Multivariate Normal Model Research Articles

Multiomic Signatures of Traffic-Related Air Pollution in London Reveal Potential Short-Term Perturbations in Gut Microbiome-Related Pathways.

This randomized crossover study investigated the metabolic and mRNA alterations associated with exposure to high and low traffic-related air pollution (TRAP) in 50 participants who were either healthy or were diagnosed with chronic pulmonary obstructive disease (COPD) or ischemic heart disease (IHD). For the first time, this study combined transcriptomics and serum metabolomics measured in the same participants over multiple time points (2 h before, and 2 and 24 h after exposure) and over two contrasted exposure regimes to identify potential multiomic modifications linked to TRAP exposure. With a multivariate normal model, we identified 78 metabolic features and 53 mRNA features associated with at least one TRAP exposure. Nitrogen dioxide (NO2) emerged as the dominant pollutant, with 67 unique associated metabolomic features. Pathway analysis and annotation of metabolic features consistently indicated perturbations in the tryptophan metabolism associated with NO2 exposure, particularly in the gut-microbiome-associated indole pathway. Conditional multiomics networks revealed complex and intricate mechanisms associated with TRAP exposure, with some effects persisting 24 h after exposure. Our findings indicate that exposure to TRAP can alter important physiological mechanisms even after a short-term exposure of a 2 h walk. We describe for the first time a potential link between NO2 exposure and perturbation of the microbiome-related pathways.

Abstract PO4-08-06: Causal Relationships and Familial Aggregation of Mammogram Risk Scores: Insights from Breast Cancer in Twins and Families

Abstract Background: Mammogram risk scores based on texture and density, determined by brightness thresholds, are associated with breast cancer risk differently and could reveal distinct information about breast cancer risk. This study aimed to investigate the causal relationships between these intercorrelated risk scores and the familial aggregation of a texture-based mammogram measure, shedding light on the relevance to breast cancer aetiology. Methods: We analysed data from the Australian Mammographic Density Twins and Sisters Study, including 3195 breast-cancer-free women from 1519 families. The dataset comprised 527 pairs of monozygotic (MZ) twins, 271 pairs of dizygotic (DZ) twins, and 1599 sisters. The average age at mammography for sister pairs ranged from 40 to 70 years. Mammogram risk scores based on texture (named Cirrus) and three density-defined areas (light, bright, and brightest) that were spatially independent were generated. The Inference about Causation from Examination of Familial Confounding (ICE FALCON) method was employed for causal inference. Familial aggregation and the variance of Cirrus were assessed as a function of age using a multivariate normal model for pedigree analysis. The classic twin model was employed but allowing for varying shared environmental effects among different sister pairs. The single-nucleotide polymorphism (SNP)-based heritability was estimated using genetic variants from both closely and distantly related individuals. Model fits were compared using likelihood ratio tests and the Akaike Information Criterion. Results: Causal analysis using ICE FALCON revealed significant positive causal effects, with Cirrus, light areas, and bright areas influencing the brightest areas (accounting for 34%, 55%, and 85% of the associations, respectively). Similarly, light areas and bright areas demonstrated causal effects on Cirrus (accounting for 37% and 28% of the associations, respectively). No age-related differences in familial correlations or Cirrus variance were found for women aged 40 to 70 years. Familial correlations were estimated at 0.51 (0.03) for MZ pairs and 0.16 (0.03) for combined DZ and non-twin sister pairs, with no significant difference between DZ and non-twin sister pairs (P=0.3). Additive genetic effects accounted for up to 32% (5%) of the variance, consistent with SNP-based heritability estimates of 36% (12%). MZ-specific environmental effects contributed to at least 20% (3%), while shared environmental effects for DZ and non-twin sibling pairs accounted for less than 40% of that for MZ pairs. Conclusion: In a mammogram, the lighter (less dense) areas causally influence the brightest (highly dense) areas, including through textural features. These causal relationships provide insights into the relative importance of different mammogram features in breast cancer aetiology. For example, the brightest areas are more aetiologically important for screen-detected breast cancer, while the light areas are more aetiologically important for interval breast cancer. Additionally, specific textural features capture aetiologically independent breast cancer risk information from dense areas. We also confirm the partial heritability of Cirrus, the texture-based mammogram measure, substantially influenced by environmental factors (familial and non-familial). As well as genetic factors, Cirrus could be determined by factors operating at times of life when MZ pairs share their environments to a greater extent than do DZ and non-twin sisters, starting in utero and prior to adulthood, and remaining constant thereafter. These insights from twin and family data enhance our understanding of mammogram risk scores and their implications for breast cancer risk assessment. Citation Format: Zhoufeng Ye, Shuai Li, Gill Dite, Tuong Nguyen, Robert MacInnis, John Hopper. Causal Relationships and Familial Aggregation of Mammogram Risk Scores: Insights from Breast Cancer in Twins and Families [abstract]. In: Proceedings of the 2023 San Antonio Breast Cancer Symposium; 2023 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2024;84(9 Suppl):Abstract nr PO4-08-06.

