. We also apply our method to a Chlamydia trachomatis genital tract infection study to demonstrate how it can be used to discover informative biomarkers that differentiate patients.

Causal discoveries for high dimensional mixed data

Causal relationships are of crucial importance for biological and medical research. Algorithms have been proposed for causal structure learning with graphical visualizations. While much of the literature focuses on biological studies where data often follow the same distribution, for example, the normal distribution for all variables, challenges emerge from epidemiological and clinical studies where data are often mixed with continuous, binary, and ordinal variables. We propose to use a mixed latent Gaussian copula model to estimate the underlying correlation structure via the rank correlation for mixed data. This correlation structure is then incorporated into a popular causal discovery algorithm, the PC algorithm, to identify causal structures. The proposed algorithm, called the latent-PC algorithm, is able to discover the true causal structure consistently under mild conditions in high dimensional settings. From simulation studies, the latent-PC algorithm delivers a competitive performance in terms of a similar or higher true positive rate and a similar or lower false positive rate, compared with other variants of the PC algorithm. In the high dimensional settings where the number of variables is more than the number of observations, the causal graphs identified by the latent-PC algorithm are closer to the true causal structures, compared to other competing algorithms. Further, we demonstrate the utility of the latent-PC algorithm in a real dataset for hepatocellular carcinoma. Causal structures for patient survival are visualized and connected with clinical interpretations in the literature.

Effects of caloric restriction on the gut microbiome are linked with immune senescence

BACKGROUND

Caloric restriction can delay the development of metabolic diseases ranging from insulin resistance to type 2 diabetes and is linked to both changes in the composition and metabolic function of the gut microbiota and immunological consequences. However, the interaction between dietary intake, the microbiome, and the immune system remains poorly described.

RESULTS

We transplanted the gut microbiota from an obese female before (AdLib) and after (CalRes) an 8-week very-low-calorie diet (800 kcal/day) into germ-free mice. We used 16S rRNA sequencing to evaluate taxa with differential abundance between the AdLib- and CalRes-microbiota recipients and single-cell multidimensional mass cytometry to define immune signatures in murine colon, liver, and spleen. Recipients of the CalRes sample exhibited overall higher alpha diversity and restructuring of the gut microbiota with decreased abundance of several microbial taxa (e.g., Clostridium ramosum, Hungatella hathewayi, Alistipi obesi). Transplantation of CalRes-microbiota into mice decreased their body fat accumulation and improved glucose tolerance compared to AdLib-microbiota recipients. Finally, the CalRes-associated microbiota reduced the levels of intestinal effector memory CD8+ T cells, intestinal memory B cells, and hepatic effector memory CD4+ and CD8+ T cells.

CONCLUSION

Caloric restriction shapes the gut microbiome which can improve metabolic health and may induce a shift towards the naïve T and B cell compartment and, thus, delay immune senescence. Understanding the role of the gut microbiome as mediator of beneficial effects of low calorie diets on inflammation and metabolism may enhance the development of new therapeutic treatment options for metabolic diseases.

TRIAL REGISTRATION

NCT01105143 , "Effects of negative energy balance on muscle mass regulation," registered 16 April 2010. Video Abstract.

Estimating Finite Mixtures of Ordinal Graphical Models

Graphical models have received an increasing amount of attention in network psychometrics as a promising probabilistic approach to study the conditional relations among variables using graph theory. Despite recent advances, existing methods on graphical models usually assume a homogeneous population and focus on binary or continuous variables. However, ordinal variables are very popular in many areas of psychological science, and the population often consists of several different groups based on the heterogeneity in ordinal data. Driven by these needs, we introduce the finite mixture of ordinal graphical models to effectively study the heterogeneous conditional dependence relationships of ordinal data. We develop a penalized likelihood approach for model estimation, and design a generalized expectation-maximization (EM) algorithm to solve the significant computational challenges. We examine the performance of the proposed method and algorithm in simulation studies. Moreover, we demonstrate the potential usefulness of the proposed method in psychological science through a real application concerning the interests and attitudes related to fan avidity for students in a large public university in the United States.

