Sequential change-point analysis of Markov chains with application to fast detection of epidemic trends.

摘要

In epidemiology, an epidemic is usually declared when mortality due to an infectious disease exceeds an epidemic threshold during a given period of time. In this thesis, we propose sequential algorithms to detect an outbreak of an epidemic statistically, by solving an appropriate change-point problem. A popular SIR epidemic model is analyzed, according to which the population counts of (S)usceptible, (I)nfected, and (R)ecovered people form a nonstationary Markov chain.;This thesis focuses on the development of efficient sequential change-point detection tools for Markov processes, which finds a number of important and useful applications in epidemiology and other fields where the standard assumptions of independent and identically distributed observations are impractical. A recently published controversial article claimed that classical change-point detection schemes preserve their optimality even for the situation of Markov chains. We disprove this claim by the rigorous evaluation of commonly used change-point detection algorithms, derived for the case of standard assumptions, and construction of a more efficient procedure under the SIR model.;An extension of the classical change-point detection algorithm, the cumulative sum (CUSUM) procedure, is proposed, which is based on conditional log-likelihood ratio statistics. It is shown to be suboptimal under the considered Markov model.;A new adaptive threshold for the CUSUM process is developed for fast detection of change-points in sequences of dependent random variables, and large sample approximations are derived. These results allow to select the change-point detection procedure that controls the expected delay or the rate of false alarms, or that minimizes a risk function representing a balance between the two measures. Replacing a standard constant threshold by the proposed adaptive threshold is shown to reduce the mean delay substantially without a significant impact on the probability of a false alarm. Our theoretical findings are confirmed by a series of simulations.;The developed sequential algorithms are applied to the detection of epidemics and pre-epidemic trends in the 2001-2008 seasonal influenza data and the 2009 influenza A (H1N1) pandemic data released by the Centers for Disease Control and Prevention. Noticeably, the proposed procedures are sufficiently sensitive to detect trends leading to epidemics before the influenza mortality achieves the epidemic threshold and epidemics are officially declared.