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Graphs/networks have become a powerful analytical approach for data modeling. Besides, with the advances in sensor technology, dynamic time-evolving data have become more common. In this context, one point of interest is a better understanding of the information flow within and between networks. Thus, we aim to infer Granger causality (G-causality) between networks’ time series. In this case, the straightforward application of the well-established vector autoregressive model is not feasible. Consequently, we require a theoretical framework for modeling time-varying graphs. One possibility would be to consider a mathematical graph model with time-varying parameters (assumed to be random variables) that generates the network. Suppose we identify G-causality between the graph models’ parameters. In that case, we could use it to define a G-causality between graphs. Here, we show that even if the model is unknown, the spectral radius is a reasonable estimate of some random graph model parameters. We illustrate our proposal’s application to study the relationship between brain hemispheres of controls and children diagnosed with Autism Spectrum Disorder (ASD). We show that the G-causality intensity from the brain’s right to the left hemisphere is different between ASD and controls.

BACKGROUND Blood pressure (BP) is associated with carotid intima-media thickness (CIMT), but few studies have explored the association between BP variability and CIMT. We aimed to investigate this association in the Brazilian Longitudinal Study of Adult Health (ELSA-Brasil) baseline. METHODS We analyzed data from 7,215 participants (56.0% women) without overt cardiovascular disease (CVD) or antihypertensive use. We included 10 BP readings in varying positions during a 6-hour visit. We defined BP variability as the SD of these readings. We performed a 2-step analysis. We first linearly regressed the CIMT values on main and all-order interaction effects of the variables age, sex, body mass index, race, diabetes diagnosis, dyslipidemia diagnosis, family history of premature CVD, smoking status, and ELSA-Brasil site, and calculated the residuals (residual CIMT). We used partial least square path analysis to investigate whether residual CIMT was associated with BP central tendency and BP variability. RESULTS Systolic BP (SBP) variability was significantly associated with residual CIMT in models including the entire sample (path coefficient [PC]: 0.046; P < 0.001), and in women (PC: 0.046; P = 0.007) but not in men (PC: 0.037; P = 0.09). This loss of significance was probably due to the smaller subsample size, as PCs were not significantly different according to sex. CONCLUSIONS We found a small but significant association between SBP variability and CIMT values. This was additive to the association between SBP central tendency and CIMT values, supporting a role for high short-term SBP variability in atherosclerosis.

Many challenging problems in biomedical research rely on understanding how variables are associated with each other and influenced by genetic and environmental factors. Probabilistic graphical models (PGMs) are widely acknowledged as a very natural and formal language to describe relationships among variables and have been extensively used for studying complex diseases and traits. In this work, we propose methods that leverage observational Gaussian family data for learning a decomposition of undirected and directed acyclic PGMs according to the influence of genetic and environmental factors. Many structure learning algorithms are strongly based on a conditional independence test. For independent measurements of normally distributed variables, conditional independence can be tested through standard tests for zero partial correlation. In family data, the assumption of independent measurements does not hold since related individuals are correlated due to mainly genetic factors. Based on univariate polygenic linear mixed models, we propose tests that account for the familial dependence structure and allow us to assess the significance of the partial correlation due to genetic (between-family) factors and due to other factors, denoted here as environmental (within-family) factors, separately. Then, we extend standard structure learning algorithms, including the IC/PC and the really fast causal inference (RFCI) algorithms, to Gaussian family data. The algorithms learn the most likely PGM and its decomposition into two components, one explained by genetic factors and the other by environmental factors. The proposed methods are evaluated by simulation studies and applied to the Genetic Analysis Workshop 13 simulated dataset, which captures significant features of the Framingham Heart Study.

Causal inference may help us to understand the underlying mechanisms and the risk factors of diseases. In Genetics, it is crucial to understand how the connectivity among variables is influenced by genetic and environmental factors. Family data have proven to be useful in elucidating genetic and environmental influences, however, few existing approaches are able of addressing structure learning of probabilistic graphical models (PGMs) and family data analysis jointly. We propose methodologies for learning, from observational Gaussian family data, the most likely PGM and its decomposition into genetic and environmental components. They were evaluated by a simulation study and applied to the Genetic Analysis Workshop 13 simulated data, which mimic the real Framingham Heart Study data, and to the metabolic syndrome phenotypes from the Baependi Heart Study. In neuroscience, one challenge consists in identifying interactions between functional brain networks (FBNs) - graphs. We propose a method to identify Granger causality among FBNs. We show the statistical power of the proposed method by simulations and its usefulness by two applications: the identification of Granger causality between the FBNs of two musicians playing a violin duo, and the identification of a differential connectivity from the right to the left brain hemispheres of autistic subjects. Inferência causal pode nos ajudar a compreender melhor as relações de dependência direta entre variáveis e, assim, a identificar fatores de riscos de doenças. Em Genética, a análise de dados agrupados em famílias permite investigar influências genéticas e ambientais nas relações entre as variáveis. Neste trabalho, nós propomos métodos para aprender, a partir de dados Gaussianos agrupados em famílias, o mais provável modelo gráfico probabilístico (dirigido ou não dirigido) e também sua decomposição em dois componentes: genético e ambiental. Os métodos foram avaliados por simulações e aplicados tanto aos dados simulados do Genetic Analysis Workshop 13, que imitam características dos dados do Framingham Heart Study, como aos dados da síndrome metabólica do estudo Corações de Baependi. Em Neurociência, um desafio consiste em identificar interações entre redes funcionais cerebrais - grafos. Nós propomos um método que identifica causalidade de Granger entre grafos e, por meio de simulações, mostramos que o método tem alto poder estatístico. Além disso, mostramos sua utilidade por meio de duas aplicações: 1) identificação de causalidade de Granger entre as redes cerebrais de dois músicos enquanto tocam um dueto de violino e 2) identificação de conectividade diferencial do hemisfério cerebral direito para o esquerdo em indivíduos autistas.

