Further, at each time point \(t\), the probability of observing a rise or drop in the future cases, given that an early warning was issued or not, can be calculated as the positive \(\left(PV_t+\right)\) and negative \(\left(PV_t-\right)\) predictive value, respectively:
\[PV_t+=P(D+\mid T+)=\frac{p_{1:t}Se_{t_{m',c'}}}{p_{1:t}Se_{t_{m',c'}}+\left(1-p_{1:t}\right)\left(1-Sp_{t_{m',c'}}\right)}\]