Fig. 1

Outline for identifying the pre-disease state by using hidden Markov model. a The progression of a complex disease can be generally divided into three states, i.e., the normal state, the pre-disease state, and the disease state. Both the normal and disease states are stable with high resilience, while the pre-disease state, a critical stage, is unstable with low resilience and sensitive to the parameter changes. Thus the biological progression of diseases in both the normal and disease states are modelled as stationary Markov processes, and that in the pre-disease state is described by a time-varying Markov process. The detection of the onset of a pre-disease state is equivalent to the identification of the end point of the stationary Markov process in a normal state. b The three networks stand for the evolution of the system respectively in three states. The thickness of links stands for the correlation between each pair of nodes. It can be seen that when the system is in the pre-disease state, a few nodes form a special subnetwork among which the correlations abruptly increase, while the correlations between the subnetwork and other nodes decrease. It is worth noting that such critical phenomenon appears only in the pre-disease state. c On the basis of hidden Markov model (HMM), we propose a consistence score (C-score) to measure the dynamical change of system, that is, the C-score curve is expected to be smooth when the system is in a stationary Markov process, while the C-score drastically decrease when the system is in a time-varying Markov process. Thus, it is possible to detect the imminent critical transition by identifying the sudden change of the C-score