Bayes and asymptotically pointwise optimal stopping rules for the detection of influenza epidemics

Abstract

Whereas it is customary to announce epidemics when influenza mortality exceeds the epidemic threshold, one can often detect the beginning of epidemics earlier, by solving a suitable change-point problem. We propose a hierarchical Bayesian change-point model for influenza epidemics. Prior probabilities of a change point depend on (random) factors that affect the spread of influenza. Theory of optimal stopping is used to obtain Bayes stopping rules for the detection of epidemic trends under the loss functions penalizing for delays and false alarms. The Bayes solution involves rather complicated computation of the corresponding payoff function. Alternatively, asymptotically pointwise optimal stopping rules can be computed easily and under weaker assumptions. Both methods are applied to the 1996–2001 influenza mortality data published by CDC.