Testing covariance structures belonging to a quadratic subspace under a doubly multivariate model

AbstractA hypothesis related to the block structure of a covariance matrix under the doubly multivariate normal model is studied. It is assumed that the block structure of the covariance matrix belongs to a quadratic subspace, and under the null hypothesis, each block of the covariance matrix also has a structure belonging to some quadratic subspace. The Rao score and the likelihood ratio test statistics are derived, and the exact distribution of the likelihood ratio test is determined. Simulation studies show the advantage of the Rao score test over the likelihood ratio test in terms of speed of convergence to the limiting chi-square distribution, while both proposed tests are competitive in terms of their power. The results are applied to both simulated and real-life example data.

A Multivariate Normal Distribution Data Generative Model in Small-Sample-Based Fault Diagnosis: Taking Traction Circuit Breaker as an Example

A Multivariate Normal Distribution Data Generative Model in Small-Sample-Based Fault Diagnosis: Taking Traction Circuit Breaker as an Example

Predictive densities for multivariate normal models based on extended models and shrinkage Bayes methods

Predictive densities for multivariate normal models based on extended models and shrinkage Bayes methods

Structured stochastic models based on multi-source heterogeneous data for predicting internal electricity load of non-residential buildings

Electricity load patterns in buildings are increasingly diverse and inherently present building-by-building and temporal variations. This study develops structured stochastic models to capture individual and temporal variations in non-residential building groups (e.g., education, office, culture, and retail buildings). Hourly electricity load data of non-residential buildings, categorized by building use, are sourced from two open datasets (Ministry of Land, Infrastructure and Transport and Korea Electric Power Corporation). First, heterogeneous public datasets are processed and utilized to provide both detailed building information and high-resolution electricity load data. Second, a structured set of four stochastic models are formulated using linear regression and multivariate normal distribution models. Model 1 utilizes the beta distribution to derive daily average electricity load per unit area for each building use. Model 2 utilizes the burr distribution to determine the daily variation of electricity load from the daily average. Models 3 and 4 utilize a multivariate normal distribution to represent the hourly average electricity load profile and its time variation, respectively. The coefficient of variation of the root mean square error (CVRMSE) for the structured probabilistic models ranges from 5.2 % to 14.8 % regarding five key load characterization variables. CVRMSEs for near-peak load, near-base load, rise time, high-load duration, and fall time are 8.5–13.9, 9.5–14.7, 7.3–14.8, 6.4–13.9, and 5.2–11.4 %, respectively. The validation results demonstrate that the proposed probabilistic models capture actual variations in measurements. Structured statistical models improve prediction performance by distinctly reflecting individual and temporal variations in electricity loads.

Discrepancy between structured matrices in the power analysis of a separability test

An important task in the analysis of multivariate data is testing of the covariance matrix structure. In particular, for assessing separability, various tests have been proposed. However, the development of a method of measuring discrepancy between two covariance matrix structures, in relation to the study of the power of the test, remains an open problem. Therefore, a discrepancy measure is proposed such that for two arbitrary alternative hypotheses with the same value of discrepancy, the power of tests remains stable, while for increasing discrepancy the power increases. The basic hypothesis is related to the separable structure of the observation matrix under a doubly multivariate normal model, as assessed by the likelihood ratio and Rao score tests. It is shown that the particular one-parameter method and the Frobenius norm fail in the power analysis of tests, while the entropy and quadratic loss functions can be efficiently used to measure the discrepancy between separable and non-separable covariance structures for a multivariate normal distribution.

Genetic and Environmental Causes of Variation in an Automated Breast Cancer Risk Factor Based on Mammographic Textures.

