Networks are everywhere, from social to biological sciences. Usually these networks are represented by graphs, i.e., mathematical objects composed of a set of vertices and a set of edges. However, a vast number of natural networks are dynamic and current methods typically ignore a third key component: time. This fact requires statistical approaches to analyze them appropriately.

In this context, we propose a methodology to identify Granger causality among graphs. By assuming that graphs are generated by models whose parameters are random variables, we define that a time series of graphs y_{i,t} does not Granger cause another time series of graphs y_{j,t} if the parameters of the model for y_{i,t} does not Granger cause the parameters of the model for y_{j,t}. The problem is that the models that generate the graphs are usually unknown and consequently the parameters cannot be estimated. However, for some random graph models, such as Erdös-Rényi, geometric, regular, Watts-Strogatz, and Barabási-Albert, it is known that the spectral radius (the largest eigenvalue of the adjacency matrix of the graph) is a function of the model parameters. For example, for the Erdos-Renyi random graph model, which is defined by the parameters n, number of vertices, and p, probability of two random vertices are connected, the spectral radius is known to be np.

Based on this idea, we propose to identify Granger causality between time series of graphs by fitting a vector autoregressive model (VAR) to the time series of spectral radii. By an extensive simulation study, we show that the methodology has good accuracy, particularly for large graphs and long time series. In addition, we show that the spectral radius performed better than other centrality measures, such as, degree, eigenvector, betweenness, and closeness centralities. Finally, we applied the methodology to identify Granger causality between brain networks.

To unravel the biological mechanism underlying complex traits and diseases, it is crucial to understand how the related phenotypes are associated with each other and how they are influenced by genetic and environmental factors. Probabilistic graphical models (PGMs) are widely used to describe relationships among variables (phenotypes) in a very intuitive and mathematically rigorous way. On the other hand, family-based studies are usually conducted to assess the influence of genetic and environmental factors on phenotypes. In this case, the polygenic model can be used to decompose the phenotypic variability into two variance components: one polygenic, for capturing the variability across families, and one environmental, for capturing the residual variability. Some algorithms for learning PGMs from observational data, known as structure learning algorithms, are strongly based on a conditional independence test. Considering the case where the observations are independent and pnormally distributed, the null hypothesis of conditional independence can be tested using classical tests for zero partial correlation and PGMs can be learned under Markov-properties equivalence. However, in family-based studies, measurements of related individuals are correlated and such dependence structure must be taken into account to obtain appropriate test statistics.

Based on the Gaussian univariate polygenic model, we derived an estimator for the partial correlation coefficient taking into account the family dependence structure and present a decomposition of the partial correlation coefficient according to the contribution of the genetic and environmental effects. Also, we derived zero partial correlation tests for these coefficients and extended the Meinshausen and Buhlmann (2006)'s approach, which learns undirected PGMs from Vertex Neighborhoods, and the IC (Pearl, 2000) / PC (Spirtes et al., 2000) algorithm, which learns directed PGMs, for learning genetic and environmental PGMs from observational family data. The performance of the proposed methodologies was assessed by using 100 replicates of simulated data, based on the Framingham Heart Study, provided by the Genetic Analysis Workshop (GAW) 13 in problem 2.

A cerveja é parte da história da humanidade e remonta dos legados deixados pelos antigos sumérios, egípcios, mesopotâmios e ibéricos há, pelo menos, 6000 a.C. Apesar disso, longe de ser considerado um processo estável, a produção da cerveja evolui e aprimora-se constantemente, a ponto de, atualmente, motivar uma indústria artesanal em franca expansão que, devido às inúmeras fontes de variabilidade intrínsecas, potencializa o espírito curioso e criativo do alquimista e o refinamento sensorial de indivíduos, independentemente de idade, gênero, condição social, etc.

Identificamos nesse universo uma janela ampla para o despertar do entusiasmo ao aprendizado de alunos do 3o ano da Graduação em Estatística na disciplina de Planejamento de Experimentos (MAE 0317) que abraçaram, imediata e vigorosamente, a proposta de produzirem cerveja como veículo ilustrativo transversal dos conceitos e ferramentas abordados na disciplina. Assim, formalizamos um projeto conjunto, a ser planejado e executado durante o 1º semestre de 2017, em sala de aula e em campo, envolvendo o professor, alunos, a monitoria e especialistas na produção de cerveja.

