A Statistical Test for Differential Network Analysis Based on Inference of Gaussian Graphical Model

A growing literature suggests that gene expression can be greatly altered in disease conditions, and identifying those changes will improve the understanding of complex diseases such as cancers or diabetes. A prevailing direction in the analysis of gene expression studies the changes in gene pathways which include sets of related genes. Therefore, introducing structured exploration to differential analysis of gene expression networks may lead to meaningful discoveries. The topic of this paper is differential network analysis, which focuses on capturing the differences between two or more precision matrices. We discuss the connection between the thresholding method and the D-trace loss method on differential network analysis in the case that the precision matrices share the common connected components. Based on this connection, we further propose the cluster D-trace loss method which directly estimates the differential network and achieves model selection consistency. Simulation studies demonstrate its improved performance and computational efficiency. Finally, the usefulness of our proposed estimator is demonstrated by a real-data analysis on non-small cell lung cancer.

BackgroundFor gene expression or gene association studies with a large number of hypotheses the number of measurements per marker in a conventional single-stage design is often low due to limited resources. Two-stage designs have been proposed where in a first stage promising hypotheses are identified and further investigated in the second stage with larger sample sizes. For two types of two-stage designs proposed in the literature we derive multiple testing procedures controlling the False Discovery Rate (FDR) demonstrating FDR control by simulations: designs where a fixed number of top-ranked hypotheses are selected and designs where the selection in the interim analysis is based on an FDR threshold. In contrast to earlier approaches which use only the second-stage data in the hypothesis tests (pilot approach), the proposed testing procedures are based on the pooled data from both stages (integrated approach).ResultsFor both selection rules the multiple testing procedures control the FDR in the considered simulation scenarios. This holds for the case of independent observations across hypotheses as well as for certain correlation structures. Additionally, we show that in scenarios with small effect sizes the testing procedures based on the pooled data from both stages can give a considerable improvement in power compared to tests based on the second-stage data only.ConclusionThe proposed hypothesis tests provide a tool for FDR control for the considered two-stage designs. Comparing the integrated approaches for both selection rules with the corresponding pilot approaches showed an advantage of the integrated approach in many simulation scenarios.

The multiplicity problem has become increasingly important in genetic studies as the capacity for high-throughput genotyping has increased. The control of False Discovery Rate (FDR) (Benjamini and Hochberg. [1995] J. R. Stat. Soc. Ser. B 57:289-300) has been adopted to address the problems of false positive control and low power inherent in high-volume genome-wide linkage and association studies. In many genetic studies, there is often a natural stratification of the m hypotheses to be tested. Given the FDR framework and the presence of such stratification, we investigate the performance of a stratified false discovery control approach (i.e. control or estimate FDR separately for each stratum) and compare it to the aggregated method (i.e. consider all hypotheses in a single stratum). Under the fixed rejection region framework (i.e. reject all hypotheses with unadjusted p-values less than a pre-specified level and then estimate FDR), we demonstrate that the aggregated FDR is a weighted average of the stratum-specific FDRs. Under the fixed FDR framework (i.e. reject as many hypotheses as possible and meanwhile control FDR at a pre-specified level), we specify a condition necessary for the expected total number of true positives under the stratified FDR method to be equal to or greater than that obtained from the aggregated FDR method. Application to a recent Genome-Wide Association (GWA) study by Maraganore et al. ([2005] Am. J. Hum. Genet. 77:685-693) illustrates the potential advantages of control or estimation of FDR by stratum. Our analyses also show that controlling FDR at a low rate, e.g. 5% or 10%, may not be feasible for some GWA studies.

The methodological advancement in microarray data analysis on the basis of false discovery rate (FDR) control, such as the q-value plots, allows the investigator to examine the FDR from several perspectives. However, when FDR control at the "customary" levels 0.01, 0.05, or 0.1 does not provide fruitful findings, there is little guidance for making the trade off between the significance threshold and the FDR level by sound statistical or biological considerations. Thus, meaningful statistical significance criteria that complement the existing FDR methods for large-scale multiple tests are desirable. Three statistical significance criteria, the profile information criterion, the total error proportion, and the guide-gene driven selection, are developed in this research. The first two are general significance threshold criteria for large-scale multiple tests; the profile information criterion is related to the recent theoretical studies of the connection between FDR control and minimax estimation, and the total error proportion is closely related to the asymptotic properties of FDR control in terms of the total error risk. The guide-gene driven selection is an approach to combining statistical significance and the existing biological knowledge of the study at hand. Error properties of these criteria are investigated theoretically and by simulation. The proposed methods are illustrated and compared using an example of genomic screening for novel Arf gene targets. Operating characteristics of q-value and the proposed significance threshold criteria are investigated and compared in a simulation study that employs a model mimicking a gene regulatory pathway. A guideline for using these criteria is provided. Splus/R code is available from the corresponding author upon request.

