In the past years, several network reconstruction methods modeled as Gaussian Graphical Model in high dimensional settings where proposed. In this work we will analyze three different methods, the Graphical Lasso (GLasso), Graphical Ridge (GGMridge) and a novel method called LPC, or Local Partial Correlation. The evaluation will be performed in high dimensional data generated from different simulated random graph structures (Erdos-Renyi, Barabasi-Albert, Watts-Strogatz ), using Receiver Operating Characteristic or ROC curve. We will also apply the methods in the reconstruction of genetic co-expression network for the differentially expressed genes in cervical cancer tumors. / Vários métodos tem sido propostos para a reconstrução de redes em alta dimensão, que e tratada como um Modelo Gráfico Gaussiano. Neste trabalho vamos analisar três métodos diferentes, o método Graphical Lasso (GLasso), Graphical Ridge (GGMridge) e um novo método chamado LPC, ou Correlação Parcial Local. A avaliação será realizada em dados de alta dimensão, gerados a partir de grafos aleatórios (Erdos-Renyi, Barabasi-Albert, Watts-Strogatz ), usando Receptor de Operação Característica, ou curva ROC. Aplicaremos também os metidos apresentados, na reconstrução da rede de co-expressão gênica para tumores de câncer cervical.

In the past years, several network reconstruction methods modeled as Gaussian Graphical Model in high dimensional settings where proposed. In this work we will analyze three different methods, the Graphical Lasso (GLasso), Graphical Ridge (GGMridge) and a novel method called LPC, or Local Partial Correlation. The evaluation will be performed in high dimensional data generated from different simulated random graph structures (Erdos-Renyi, Barabasi-Albert, Watts-Strogatz ), using Receiver Operating Characteristic or ROC curve. We will also apply the methods in the reconstruction of genetic co-expression network for the differentially expressed genes in cervical cancer tumors. / Vários métodos tem sido propostos para a reconstrução de redes em alta dimensão, que e tratada como um Modelo Gráfico Gaussiano. Neste trabalho vamos analisar três métodos diferentes, o método Graphical Lasso (GLasso), Graphical Ridge (GGMridge) e um novo método chamado LPC, ou Correlação Parcial Local. A avaliação será realizada em dados de alta dimensão, gerados a partir de grafos aleatórios (Erdos-Renyi, Barabasi-Albert, Watts-Strogatz ), usando Receptor de Operação Característica, ou curva ROC. Aplicaremos também os metidos apresentados, na reconstrução da rede de co-expressão gênica para tumores de câncer cervical.

The wide application of the genomic microarray technology triggers a tremendous need in the development of the high dimensional genetic data analysis. Many statistical methods for the microarray data analysis consider one gene at a time, but they may miss subtle changes at the single gene level. This limitation may be overcome by considering a set of genes simultaneously where the gene sets are derived from the prior biological knowledge and are called "pathways". We have made contributions on two specific research topics related to the high dimensional genetic pathway data. One is to propose a semi- parametric model for identifying pathways related to the zero inflated clinical outcomes; the other is to propose a multilevel Gaussian graphical model for exploring both pathway and gene level network structures. For the first problem, we develop a semiparametric model via a Bayesian hierarchical framework. We model the pathway effect nonparametrically into a zero inflated Poisson hierarchical regression model with unknown link function. The nonparametric pathway effect is estimated via the kernel machine and the unknown link function is estimated by transforming a mixture of beta cumulative density functions. Our approach provides flexible semiparametric settings to describe the complicated association between gene microarray expressions and the clinical outcomes. The Metropolis-within-Gibbs sampling algorithm and Bayes factor are used to make the statistical inferences. Our simulation results support that the semiparametric approach is more accurate and flexible than the zero inflated Poisson regression with the canonical link function, this is especially true when the number of genes is large. The usefulness of our approaches is demonstrated through its applications to a canine gene expression data set (Enerson et al., 2006). Our approaches can also be applied to other settings where a large number of highly correlated predictors are present. Unlike the first problem, the second one is to take into account that pathways are not independent of each other because of shared genes and interactions among pathways. Multi-pathway analysis has been a challenging problem because of the complex dependence structure among pathways. By considering the dependency among pathways as well as genes within each pathway, we propose a multi-level Gaussian graphical model (MGGM): one level is for pathway network and the second one is for gene network. We develop a multilevel L1 penalized likelihood approach to achieve the sparseness on both levels. We also provide an iterative weighted graphical LASSO algorithm (Guo et al., 2011) for MGGM. Some asymptotic properties of the estimator are also illustrated. Our simulation results support the advantages of our approach; our method estimates the network more accurate on the pathway level, and sparser on the gene level. We also demonstrate usefulness of our approach using the canine genes-pathways data set. / Ph. D.