sPGGM: a sample-perturbed Gaussian graphical model for identifying pre-disease stages and signaling molecules of disease progression.

Complex disease progression typically involves sudden and non-linear transitions accompanied by devastating effects. Uncovering such critical states or pre-disease stages and discovering dynamic network biomarkers (signaling molecules) is vital for both comprehending disease progression and preventing or delaying disease deterioration. However, the detection of critical points using high-dimensional limited sample data or single-cell data proves notably challenging, as traditional statistical approaches often fail to deliver accurate results. In this study, based on optimal transport theory and Gaussian graphical models, we present an innovative computational framework, the sample-perturbed Gaussian graphical model (sPGGM), designed to analyze disease progression and identify pre-disease stages at the specific sample/cell level. Specifically, by employing population-level optimal transport and Gaussian graphical models, the proposed sPGGM effectively characterizes dynamic differences between the baseline distribution and the perturbed distribution relative to the specific case sample, thus enabling the identification of pre-disease stages and the discovery of signaling molecules during disease progression. The reliability and effectiveness of our method is demonstrated by conducting a simulated dataset and evaluating various data types, including four single-cell datasets, influenza infection data, and six distinct bulk tumour datasets. In comparison with existing single-sample methods, our proposed method exhibits improved capability in pinpointing critical point or pre-disease stages. Moreover, the effectiveness of computational results is highlighted through the analysis of the functional roles of signaling molecules.