Gaussian copula correlation network analysis of mixed-type data using a semi-parametric pairwise likelihood with a multi-omics application

Reconstructing gene regulatory networks from large-scale heterogeneous data is a key challenge in biology. In multi-omics data analysis, networks based on pairwise statistical association measures remain popular, as they are easy to build and understand. In the presence of mixed-type (discrete and continuous) data, however, the choice of good association measures remains an important issue. It is proposed a novel approach based on the Gaussian copula, the parameters of which represent the links of the network. Novel properties of the model are obtained to guide the interpretation of the network. To estimate the copula parameters, a semiparametric pairwise likelihood for mixed data was calculated. An extensive simulation study showed that the proposed estimation procedure was able to accurately estimate the copula correlation matrix. The proposed methodology was also applied to a real ICGC dataset on breast cancer, and is implemented in a freely available R package heterocop.