Multilevel regularized regression for simultaneous taxa selection and network construction with metagenomic count data

Motivation: Identifying disease associated taxa and constructing networks for bacteria interactions are two important tasks usually studied separately. In reality, differentiation of disease associated taxa and correlation among taxa may affect each other. One genus can be differentiated because it is highly correlated with another highly differentiated one. In addition, network structures may vary under different clinical conditions. Permutation tests are commonly used to detect differences between networks in distinct phenotypes, and they are time-consuming. Results: In this manuscript, we propose a multilevel regularized regression method to simultaneously identify taxa and construct networks. We also extend the framework to allow construction of a common network and differentiated network together. An efficient algorithm with dual formulation is developed to deal with the large-scale n << m problem with a large number of taxa (m) and a small number of samples (n) efficiently. The proposed method is regularized with a general L-p (p is an element of [0, 2]) penalty and models the effects of taxa abundance differentiation and correlation jointly. We demonstrate that it can identify both true and biologically significant genera and network structures. Availability and implementation: Software MLRR in MATLAB is available at http://biostatistics.csmc.edu/mlrr/.