Cirrus is an automated risk predictor for breast cancer that comprises texture-based mammographic features and is mostly independent of mammographic density. We investigated genetic and environmental variance of variation in Cirrus. We measured Cirrus for 3,195 breast cancer-free participants, including 527 pairs of monozygotic (MZ) twins, 271 pairs of dizygotic (DZ) twins, and 1,599 siblings of twins. Multivariate normal models were used to estimate the variance and familial correlations of age-adjusted Cirrus as a function of age. The classic twin model was expanded to allow the shared environment effects to differ by zygosity. The SNP-based heritability was estimated for a subset of 2,356 participants. There was no evidence that the variance or familial correlations depended on age. The familial correlations were 0.52 (SE, 0.03) for MZ pairs and 0.16(SE, 0.03) for DZ and non-twin sister pairs combined. Shared environmental factors specific to MZ pairs accounted for 20% of the variance. Additive genetic factors accounted for 32% (SE = 5%) of the variance, consistent with the SNP-based heritability of 36% (SE = 16%). Cirrus is substantially familial due to genetic factors and an influence of shared environmental factors that was evident for MZ twin pairs only. The latter could be due to nongenetic factors operating in utero or in early life that are shared by MZ twins. Early-life factors, shared more by MZ pairs than DZ/non-twin sister pairs, could play a role in the variation in Cirrus, consistent with early life being recognized as a critical window of vulnerability to breast carcinogens.

Bayesian Analysis of Singly Imputed Synthetic Data under the Multivariate Normal Model

We develop appropriate Bayesian procedures to draw inference about the parameters under a multivariate normal model based on synthetic data. We consider two standard forms of synthetic data, generated under plug in sampling method and posterior predictive sampling method. In addition to point estimates of the mean vector and dispersion matrix, Bayesian credible sets for the mean vector and the generalized variance are also provided under both the scenarios. The analysis in the case when some (partial) features are sensitive and need to be hidden is also briey indicated.
 Vol. 23(2), November, 2023, pp 1-18

Bayesian profile regression for clustering analysis involving a longitudinal response and explanatory variables.

The identification of sets of co-regulated genes that share a common function is a key question of modern genomics. Bayesian profile regression is a semi-supervised mixture modelling approach that makes use of a response to guide inference toward relevant clusterings. Previous applications of profile regression have considered univariate continuous, categorical, and count outcomes. In this work, we extend Bayesian profile regression to cases where the outcome is longitudinal (or multivariate continuous) and provide PReMiuMlongi, an updated version of PReMiuM, the R package for profile regression. We consider multivariate normal and Gaussian process regression response models and provide proof of principle applications to four simulation studies. The model is applied on budding yeast data to identify groups of genes co-regulated during the Saccharomyces cerevisiae cell cycle. We identify 4 distinct groups of genes associated with specific patterns of gene expression trajectories, along with the bound transcriptional factors, likely involved in their co-regulation process.

Recursive Parameter Estimation and Its Convergence for Multivariate Normal Hidden Markov Inhomogeneous Models

In this paper, will discussed parameter estimation and convergence analysis of multivariate normal hidden inhomogeneous Markov models. The results of this research show that by using the expectation maximization algorithm, a sequence of parameter estimators converges to a stationary point of the likelihood function in a monotonically increasing manner.

Consistency factor for the MCD estimator at the Student-t distribution

It is well known that trimmed estimators of multivariate scatter, such as the Minimum Covariance Determinant (MCD) estimator, are inconsistent unless an appropriate factor is applied to them in order to take the effect of trimming into account. This factor is widely recommended and applied when uncontaminated data are assumed to come from a multivariate normal model. We address the problem of computing a consistency factor for the MCD estimator in a heavy-tail scenario, when uncontaminated data come from a multivariate Student-t distribution. We derive a remarkably simple computational formula for the appropriate factor and show that it reduces to an even simpler analytic expression in the bivariate case. Exploiting our formula, we then develop a robust Monte Carlo procedure for estimating the usually unknown number of degrees of freedom of the assumed and possibly contaminated multivariate Student-t model, which is a necessary ingredient for obtaining the required consistency factor. Finally, we provide substantial simulation evidence about the proposed procedure and apply it to data from image processing and financial markets.

Joint Imputation of General Data.

High-dimensional complex survey data of general structures (e.g., containing continuous, binary, categorical, and ordinal variables), such as the US Department of Defense's Health-Related Behaviors Survey (HRBS), often confound procedures designed to impute any missing survey data. Imputation by fully conditional specification (FCS) is often considered the state of the art for such datasets due to its generality and flexibility. However, FCS procedures contain a theoretical flaw that is exposed by HRBS data-HRBS imputations created with FCS are shown to diverge across iterations of Markov Chain Monte Carlo. Imputation by joint modeling lacks this flaw; however, current joint modeling procedures are neither general nor flexible enough to handle HRBS data. As such, we introduce an algorithm that efficiently and flexibly applies multiple imputation by joint modeling in data of general structures. This procedure draws imputations from a latent joint multivariate normal model that underpins the generally structured data and models the latent data via a sequence of conditional linear models, the predictors of which can be specified by the user. We perform rigorous evaluations of HRBS imputations created with the new algorithm and show that they are convergent and of high quality. Lastly, simulations verify that the proposed method performs well compared to existing algorithms including FCS.