A ideia é combinar estatisticamente respostas que mensuram a qualidade da cerveja, tais como, densidade, estabilidade da espuma e experiência sensorial (corpo, amargor, doçura, aroma, transparência, etc.) contra fatores de variabilidade que podem ser controlados experimentalmente, tais como, a temperatura de cozimento, a carbonatação e a maturação. Considerando os resultados preliminares obtidos até agora e as perspectivas manifestas, acreditamos que o projeto permite trabalhar a percepção do conteúdo da disciplina pelo aluno, de tal forma a transformar o aprendizado de conceitos teóricos densos em uma experiência prazerosa, estimulante e interativa.

A challenging task in biomedical research is to understand precisely the complex network of causal associations among phenotypes and outcomes. Experimental studies such as clinical trials are the most trustworthy method of causality assessment. However, it may be unfeasible to carry out randomized experiments to discover all possible causal relationships when the number of variables is large. In systems genetics, causal inference is supported by Mendelian randomization, which provides a natural randomization process where genotypes, rather than treatments, are randomly allocated to individuals. Furthermore, genetic variants robustly associated with phenotypes can be seen as instrumental variables, allowing inferences on the causal relation between phenotypes and outcomes.

In this work, we made a comparative study among four recent algorithms that use genetic variants as instrumental variables for learning the structure of a genotype-phenotype network, namely, (i) QTL-directed Dependency Graph (QDG), (ii) QTL-driven phenotype network (QTLnet), (iii) Sparsity-aware Maximum Likelihood (SML), and (iv) QTL+Phenotype Supervised Orientation (QPSO). These algorithms are similar in the sense that they use QTL information to determine the causal direction among phenotypes. However, they were designed under different assumptions and therefore some may be more suitable than others for a particular biological application. By simulation studies, we investigated advantages and limitations of these methodologies, under different configurations. Finally, we applied the algorithms to real data involving cardiovascular phenotypes of F2 rats and compared the inferred causal networks.

Massage therapies are associated with pathological improvements, and have also been extensively used for esthetic purposes. This study aimed to evaluate part of the molecular mechanisms involved in massage by investigating modulation of gene expression associated with cell adhesion and the ECM (extracellular matrix) induced by esthetic massage combined with a cosmetic emulsion. Thirteen female volunteers clinically characterized as having grade II or III cellulite were recruited and were subjected to skin biopsies in the gluteofemoral region before and after treatment. Each volunteer’s leg was considered an experimental unit to reduce individual variability. The study population was divided into: (1) legs treated with a cosmetic emulsion and (2) legs treated with a cosmetic emulsion and massage. Examination of 84 genes analyzed by qPCR revealed a predominance of up-regulation in individuals treated with the emulsion and massage in comparison to individuals treated only with the emulsion (fold change > 1.5, and p < 0.05). The main genes modulated were: ECM proteases (ADAMTS8, MMP1, MMP3, MMP9 and MMP11), transmembrane molecules (HAS1, ITGAL), adhesion molecules (COL8A1 and LAMA1) and cell-matrix adhesion molecules (ADAMTS13). Concluding, the combination (cosmetic emulsion and massage) is therefore recommended to increase the effectiveness of a product and obtain the desired benefits in the treatment of skin disorders such as cellulite. The lack of scientific data on this technique can very often lead to skepticism among health professionals and even patients or consumers of cosmetic treatments. This study helps to elucidate some of the molecular phenomena associated with this therapy.

Most analyses of two-color microarray data are based on point estimation of the log-ratio of the two channel intensities. These estimates, commonly named M values, are conventionally obtained from some location measure of the pixel intensities of each channel, ignoring any imprecision. It is well known that the microarray technology is associated with many noise sources, and it has been shown that improved inferences can be obtained by including the inaccuracies involved and propagating them to downstream analysis. Using the multivariate delta method, we propose new estimators for the mean and the variance of the M values that take into account the probe-level inaccuracies in the analysis.