Change-Point Detection in Binomial Thinning Processes, with Applications in Epidemiology

Abstract

Most of the classical change-point detection schemes are designed for the sequences of independent and identically distributed (i.i.d.) random variables. In this article, motivated by the outbreak of 2009 H1N1 pandemic influenza, we develop change-point detection procedures for the susceptible–infected–recovered (SIR) epidemic model, where a change-point in the infection rate parameter signifies either the beginning or the end of an epidemic trend.

The considered model falls into a general class of binomial thinning processes, which is a Markov chain. The cumulative sum (CUSUM) change-point detection procedure is developed for this class, and its performance is evaluated. Apparently, the CUSUM stopping rule is no longer optimal for this non-i.i.d. case. It can be improved by introducing a non constant adaptive threshold. The resulting modified scheme attains a shorter mean delay and at the same time a longer expected time of a false alarm, given that a false alarm eventually occurs.

Proposed detection procedures are applied to the 2001–2012 influenza data published by the Centers for Disease Control and Prevention.

Keywords:

• Adaptive threshold
• Change-point detection
• CUSUM
• Markov chain
• SIR
• Thinning process

Subject Classification:

• 62L10
• 62L15
• 62M05
• 92D30
• 94C12

ACKNOWLEDGMENTS

The authors are thankful to the Editor and the Associate Editor of Sequential Analysis for their helpful comments. Research of M. Baron was funded by the National Science Foundation and the National Security Agency. This support is greatly appreciated.

Notes

Recommended by Ivan Chang