A major challenge in biomedical research is to identify causal relationships among genotypes, phenotypes, and clinical outcomes from high-dimensional measurements. Causal networks have been widely used in systems genetics for modeling gene regulatory systems and for identifying causes and risk factors of diseases. In this chapter, we describe fundamental concepts and algorithms for constructing causal networks from observational data. In biological context, causal inferences can be drawn from the natural experimental setting provided by Mendelian randomization, a term that refers to the random assignment of genotypes at meiosis. We show that genetic variants may serve as instrumental variables, improving estimation accuracy of the causal effects. In addition, identifiability issues that commonly arise when learning network structures may be overcome by using prior information on genotype–phenotype relations. We discuss four recent algorithms for genotype–phenotype network structure learning, namely (1) QTL-directed dependency graph, (2) QTL+Phenotype supervised orientation, (3) QTL-driven phenotype network, and (4) sparsity-aware maximum likelihood (SML).

Toda medida, desde que feita por um instrumento real, tem uma imprecisão associada. Neste trabalho, abordamos a questão das imprecisões em experimentos de microarranjos de cDNA de dois canais, uma tecnologia que tem sido muito explorada nos últimos anos e que ainda é um importante auxiliar nos estudos de expressões gênicas. Dezenas de milhares de representantes de genes são impressos em uma lâmina de vidro e hibridizados simultaneamente com RNA mensageiro de duas amostras diferentes de células. Essas amostras são marcadas com corantes fluorescentes diferentes e a lâmina, após a hibridização, é digitalizada, obtendo-se duas imagens. As imagens são analisadas com programas especiais que segmentam os locais que estavam os genes e extraem estatísticas dos píxeis de cada local. Por exemplo, a média, a mediana e a variância das intensidades do conjunto de píxeis de cada local (o mesmo é feito normalmente para uma área em volta de cada local, chamada de fundo). Estimadores estatísticos como o da variância nos dão uma estimativa de quão precisa é uma certa medida. Uma vez de posse das estimativas das intensidades de cada local, para se obter a efetiva expressão de um gene, algumas transformações são feitas nos dados de forma a eliminar variabilidades sistemáticas. Neste trabalho, mostramos como podem ser feitas as análises a partir de uma medida de expressão gênica com um erro estimado. Mostramos como estimar essa imprecisão e estudamos, em termos de propagação da imprecisão, os efeitos de algumas transformações realizadas nos dados, por exemplo, a remoção do viés estimado pelo método de regressão local robusta, mais conhecido como \\textit{lowess}. Uma vez obtidas as estimativas das imprecisões propagadas, mostramos também como utilizá-las na determinação dos genes diferencialmente expressos entre as amostras estudadas. Por fim, comparamos os resultados com os obtidos por formas clássicas de análise, em que são desconsideradas as imprecisões das medidas. Concluímos que a modelagem das imprecisões das medidas pode favorecer as análises, já que os resultados obtidos em uma aplicação com dados reais de expressões gênicas foram condizentes com os que encontramos na literatura. Any measurement, since it is made for a real instrument, has an uncertainty associated with it. In the present paper, we address this issue of uncertainty in two-channel cDNA Microarray experiments, a technology that has been widely used in recent years and is still an important tool for gene expression studies. Tens of thousands of gene representatives are printed onto a glass slide and hybridized simultaneously with mRNA from two different cell samples. Different fluorescent dyes are used for labeling both samples. After hybridization, the glass slide is scanned yielding two images. Image processing and analysis programs are used for spot segmentation and pixel statistics computation, for instance, the mean, median and variance of pixel intensities for each spot. The same statistics are computed for the pixel intensities in the background region. Statistical estimators such as the variance gives us an estimate of the accuracy of a measurement. Based on the intensity estimates for each spot, some data transformations are applied in order to eliminate systematic variability so we can obtain the effective gene expression. This paper shows how to analyze gene expression measurements with an estimated error. We presented an estimate of this uncertainty and we studied, in terms of error propagation, the effects of some data transformations. An example of data transformation is the correction of the bias estimated by a robust local regression method, also known as \\textit{lowess}. With the propagated errors obtained, we also showed how to use them for detecting differentially expressed genes between different conditions. Finally, we compared the results with those obtained by classical analysis methods, in which the measurement errors are disregarded. We conclude that modeling the measurements uncertainties can improve the analysis, since the results obtained in a real gene expressions data base were consistent with the literature.