A comprehensive comparison of copula models and multivariate normal distribution for geo-material parametric data

Multivariate distribution models for geo-material parametric data play a crucial role in reliability-based design. Currently, two major models are commonly used: the conventional multivariate normal distribution model and the copula model (including subtypes like the elliptical copula model and Vine copula model). This study aims to assess the performance of different models including three specific copula models (Gaussian copula, t copula, and D-Vine copula models) and the conventional normal distribution model. To this end, this study employs an incomplete database comprising 693 data samples related to lacustrine soils near Dianchi Lake in Kunming city, China. Results indicate that copula models generally exhibit lower model uncertainty compared to the conventional multivariate normal distribution model. Using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), the elliptical copula ranks first, followed by Gaussian copula, with D-Vine copula ranking third. For a balanced evaluation of performance and complexity, the conventional multivariate normal distribution model is favored. This study provides valuable insights for selecting appropriate models for geo-material parametric data, aiding reliability-based design in geotechnical engineering. Additionally, it is demonstrated that sampling with replacement in the Bootstrapping technique has only a slight effect on the estimation of correlation matrices for the incomplete database.

Combining Probability and Nonprobability Samples by Using Multivariate Mass Imputation Approaches with Application to Biomedical Research.

Nonprobability samples have been used frequently in practice including public health study, economics, education, and political polls. Naïve estimates based on nonprobability samples without any further adjustments may suffer from serious selection bias. Mass imputation has been shown to be effective in practice to improve the representativeness of nonprobability samples. It builds an imputation model based on nonprobability samples and generates imputed values for all units in the probability samples. In this paper, we compare two mass imputation approaches including latent joint multivariate normal model mass imputation (e.g., Generalized Efficient Regression-Based Imputation with Latent Processes (GERBIL)) and fully conditional specification (FCS) procedures for integrating multiple outcome variables simultaneously. The Monte Carlo simulation study shows the benefits of GERBIL and FCS with predictive mean matching in terms of balancing the Monte Carlo bias and variance. We further evaluate our proposed method by combining the information from Tribal Behavioral Risk Factor Surveillance System and Behavioral Risk Factor Surveillance System data files.

Combining Continuous and Categorical Data Modeling in Developmental Age Estimation Using Hierarchical Bayes

Residual correlations (correlations that persist after accounting for the effect of chronological age) between variables can have a significant impact on final age estimates. Such correlations can result in overly narrow age intervals and high error rates when not accounted for. Modeling correlations can be mathematically problematic across mixed data types. Hierarchical modeling can incorporate continuous and categorical traits into a single model that accounts for correlated variables while reducing computationally expensive calculations. This paper demonstrates a Bayesian hierarchical modeling approach in which trait variables were grouped by data type or bodily system and used to produce separate age estimates with any appropriate model. These age estimates were combined into a single estimate using a multivariate normal model via nested cross-validation. The data used included nine diaphyseal length measurements and 29 epiphyseal fusion and ossification sites from 179 individuals in the publicly available U.S. Subadult Virtual Anthropology Database. Diaphyseal ages were modeled with linear regression and epiphyseal ages with random forest regression. Age estimates from the hierarchical model had reduced bias relative to diaphyseal or epiphyseal maximum likelihood estimates alone. Combined-indicator age intervals from 95% highest density regions (HDRs) were on average 15% narrower than those from diaphyseal 95% HDRs while success rates were 2% lower (91% vs. 93%). Functional example code is provided. A general hierarchical modeling approach may be applicable to other areas of skeletal analysis that employ correlated variables of mixed data types including adult age estimation and ancestry estimation.

Comparing and combining data from immune assays based on left-censored multivariate normal model assuming common assay differences across settings.

In vaccine research towards the prevention of infectious diseases, immune response biomarkers serve as an important tool for comparing and ranking vaccine candidates based on their immunogenicity and predicted protective effect. However, analyses of immune response outcomes can be complicated by differences across assays when immune response data are acquired from multiple groups/laboratories. Motivated by a real-world problem to accommodate the use of two different neutralization assays in COVID-19 vaccine trials, we propose methods based on left-censored multivariate normal model assuming common assay differences across settings, to adjust for differences between assays with respect to measurement error and the lower limit of detection. Our proposed methods integrate external paired-sample data with bridging assumptions to achieve two objectives, both using pooled data acquired from different assays: (i) comparing immunogenicity between vaccine regimens, and (ii) evaluating correlates of risk. In simulation studies, for the first objective, our method leads to unbiased calibrated assay mean with good coverage of bootstrap confidence interval, as well as valid test for immunogenicity comparison, while the alternative method assuming constant calibration model between assays leads to biased estimate of assay mean with undercoverage problem and invalid test with inflated type-I error; for the second objective, in the presence of noticeable left-censoring rate, our proposed method can drastically outperform the existing method that ignores left-censoring, in terms of reduced bias and improved precision. We apply the proposed methods to SARS-CoV-2 spike-pseudotyped virus neutralization assay data generated in vaccine and convalescent samples by two different laboratories.

