\[PV_t-=P(D-\mid T-)=\frac{\left(1-p_{1:t}\right)Sp_{t_{m',c'}}}{\left(1-p_{1:t}\right)Sp_{t_{m',c'}}+p_{1:t}\left(1-Se_{t_{m',c'}}\right)}\] where \(p_{1:t}\) is the proportion of events satisfying the condition of Eq. 4 up to time point \(t\).
Once the entire time series data have been observed, the overall \(Se_{EVI}\) can be estimated as the fraction of the total number of occurrences for which an early warning has been issued, given that the case definition (Eq. 4 ) holds \((P (T+ \mid D+))\), divided by the total number of occurrences that the case definition holds \((P(D+))\). Similarly, the overall \(Sp_{EVI}\) is calculated as the fraction of the total number of occurrences for which an early warning was not issued given that the expected rise of cases was not observed, that is, the case definition is not true, \((P(T- \mid D- ))\) divided by the total number of occurrences that the case definition is not true \(\left(P\left(D-\right)\right)\):