The intratumoral CXCR3 chemokine system is predictive of chemotherapy response in human bladder cancer

Chemotherapy has direct toxic effects on cancer cells; however, long-term cancer control and complete remission are likely to involve CD8⁺ T cell immune responses. To study the role of CD8⁺ T cell infiltration in the success of chemotherapy, we examined patients with muscle invasive bladder cancer (MIBC) who were categorized on the basis of the response to neoadjuvant chemotherapy (NAC). We identified the intratumoral CXCR3 chemokine system (ligands and receptor splice variants) as a critical component for tumor eradication upon NAC in MIBC. Through characterization of CD8⁺ T cells, we found that stem-like T cell subpopulations with abundant CXCR3alt, a variant form of the CXCL11 receptor, responded to CXCL11 in culture as demonstrated by migration and enhanced effector function. In tumor biopsies of patients with MIBC accessed before treatment, CXCL11 abundance correlated with high numbers of tumor-infiltrating T cells and response to NAC. The presence of CXCR3alt and CXCL11 was associated with improved overall survival in MIBC. Evaluation of both CXCR3alt and CXCL11 enabled discrimination between responder and nonresponder patients with MIBC before treatment. We validated the prognostic role of the CXCR3-CXCL11 chemokine system in an independent cohort of chemotherapy-treated and chemotherapy-naïve patients with MIBC from data in TCGA. In summary, our data revealed stimulatory activity of the CXCR3alt-CXCL11 chemokine system on CD8⁺ T cells that is predictive of chemotherapy responsiveness in MIBC. This may offer immunotherapeutic options for targeted activation of intratumoral stem-like T cells in solid tumors.

A Latent Gaussian Copula Model for Mixed Data Analysis in Brain Imaging Genetics

Recent advances in imaging genetics make it possible to combine different types of data including medical images like functional magnetic resonance imaging (fMRI) and genetic data like single nucleotide polymorphisms (SNPs) for comprehensive diagnosis of mental disorders. Understanding complex interactions among these heterogeneous data may give rise to a new perspective, while at the same time demand statistical models for their integration. Various graphical models have been proposed for the study of interaction or association networks with continuous, binary, and count data as well as the mixture of them. However, limited efforts have been made for the multinomial case, for instance, SNP data. Our goal is therefore to fill the void by developing a graphical model for the integration of fMRI image and SNP data, which can provide deeper understanding of the unknown neurogenetic mechanism. In this article, we propose a latent Gaussian copula model for mixed data containing multinomial components. We assume that the discrete variable is obtained by discretizing a latent (unobserved) continuous variable and then create a semi-rank based estimator of the graph structure. The simulation results demonstrate that the proposed latent correlation has more steady and accurate performance than several existing methods in detecting graph structure. When applying to a real schizophrenia data consisting of SNP array and fMRI image collected by the Mind Clinical Imaging Consortium (MCIC), the proposed method reveals a set of distinct SNP-brain associations, which are verified to be biologically significant. The proposed model is statistically promising in handling mixed types of data including multinomial components, which can find widespread applications. To promote reproducible research, the R code is available at https://github.com/Aiying0512/LGCM.

A Joint Graphical Model for Inferring Gene Networks Across Multiple Subpopulations and Data Types

Reconstructing gene networks from gene expression data is a long-standing challenge. In most applications, the observations can be divided into several distinct but related subpopulations and the gene expression measurements can be collected from multiple data types. Most existing methods are designed to estimate a single gene network from a single dataset. These methods may be suboptimal since they do not exploit the similarities and differences among different subpopulations and data types. In this article, we propose a joint graphical model to estimate the multiple gene networks simultaneously. Our model decomposes each subpopulation-specific gene network as a sum of common and unique components and imposes a group lasso penalty on gene networks corresponding to different data types. The gene network variations across subpopulations can be learned automatically by the decompositions of networks, and the similarities and differences among data types can be captured by the group lasso penalty. The simulation studies demonstrate that our method outperforms the state-of-the-art methods. We also apply our method to the cancer genome atlas breast cancer datasets to reconstruct subtype-specific gene networks. Hub nodes in the estimated subnetworks unique to individual cancer subtypes rediscover well-known genes associated with breast cancer subtypes and provide interesting predictions.

