Identifying critical state of complex diseases by single-sample Kullback–Leibler divergence

Abstract

Background: Developing effective strategies for signaling the pre-disease state of complex diseases, a state with high susceptibility before the disease onset or deterioration, is urgently needed because such state usually followed by a catastrophic transition into a worse stage of disease. However, it is a challenging task to identify such pre-disease state or tipping point in clinics, where only one single sample is available and thus results in the failure of most statistic approaches. Methods: In this study, we presented a single-sample-based computational method to detect the early-warning signal of critical transition during the progression of complex diseases. Specifically, given a set of reference samples which were regarded as background, a novel index called single-sample Kullback–Leibler divergence (sKLD), was proposed to explore and quantify the disturbance on the background caused by a case sample. The pre-disease state is then signaled by the significant change of sKLD. Results: The novel algorithm was developed and applied to both numerical simulation and real datasets, including lung squamous cell carcinoma, lung adenocarcinoma, stomach adenocarcinoma, thyroid carcinoma, colon adenocarcinoma, and acute lung injury. The successful identification of pre-disease states and the corresponding dynamical network biomarkers for all six datasets validated the effectiveness and accuracy of our method. Conclusions: The proposed method effectively explores and quantifies the disturbance on the background caused by a case sample, and thus characterizes the criticality of a biological system. Our method not only identifies the critical state or tipping point at a single sample level, but also provides the sKLD-signaling markers for further practical application. It is therefore of great potential in personalized pre-disease diagnosis.