BackgroundHigh-throughput technologies, such as DNA microarray, have significantly advanced biological and biomedical research by enabling researchers to carry out genome-wide screens. One critical task in analyzing genome-wide datasets is to control the false discovery rate (FDR) so that the proportion of false positive features among those called significant is restrained. Recently a number of FDR control methods have been proposed and widely practiced, such as the Benjamini-Hochberg approach, the Storey approach and Significant Analysis of Microarrays (SAM).MethodsThis paper presents a straight-forward yet powerful FDR control method termed miFDR, which aims to minimize FDR when calling a fixed number of significant features. We theoretically proved that the strategy used by miFDR is able to find the optimal number of significant features when the desired FDR is fixed.ResultsWe compared miFDR with the BH approach, the Storey approach and SAM on both simulated datasets and public DNA microarray datasets. The results demonstrated that miFDR outperforms others by identifying more significant features under the same FDR cut-offs. Literature search showed that many genes called only by miFDR are indeed relevant to the underlying biology of interest.ConclusionsFDR has been widely applied to analyzing high-throughput datasets allowed for rapid discoveries. Under the same FDR threshold, miFDR is capable to identify more significant features than its competitors at a compatible level of complexity. Therefore, it can potentially generate great impacts on biological and biomedical research.AvailabilityIf interested, please contact the authors for getting miFDR.

Recent genetic/genomic studies have shown that genetic markers can have potential effects on the dependence structure of genes. Motivated by such findings, we are interested in the estimation of covariate-adjusted Gaussian graphical model (CGGM). Most existing approaches depend on regularization techniques, which makes the precise relationship between the regularized parameter and the number of false discovered edges in CGGM estimation ambiguous. In this paper, we formulate CGGM estimation as a multiple testing problem. A new test statistic is introduced and shown to be asymptotic normal null distribution. We then propose a multiple testing procedure for CGGM estimation. The procedure is shown to control the false discovery rate (FDR) at any pre-specified significance level asymptotically. Finally, we provide numerical results to show the performance of our method in both simulation studies and real data analysis.

BackgroundFirefighters have frequent exposure to carcinogens and an increased risk of cancer. Wildland-urban interface (WUI) fires, which involve both structures and undeveloped wildland fuels, pose unique challenges to the health of firefighters. However, the extent of health risks associated with these fires remains underexplored.ObjectivesThis study aims to identify altered urine metabolites and metabolic processes among male firefighters that were associated with WUI fires as compared with municipal structure fires (MSF).MethodsUntargeted metabolomic profiling was applied to pre-exposure (baseline) and postfire urine samples collected from firefighters responding to WUI and MSF fires. Differential analysis was conducted by fitting linear mixed effects regression models on preprocessed ion intensity and exposure status while adjusting for demographic covariates. Differential metabolites by post-exposure status were identified using a false discovery rate (FDR) threshold of < 0.05. Pathway analysis was performed to identify pathways that were significantly perturbed at a Bonferroni adjusted p-value < 0.05 level. We conducted differential and pathway analyses in both the WUI and MSF cohorts and compared the two fire types in terms of the number of differentially expressed metabolites and patterns of metabolic pathway enrichment.ResultsEighty-five firefighters contributed paired baseline and post-fire samples from WUI events, and 98 firefighters contributed paired baseline and post-fire samples from MSF events. We performed metabolic profiling on baseline and postfire urine samples from WUI and MSF using four modes: HILIC(-), HILIC(+), C18(-), and C18(+) and identified metabolites against an in-house library. We identified 244, 297, 320, and 266 level-1 metabolites from the four respective modes. In the statistical analysis, the main model identified a total of 176 differential metabolites from WUI fires. For MSF, the model identified a total of 652 differential metabolites from the four respective modes. Most metabolites with significant changes after a WUI fire also changed significantly after an MSF event. Two metabolic pathways were significantly enriched after WUI fires, while 7 pathways were significantly enriched after MSF exposure and 2 pathways overlapped between the two types of fires.ConclusionFire exposure induces numerous metabolic perturbations in firefighters responding to WUI fires, potentially contributing to their elevated cancer risk. Although individual metabolites changed in a similar fashion across both WUI and MSF, MSF were associated with an increased number of metabolite changes and some of the enriched pathways differed between exposures to WUI fires vs. MSF. These findings suggest that WUI and MSF exposures may share common biological responses while also posing unique health risks to firefighters.Supplementary InformationThe online version contains supplementary material available at 10.1186/s12940-025-01239-7.