Joint Microbial and Metabolomic Network Estimation with the Censored Gaussian Graphical Model

Joint analysis of microbiome and metabolomic data represents an imperative objective as the field moves beyond basic microbiome association studies and turns towards mechanistic and translational investigations. We present a censored Gaussian graphical model framework, where the metabolomic data are treated as continuous and the microbiome data as censored at zero, to identify direct interactions (defined as conditional dependence relationships) between microbial species and metabolites. Simulated examples show that our method metaMint performs favorably compared to the existing ones. metaMint also provides interpretable microbe-metabolite interactions when applied to a bacterial vaginosis data set. R implementation of metaMint is available on GitHub.

Joint estimation of multiple mixed graphical models for pan-cancer network analysis

Graphical models have been used in many scientific fields for exploration of conditional independence relationships for a large set of random variables. Although a variety of methods have been proposed in the literature for estimating graphical models with different types of data, none of them is applicable for jointly estimating multiple mixed graphical models. To tackle this problem, we propose a joint mixed learning method. The proposed method is very flexible, which works for various mixed types of data, such as those mixed with Gaussian, multinomial, and Poisson, and also allows people to incorporate domain knowledge into network construction by restricting some links to be included in or excluded from the networks. As an application, the proposed method is applied to pan-cancer network analysis for six types of cancer with data from The Cancer Genome Atlas. To our knowledge, this is the first work for joint estimation of multiple mixed graphical models.

High-dimensional integrative copula discriminant analysis for multiomics data

Multiomics or integrative omics data have been increasingly common in biomedical studies, holding a promise in better understanding human health and disease. In this article, we propose an integrative copula discrimination analysis classifier in the context of two-class classification, which relaxes the common Gaussian assumption and gains power by borrowing information from multiple omics data types in discriminant analysis. Numerical studies are conducted to assess the finite sample performance of the new classifier. We apply our model to the Religious Orders Study and Memory and Aging Project (ROSMAP) Study, integrating gene expression and DNA methylation data for better prediction.

Sparse semiparametric canonical correlation analysis for data of mixed types

Canonical correlation analysis investigates linear relationships between two sets of variables, but often works poorly on modern datasets due to high-dimensionality and mixed data types (continuous/binary/zero-inflated). We propose a new approach for sparse canonical correlation analysis of mixed data types that does not require explicit parametric assumptions. Our main contribution is the use of truncated latent Gaussian copula to model the data with excess zeroes, which allows us to derive a rank-based estimator of latent correlation matrix without the estimation of marginal transformation functions. The resulting semiparametric sparse canonical correlation analysis method works well in high-dimensional settings as demonstrated via numerical studies, and application to the analysis of association between gene expression and micro RNA data of breast cancer patients.

Using Bayesian Latent Gaussian Graphical Models to Infer Symptom Associations in Verbal Autopsies

Learning dependence relationships among variables of mixed types provides insights in a variety of scientific settings and is a well-studied problem in statistics. Existing methods, however, typically rely on copious, high quality data to accurately learn associations. In this paper, we develop a method for scientific settings where learning dependence structure is essential, but data are sparse and have a high fraction of missing values. Specifically, our work is motivated by survey-based cause of death assessments known as verbal autopsies (VAs). We propose a Bayesian approach to characterize dependence relationships using a latent Gaussian graphical model that incorporates informative priors on the marginal distributions of the variables. We demonstrate such information can improve estimation of the dependence structure, especially in settings with little training data. We show that our method can be integrated into existing probabilistic cause-of-death assignment algorithms and improves model performance while recovering dependence patterns between symptoms that can inform efficient questionnaire design in future data collection.

