FastGGM: An Efficient Algorithm for the Inference of Gaussian Graphical Model in Biological Networks

Abstract\ud \ud Biological networks provide additional information for the analysis of human diseases, beyond the traditional analysis that focuses on single variables. Gaussian graphical model (GGM), a probability model that characterizes the conditional dependence structure of a set of random variables by a graph, has wide applications in the analysis of biological networks, such as inferring interaction or comparing differential networks. However, existing approaches are either not statistically rigorous or are inefficient for high-dimensional data that include tens of thousands of variables for making inference. In this study, we propose an efficient algorithm to implement the estimation of GGM and obtain p-value and confidence interval for each edge in the graph, based on a recent proposal by Ren et al., 2015. Through simulation studies, we demonstrate that the algorithm is faster by several orders of magnitude than the current implemented algorithm for Ren et al. without losing any accuracy. Then, we apply our algorithm to two real data sets: transcriptomic data from a study of childhood asthma and proteomic data from a study of Alzheimer’s disease. We estimate the global gene or protein interaction networks for the disease and healthy samples. The resulting networks reveal interesting interactions and the differential networks between cases and controls show functional relevance to the diseases. In conclusion, we provide a computationally fast algorithm to implement a statistically sound procedure for constructing Gaussian graphical model and making inference with high-dimensional biological data. The algorithm has been implemented in an R package named “FastGGM”.\ud \ud Author Summary\ud \ud Gaussian graphical model (GGM), a probability model for characterizing conditional dependence among a set of random variables, has been widely used in studying biological networks. It is important and practical to make inference with rigorous statistical properties and high efficiency under a high-dimensional setting, which is common in biological systems that usually contain tens of thousands of molecular elements, such as genes and proteins. This work proposes a novel efficient algorithm, FastGGM, to implement asymptotically normal estimation of large GGM established by Ren et al [1]. It quickly estimates the precision matrix, partial correlations, as well as p-values and confidence intervals for the graph. Simulation studies demonstrate our algorithm outperforms the current algorithm for Ren et al. and algorithms for some other estimation methods, and real data analyses further prove its efficiency in studying biological networks. In conclusion, FastGGM is a statistically sound and computationally fast algorithm for constructing GGM with high-dimensional data. An R package for implementation can be downloaded from http://www.pitt.edu/~wec47/FastGGM.html