The recent RNA-seq technology is an attractive method to study gene expression. One of the most important goals in RNA-seq data analysis is to detect genes differentially expressed across treatments. Although several statistical methods have been published, there are no theoretical justifications for whether these methods are optimal or how to search for the optimal test. Furthermore, most proposed tests are designed for testing whether the mean expression levels are exactly the same or not across treatments, whereas sometimes, biologists are interested in detecting genes with expression changes larger than a certain threshold. Another issue with current methods is that the false discovery rate (FDR) control is not well studied. In this manuscript, we propose a test to address all the above issues. Under model assumptions, we derive an optimal test that achieves the maximum of average power among those that control FDR at the same level. We also provide an approximated version, the approximated most average powerful (AMAP) test, for practical implementation. The proposed method allows for testing null hypotheses that are much more general than the ones most previous studies have considered, and it leads to a natural way of controlling the FDR. Through simulation studies, we show that our test has a higher power than other methods, including the widely-used edgeR, DESeq, and baySeq methods, as well as better FDR control than two other FDR control procedures commonly used in practice. For demonstration, we also apply the proposed method to a real RNA-seq dataset obtained from maize.

Differential network analysis has become a widely used technique to investigate changes of interactions among different conditions. Although the relationship between observed interactions and biochemical mechanisms is hard to establish, differential network analysis can provide useful insights about dysregulated pathways and candidate biomarkers. The available methods to detect differential interactions are heterogeneous and often rely on assumptions that are unrealistic in many applications. To address these issues, we develop a novel method for differential network analysis, using the so-called disparity filter as network reduction technique. In addition, we propose a classification model based on the inferred network interactions. The main novelty of this work lies in its ability to preserve connections that are statistically significant with respect to a null model without favouring any resolution scale, as a hard threshold would do, and without Gaussian assumptions. The method was tested using a published metabolomic dataset on colorectal cancer (CRC). Detected hub metabolites were consistent with recent literature and the classifier was able to distinguish CRC from polyp and healthy subjects with great accuracy. In conclusion, the proposed method provides a new simple and effective framework for the identification of differential interaction patterns and improves the biological interpretation of metabolomics data.

False discovery rate (FDR) control serves as a critical safeguard in high-dimensional statistical analysis, increasing reliability and ensuring reproducibility of discoveries. Although extensively studied for real-valued data, FDR methodologies remain underdeveloped for the complex-valued data domain despite their importance in signal processing, physics, and engineering applications. This work confronts a central challenge in FDR-controlled analysis: settings in which the data contain groups of highly correlated variables. To achieve this, we advance our Complex-Valued Terminating-Random Experiments (CT-Rex) framework by developing the CT-Rex+GVS, a grouped variable selector. The method comes in two variants: the elastic net <tex>$(E N)$</tex> and the informed elastic net (IEN), both with isotropic and phase agnostic regularization. We validate the framework by benchmarking it in the selection of complex-valued grouped variables for linear regression and in the estimation of the singlesnapshot direction-of-arrival (DOA) based on compressed sensing using uniform linear arrays (ULA). The conducted numerical experiments confirm the FDR control property and demonstrate favorable performance compared to existing approaches.

Brain connectivity analysis is now at the foreground of neuroscience research. A connectivity network is characterized by a graph, where nodes represent neural elements such as neurons and brain regions, and links represent statistical dependence that is often encoded in terms of partial correlation. Such a graph is inferred from the matrix-valued neuroimaging data such as electroencephalography and functional magnetic resonance imaging. There have been a good number of successful proposals for sparse precision matrix estimation under normal or matrix normal distribution; however, this family of solutions does not offer a direct statistical significance quantification for the estimated links. In this article, we adopt a matrix normal distribution framework and formulate the brain connectivity analysis as a precision matrix hypothesis testing problem. Based on the separable spatial-temporal dependence structure, we develop oracle and data-driven procedures to test both the global hypothesis that all spatial locations are conditionally independent, and simultaneous tests for identifying conditional dependent spatial locations with false discovery rate control. Our theoretical results show that the data-driven procedures perform asymptotically as well as the oracle procedures and enjoy certain optimality properties. The empirical finite-sample performance of the proposed tests is studied via intensive simulations, and the new tests are applied on a real electroencephalography data analysis.