Joint Learning of Multiple Differential Networks With Latent Variables

Graphical models have been widely used to learn the conditional dependence structures among random variables. In many controlled experiments, such as the studies of disease or drug effectiveness, learning the structural changes of graphical models under two different conditions is of great importance. However, most existing graphical models are developed for estimating a single graph and based on a tacit assumption that there is no missing relevant variables, which wastes the common information provided by multiple heterogeneous data sets and underestimates the influence of latent/unobserved relevant variables. In this paper, we propose a joint differential network analysis (JDNA) model to jointly estimate multiple differential networks with latent variables from multiple data sets. The JDNA model is built on a penalized D-trace loss function, with group lasso or generalized fused lasso penalties. We implement a proximal gradient-based alternating direction method of multipliers to tackle the corresponding convex optimization problems. Extensive simulation experiments demonstrate that JDNA model outperforms state-of-the-art methods in estimating the structural changes of graphical models. Moreover, a series of experiments on several real-world data sets have been performed and experiment results consistently show that our proposed JDNA model is effective in identifying differential networks under different conditions.

Microbial Networks in SPRING - Semi-parametric Rank-Based Correlation and Partial Correlation Estimation for Quantitative Microbiome Data

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.

Learning Moral Graphs in Construction of High-Dimensional Bayesian Networks for Mixed Data

Bayesian networks have been widely used in many scientific fields for describing the conditional independence relationships for a large set of random variables. This letter proposes a novel algorithm, the so-called p-learning algorithm, for learning moral graphs for high-dimensional Bayesian networks. The moral graph is a Markov network representation of the Bayesian network and also the key to construction of the Bayesian network for constraint-based algorithms. The consistency of the p-learning algorithm is justified under the small-n, large-p scenario. The numerical results indicate that the p-learning algorithm significantly outperforms the existing ones, such as the PC, grow-shrink, incremental association, semi-interleaved hiton, hill-climbing, and max-min hill-climbing. Under the sparsity assumption, the p-learning algorithm has a computational complexity of O(p2) even in the worst case, while the existing algorithms have a computational complexity of O(p3) in the worst case.

A new insight into underlying disease mechanism through semi-parametric latent differential network model

BACKGROUND

In genomic studies, to investigate how the structure of a genetic network differs between two experiment conditions is a very interesting but challenging problem, especially in high-dimensional setting. Existing literatures mostly focus on differential network modelling for continuous data. However, in real application, we may encounter discrete data or mixed data, which urges us to propose a unified differential network modelling for various data types.

RESULTS

We propose a unified latent Gaussian copula differential network model which provides deeper understanding of the unknown mechanism than that among the observed variables. Adaptive rank-based estimation approaches are proposed with the assumption that the true differential network is sparse. The adaptive estimation approaches do not require precision matrices to be sparse, and thus can allow the individual networks to contain hub nodes. Theoretical analysis shows that the proposed methods achieve the same parametric convergence rate for both the difference of the precision matrices estimation and differential structure recovery, which means that the extra modeling flexibility comes at almost no cost of statistical efficiency. Besides theoretical analysis, thorough numerical simulations are conducted to compare the empirical performance of the proposed methods with some other state-of-the-art methods. The result shows that the proposed methods work quite well for various data types. The proposed method is then applied on gene expression data associated with lung cancer to illustrate its empirical usefulness.

CONCLUSIONS

The proposed latent variable differential network models allows for various data-types and thus are more flexible, which also provide deeper understanding of the unknown mechanism than that among the observed variables. Theoretical analysis, numerical simulation and real application all demonstrate the great advantages of the latent differential network modelling and thus are highly recommended.

Identifying gene network rewiring by combining gene expression and gene mutation data

Understanding how gene dependency networks rewire between different disease states is an important task in genomic research. Although many computational methods have been proposed to undertake this task via differential network analysis, most of them are designed for a predefined data type. With the development of the high throughput technologies, gene activity measurements can be collected from different aspects (e.g., mRNA expression and DNA mutation). Different data types might share some common characteristics and include certain unique properties. New methods are needed to explore the similarity and difference between differential networks estimated from different data types. In this study, we develop a new differential network inference model which identifies gene network rewiring by combining gene expression and gene mutation data. Similarity and difference between different data types are learned via a group bridge penalty function. Simulation studies have demonstrated that our method consistently outperforms the competing methods. We also apply our method to identify gene network rewiring associated with ovarian cancer platinum resistance. There are certain differential edges common to both data types and some differential edges unique to individual data types. Hub genes in the differential networks inferred by our method play important roles in ovarian cancer drug resistance.