Challenges and Opportunities in Single-Sample Network Modeling

1 Analysis of biological networks can provide unprecedented insights into the mechanisms underlying disease. Although many methods have been developed to estimate biological networks, these approaches typically use multiple experimental samples to estimate a single 'aggregate' network, which fails to capture population-level heterogeneity. Recently, several methods have been developed that overcome this limitation by inferring networks for individual samples, i.e. single-sample networks. However, each approach for inferring single-sample networks has been formulated differently, making it challenging to compare them. To address this issue, we re-cast the mathematics of several single-sample network methods using common variables. We then systematically explore the parameters, caveats, and underlying assumptions made by each method and examine how these differences impact single-sample network prediction. Our analyses point to a critical trade-off that occurs when trying to simultaneously predict network edges that are both shared across samples as well as edges that are specific to a given sample. For example, the mathematics of both SWEET and BONOBO includes a scale factor that drives the weights of edges in the predicted single-sample networks toward a background network. The result is that, although networks predicted by these methods tend to have the highest accuracy, this often comes at the cost of very low specificity, an important caveat since the primary goal of sample-specific network modeling is to obtain networks that are <i>specific</i> to each input sample. In contrast, SSN estimates the most specific but least accurate networks, while LIONESS straddles these domains, with an accuracy almost as high as SWEET and BONOBO and a specificity almost as high as SSN. Overall, our analyses highlight some of the broader challenges in this emerging field. However, they also point to important methodological synergies, providing an opportunity to create a common framework that can be used to improve single-sample network inference.