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Functional pathways involve a series of biological alterations that may result in the occurrence of many diseases including cancer. With the availability of various “omics” technologies it becomes feasible to integrate information from a hierarchy of biological layers to provide a more comprehensive understanding to the disease. In many diseases, it is believed that only a small number of networks, each relatively small in size, drive the disease. Our goal in this study is to develop methods to discover these functional networks across biological layers correlated with the phenotype. We derive a novel Network Summary Matrix (NSM) that highlights potential pathways conforming to least squares regression relationships. An algorithm called Decomposition of Network Summary Matrix via Instability (DNSMI) involving decomposition of NSM using instability regularization is proposed. Simulations and real data analysis from The Cancer Genome Atlas (TCGA) program will be shown to demonstrate the performance of the algorithm.

Maximum likelihood is a common method of estimating a phylogenetic tree based on a set of genetic data. However, models of evolution for certain types of genetic data are highly flawed in their specification, and this misspecification can have an adverse impact on phylogenetic inference. Our attention here is focused on extending an existing class of models for estimating phylogenetic trees from discrete morphological characters. The main advance of this work is a model that allows unequal equilibrium frequencies in the estimation of phylogenetic trees from discrete morphological character data using likelihood methods. Possible extensions of the proposed model will also be discussed.

In this study, we conduct a comparison of three most recent statistical methods for joint variable selection and covariance estimation with application of detecting expression quantitative trait loci (eQTL) and gene network estimation, and introduce a new hierarchical Bayesian method to be included in the comparison. Unlike the traditional univariate regression approach in eQTL, all four methods correlate phenotypes and genotypes by multivariate regression models that incorporate the dependence information among phenotypes, and use Bayesian multiplicity adjustment to avoid multiple testing burdens raised by traditional multiple testing correction methods. We presented the performance of three methods (MSSL – Multivariate Spike and Slab Lasso, SSUR – Sparse Seemingly Unrelated Bayesian Regression, and OBFBF – Objective Bayes Fractional Bayes Factor), along with the proposed, JDAG (Joint estimation via a Gaussian Directed Acyclic Graph model) method through simulation experiments, and publicly available HapMap real data, taking asthma as an example. Compared with existing methods, JDAG identified networks with higher sensitivity and specificity under row-wise sparse settings. JDAG requires less execution in small-to-moderate dimensions, but is not currently applicable to high dimensional data. The eQTL analysis in asthma data showed a number of known gene regulations such as STARD3, IKZF3 and PGAP3, all reported in asthma studies. The code of the proposed method is freely available at GitHub (https://github.com/xuan-cao/Joint-estimation-for-eQTL).