Resampling in network modeling of high-dimensional genomic data

Abstract: Network modeling is an effective approach for the interpretation of high-dimensional data sets for which a sparse dependence structure can be assumed. Genomic data is a challenging and important example. In genomics, network modeling aids the discovery of biological mechanistic relationships and therapeutic targets. The usefulness of methods for network modeling is improved when they produce networks that are accompanied by a reliability estimate. Furthermore, for methods to produce reliable networks they need to have a low sensitivity to occasional outlier observations. In this thesis, the problem of robust network modeling with error control in terms of the false discovery rate (FDR) of edges is studied. As a background, existing types of genomic data are described and the challenges of high-dimensional statistics and multiple hypothesis testing are explained. Methods for estimation of sparse dependency structures in single samples of genomic data are reviewed. Such methods have a regularization parameter that controls sparsity of estimates. Methods that are based on a single sample are highly sensitive to outlier observations and to the value of the regularization parameter. We introduce the method ROPE, resampling of penalized estimates, that makes robust network estimates by using many data subsamples and several levels of regularization. ROPE controls edge FDR at a specified level by modeling edge selection counts as coming from an overdispersed beta-binomial mixture distribution. Previously existing resampling based methods for network modeling are reviewed. ROPE was evaluated on simulated data and gene expression data from cancer patients. The evaluation shows that ROPE outperforms state-of-the-art methods in terms of accuracy of FDR control and robustness. Robust FDR control makes it possible to make a principled decision of how many network links to use in subsequent analysis steps.