Abstract
Many complex diseases (chronic disease onset, development and differentiation, self-assembly, etc.) are reminiscent of phase transitions in a dynamical system: quantitative changes accumulate largely unnoticed until a critical threshold is reached, which causes abrupt qualitative changes of the system. Understanding such nonlinear behaviors is critical to dissect the multiple genetic/environmental factors that together shape the genetic and physiological landscape underlying basic biological functions and to identify the key driving molecules. Based on stochastic differential equation (SDE) model, we theoretically derive three statistical indicators, that is, coefficient of variation (CV), transformed Pearson's correlation coefficient (TPC), and transformed probability distribution (TPD), to identify critical transitions and detect the early-warning signals of the phase transition in complex diseases. To verify the effectiveness of these early-warning indexes, we use high-throughput data for three complex diseases, including influenza caused by either H3N2 or H1N1 and acute lung injury, to extract the dynamical network biomarkers (DNBs) responsible for catastrophic transition into the disease state from predisease state. The numerical results indicate that the derived indicators provide a data-based quantitative analysis for early-warning signals for critical transitions in complex diseases or other dynamical systems.
Highlights
A sudden change of a system is a recurrent phenomenon in many complex diseases, which often occurs at a critical threshold, or the so-called “tipping point,” and can be interpreted as the fact that the system shifts abruptly from one asymptotically stable equilibrium to another one [1]
Combining the qualitative theory of fast-slow dynamical systems, probability theory, and statistical analysis, we theoretically prove that three statistical indicators, that is, coefficient of variation (CV), transformed Pearson’s correlation coefficient (TPC), and transformed probability distribution (TPD), can distinguish the early-warning signals of the critical transition in complex systems
Method for Identifying Dynamical Network Biomarkers (DNBs) for Complex Diseases Based on Real Data
Summary
A sudden change of a system is a recurrent phenomenon in many complex diseases, which often occurs at a critical threshold, or the so-called “tipping point,” and can be interpreted as the fact that the system shifts abruptly from one asymptotically stable equilibrium to another one [1]. There exists a sudden catastrophic shift during the progress of gradual health deterioration that results in a drastic transition to a disease state. A variety of empirical studies based on analysis of time-series data have suggested that some statistical signatures, such as variance, Pearson’s correlation coefficient (PCC), autocorrelation, and coefficient of variation (CV), may be used to predict the critical transition [6,7,8,9,10,11,12,13,14]. Combining the qualitative theory of fast-slow dynamical systems, probability theory, and statistical analysis, we theoretically prove that three statistical indicators, that is, coefficient of variation (CV), transformed Pearson’s correlation coefficient (TPC), and transformed probability distribution (TPD), can distinguish the early-warning signals of the critical transition in complex systems. We use real high-throughput data for three complex diseases, including influenza caused by either H3N2
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