Prospects for detecting early warning signals in discrete event sequence data: application to epidemiological incidence data

Emma Southall; Michael J. Tildesley; Louise Dyson

A score close to 1 indicates nearly perfect sensitivity and specificity. For each EWS, 448 we assume that an increasing trend represents a disease going through a critical 449 transition. As a result a AUC score of 1 informs us that the indicator is increasing and 450 that it is possible to identify all Ext/Emg simulations when compared to the null 451 simulations by its increasing trend. Notably, in Fig. 3 coefficient of variation calculated 452 on all types of disease data (rate of incidence, incidence and prevalence) and for both For each ROC curve, we measured the AUC which is an indication of how predictive each indicator is by its ability to distinguish between elimination simulations and the null model. A score closer to 0.5 signifies the worst performance (random diagnosis). We evaluate the Kendall-tau score up to before the critical transition (t 1 = 390) and after the critical transition (t 2 = 450), which gives an indication if the EWS is increasing or decreasing. A score of 1 demonstrates that it is possible to identify all Ext simulations when compared to null simulations by its increasing trend (i.e. perfect sensitivity, true positive rate). A score of 0 means that there is zero sensitivity and instead the simulations are decreasing. indicators (AUC close to 0.5). In particular, as discussed in the previous section, 460 variance always increases prior to disease emergence ( Fig. 3(b) ). However, for disease 461 elimination (Model 1: Fig. 3 (a) and Model 2: S11 Fig) results are substantially different 462 when we compare variance calculated in rate of incidence and prevalence (orange and red 463 bars respectively) with incidence (green bars). For RoI and prevalence data types, the 464 statistical signature is an increasing variance with an AUC near 1. This is in contrast to 465 the latter where the trend is decreasing with an AUC near 0. However, the results for 466 variance (both increasing and decreasing) are highly predictive (|AU C − 0.5| ≈ 0.5).