Intrusion Detection System Based on Pattern Recognition.

Artificial intelligence has been developed to be able to solve difficult problems that involve huge amounts of data and that require rapid decision-making in most branches of science and business. Machine learning is one of the most prominent areas of artificial intelligence, which has been used heavily in the last two decades in the field of network security, especially in Intrusion Detection Systems (IDS). Pattern recognition is a machine learning method applied in medical applications, image processing, and video processing. In this article, two layers' IDS is proposed. The first layer classifies the network connection according to the used service. Then, a minimum number of features that optimize the detection accuracy of malicious activities on that service are identified. Using those features, the second layer classifies each network connection as an attack or normal activity based on the pattern recognition method. In the training phase, two multivariate normal statistical models are created: the normal behavior model and the attack behavior model. In the testing and running phases, a maximum likelihood estimation function is used to classify a network connection into attack or normal activity using the two multivariate normal statistical models. The experimental results prove that the proposed IDS has superiority over related IDSs for network intrusion detection. Using only four features, it successfully achieves DR of 97.5%, 0.001 FAR, MCC 95.7%, and 99.8% overall accuracy.

Efficient and feasible inference for high-dimensional normal copula regression models

The composite likelihood (CL) is amongst the computational methods used for the estimation of high-dimensional multivariate normal (MVN) copula models with discrete responses. Its computational advantage, as a surrogate likelihood method, is that is based on the independence likelihood for the univariate marginal regression and non-regression parameters and pairwise likelihood for the correlation parameters. Nevertheless, the efficiency of the CL method for estimating the univariate regression and non-regression marginal parameters can be low. For a high-dimensional discrete response, weighted versions of the composite likelihood estimating equations and an iterative approach to determine good weight matrices are proposed. The general methodology is applied to the MVN copula with univariate ordinal regressions as the marginals. Efficiency calculations show that the proposed method is nearly as efficient as the maximum likelihood for fully specified MVN copula models. Illustrations include simulations and real data applications regarding longitudinal (low-dimensional) and time (high-dimensional) series ordinal response data with covariates. Our studies suggest that there is a substantial gain in efficiency via the weighted CL method.

Multi-omics signatures of exposure to disinfection by-products in swimming

Background and aims: Untargeted HRMS metabolomics provides an agnostic global profiling of small molecules in a biological system capturing an overview of exposure to exogenous compounds, and their effects on metabolic pathways, rendering an essential tool for characterising the exposome. Disinfection by-products (DBPs) are a complex mixture of halogenated organic compounds present in drinking and swimming pool water. Although several epidemiological studies have pointed their potential to induce adverse health outcomes such as bladder cancer, their mixture effect and the downstream molecules perturbed by their exposure have been poorly explored. In this work, we aim to identify molecular signatures of exposures to mixtures of DBPs in individuals with measured exposures. Methods: In PISCINA-II study, metabolomics, transcriptomics, proteomics in serum, and levels of DBPs in exhaled breaths, were measured in 60 subjects before and after swimming. Pre-processing of HRMS data from PISCINA-II study was customised to include more halogenated compounds. Multivariate normal (MVN) and partial least square (PLS) models were used to identify metabolic features associated with DBP exposures. Conditional correlation networks were constructed to understand the holistic relationship amongst the metabolic features and their relationship with proteomics and transcriptomics. Results: 98 metabolic features were identified to be associated with exposure to DBP mixture, of which 39 were not identified in the previous analysis without specific reprocessing and inclusion of halogenated compounds. In conditional network analysis, the 98 features showed cluster structures, suggesting they could contribute to different downstream biological pathways. Multi-omic networks showed that transcriptomic and proteomic signals were differentially connected to the different clusters of the metabolic signatures. Conclusions: New data processing approach allowed identification of novel metabolic signatures of DBP mixture exposure. Conditional correlation network implied the functional proximity of these signatures with other measured omic signals. Keywords: Disinfection by-products, PLS, network analysis, omics, exposome, statistical analysis