In this work I propose three network modeling approaches that estimate and leverage dependence in novel ways across and within networks to enhance the inference of complex modern biomedical data. Specifically, our methods are motivated by the personalized drug discovery problem in precision medicine and by the identification of factors explaining inter-subject variability in functional connectivity brain networks.

I first present NetCellMatch, a network-based multiscale matching algorithm de- signed for mapping patient tumors to in-vitro cancer cell lines for personalized drug discovery. Our algorithm first constructs a global network across all patient-cell line samples using their genomic similarity. Then, a multi-scale community detection algorithm integrates information across topologically meaningful clustering scales to obtain Network-Based Matching Scores (NBMS). NBMS are measures of cluster robustness which map patient tumors to cell lines. I apply NetCellMatch to reverse-phase protein array data obtained from the Cancer Genome Atlas for patients and from the MD Anderson Cell Lines Project for cell lines. Along with ”avatar” cell line identification for subgroups of patients, I evaluate connectivity patterns for breast, lung, and colon cancer and explore the proteomic profiles of avatars and their corresponding top matching patients. Our results demonstrate our framework’s ability to identify both patient-cell line matches and potential proteomic drivers of similarity. Our algorithm is general and can be easily adapted to integrate multi-omic datasets.

Next, I present general methodology to regress subject-specific networks on a set of covariates that produces both multiplicity-adjusted hypothesis tests for which covariates affect networks and statistical measures indicating which network edges are driving these differences. Our strategy projects subject-specific empirical correlation matrices into an alternative space using a matrix logarithm transform, which ensures positive-semidefiniteness and justifies Gaussian modeling. Using a Gaussian multivariate regression framework in this space with cutting-edge sparsity priors, I regress the networks on predictors while discovering and accounting for second-order dependence across network edges which I show leads to greater efficiency and power for statistical inference. I validate our framework via extensive simulation and apply our approach to analyze functional connectivity networks of 1003 healthy young patients taken from the Human Connectome Project (HCP), demonstrating concordance be- tween results in the transformed and original space.

Our second project is limited to the consideration of strictly linear associations between covariates and network edges. Seeking to extend the framework of the previous project, I conclude by developing methodology to solve multivariate sparse generalized additive models. I jointly select between null, linear, and non-linear effects in an efficient, theoretically justified parallelizable manner while accounting for estimated sparse residual structure. I provide validation for our method via simulation, demonstrating the benefits of accounting for residual structure in the selection and estimation of linear and non-linear associations in a manner analogous to the principles of seemingly unrelated regression. Our method is applied to the aforementioned dataset from the HCP to explore potential non-linear effects between covariates and network edges.