Estimation and inference in directed acyclic graphical models for biological networks

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Summary As biotechnology advances, biomedical investigations have become more complex due to high-throughput and high-dimensional data collected at a genomic scale. Of paramount importance is unraveling the regulatory roles of genetic variants on genes and gene-to-gene regulatory relationships. On this ground, biomedical researchers can identify causal Single-Nucleotide Polymorphisms (SNPs) and genes for complex traits and neurodegenerative diseases such as Alzheimer's disease (AD) to develop treatment strategies. Given the urgent need to under- stand the progression and etiology of these diseases, particularly AD, the PIs propose to develop statistical and computational tools for accurate estimation and inference of gene regulatory networks, with a focus on AD and other complex traits. The project consists of two major components: estimation and inference of gene regulatory networks with SNPs as instrumental variables (IVs). The main thrust will be on causal network reconstruction and inference with IVs as interventions in the possible presence of invalid IVs and hidden confounders, with particular effort on high-dimensional data, in which the number of variables may exceed the sample size. Concerning causal network reconstruction, the project will develop novel methods of reconstructing gene regulatory networks as directed acyclic graphs describing casual relationships among the SNPs (interventions), genes, and traits such as AD. The project will develop high-dimensional inferential tools based on modified likelihood ratio tests and a data perturbation scheme to account for the uncertainty involved in a discovery process. Moreover, it will focus on hypothesis testing on (1) the directionality and strength of multiple (linear/nonlinear) causal relations and (2) the presence of a pathway of causal relations. Computationally, the project will develop innovative methods and algorithms for large-scale problems. For application, based on the reconstructed gene regulatory networks, we will first identify causal genes for AD and AD's risk factors, such as lipids, then infer which of the risk factors are (putatively) causal to AD.