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Activity Number: 297
Type: Contributed
Date/Time: Tuesday, July 31, 2012 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistics in Epidemiology
Abstract - #304347
Title: Sequential Change-Point Analysis of Markov Chains with Application in Early Detection of Epidemics
Author(s): Xian Yu*+ and Michael Baron and Pankaj Choudhary
Companies: The University of Texas at Dallas and University of Arkansas at Little Rock
Address: 2801 S. Univesity Ave, Little Rock, AR, 72204, United States
Keywords: change-point detection ; Markov chains ; CUSUM ; adaptive threshold ; epidemics ; Binomial model
Abstract:

In epidemiology, an epidemic is declared when mortality rate exceeds an epidemic threshold. However, it is often possible to detect an epidemic earlier. We focus 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 i.i.d. observations are impractical.

An extension of CUSUM based on conditional log-likelihood ratio for Markov chains is proposed. 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. The properties of the new method are explored both theoretically and by simulation.

The proposed algorithms are applied to detect the epidemics trends in the 2001-2008 seasonal influenza data and the 2009 influenza A (H1N1) pandemic data(CDC). 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.


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