Despite years of effort, exact pathogenesis of nonalcoholic fatty liver disease (NAFLD) remains obscure. To gain an insight into the regulatory roles of microRNAs (miRNAs) in aberrant energy metabolic status and pathogenesis of NAFLD, we analyzed the expression of miRNAs in livers of ob/ob mice, streptozotocin (STZ)-induced type 1 diabetic mice, and normal C57BL/6 mice by miRNA microarray. Compared with normal C57BL/6 mice, ob/ob mice showed upregulation of eight miRNAs and downregulation of four miRNAs in fatty livers. Upregulation of miR-34a and downregulation of miR-122 was found in livers of STZ-induced diabetic mice. These results demonstrate that distinct miRNAs are strongly dysregulated in NAFLD and hyperglycemia. Comparison between miRNA expressions in livers of ob/ob mice and STZ-administered mice further revealed upregulation of four miRNAs and downregulation of two miRNAs in livers of ob/ob mice, indicating that these miRNAs may represent a molecular signature of NAFLD. A distinctive miRNA expression pattern was identified in ob/ob mouse liver, and hierarchical clustering of this pattern could clearly discriminate ob/ob mice from either normal C57BL/6 mice or STZ-administered mice. These findings suggest an important role of miRNAs in hepatic energy metabolism and implicate the participation of miRNAs in the pathophysiological processes of NAFLD.

Gaussian graphical models (GGM) are powerful tools to examine partial correlation structures in high-dimensional omics datasets. Partial correlation networks can explain complex relationships between genes or other biological variables. Bayesian implementations of GGMs have recently received more attention. Usually, the most demanding parts of GGM implementations are: (i) hyperparameter tuning, (ii) edge selection, (iii) scalability for large datasets, and (iv) the prior choice for Bayesian GGM. To address these limitations, we introduce a novel Bayesian GGM using a hierarchical matrix-F prior with a fast implementation. We show, with extensive simulations and biological example analyses, that this prior has competitive network recovery capabilities compared to state-of-the-art approaches and good properties for recovering meaningful networks. We present a new way of tuning the shrinkage hyperparameter by constraining the condition number of the estimated precision matrix. For edge selection, we propose using approximated credible intervals (CI) whose width is controlled by the false discovery rate. An optimal CI is selected by maximizing an estimated F1-score via permutations. In addition, a specific choice of hyperparameter can make the proposed prior better suited for clustering and community detection. Our method, with a generalized expectation-maximization algorithm, computationally outperforms existing Bayesian GGM approaches that use Markov chain Monte Carlo algorithms. The method is implemented in the R package HMFGraph, found on GitHub at https://github.com/AapoKorhonen/HMFGraph. All codes to reproduce the results are found on GitHub at https://github.com/AapoKorhonen/HMFGraph-Supplementary.

The target-decoy database search strategy is widely accepted as a standard method for estimating the false discovery rate (FDR) of peptide identification, based on which peptide-spectrum matches (PSMs) from the target database are filtered. To improve the sensitivity of protein identification given a fixed accuracy (frequently defined by a protein FDR threshold), a postprocessing procedure is often used that integrates results from different peptide search engines that had assayed the same data set. In this work, we show that PSMs that are grouped by the precursor charge, the number of missed internal cleavage sites, the modification state, and the numbers of protease termini and that the proteins grouped by their unique peptide count should be filtered separately according to the given FDR. We also develop an iterative procedure to filter the PSMs and proteins simultaneously, according to the given FDR. Finally, we present a general framework to integrate the results from different peptide search engines using the same FDR threshold. Our method was tested with several shotgun proteomics data sets that were acquired by multiple LC/MS instruments from two different biological samples. The results showed a satisfactory performance. We implemented the method in a user-friendly software package called BuildSummary, which can be downloaded for free from http://www.proteomics.ac.cn/software/proteomicstools/index.htm as part of the software suite ProteomicsTools.

We propose Bayesian methods for Gaussian graphical models that lead to sparse and adaptively shrunk estimators of the precision (inverse covariance) matrix. Our methods are based on lasso-type regularization priors leading to parsimonious parameterization of the precision matrix, which is essential in several applications involving learning relationships among the variables. In this context, we introduce a novel type of selection prior that develops a sparse structure on the precision matrix by making most of the elements exactly zero, in addition to ensuring positive definiteness - thus conducting model selection and estimation simultaneously. More importantly, we extend these methods to analyze clustered data using finite mixtures of Gaussian graphical model and infinite mixtures of Gaussian graphical models. We discuss appropriate posterior simulation schemes to implement posterior inference in the proposed models, including the evaluation of normalizing constants that are functions of parameters of interest, which result from the restriction of positive definiteness on the correlation matrix. We evaluate the operating characteristics of our method via several simulations and demonstrate the application to real data examples in genomics.