Anticipating epidemic transitions with imperfect data

Epidemic transitions are an important feature of infectious disease systems. As the transmissibility of a pathogen increases, the dynamics of disease spread shifts from limited stuttering chains of transmission to potentially large scale outbreaks. One proposed method to anticipate this transition are early-warning signals (EWS), summary statistics which undergo characteristic changes as the transition is approached. Although theoretically predicted, their mathematical basis does not take into account the nature of epidemiological data, which are typically aggregated into periodic case reports and subject to reporting error. The viability of EWS for epidemic transitions therefore remains uncertain. Here we demonstrate that most EWS can predict emergence even when calculated from imperfect data. We quantify performance using the area under the curve (AUC) statistic, a measure of how well an EWS distinguishes between numerical simulations of an emerging disease and one which is stationary. Values of the AUC statistic are compared across a range of different reporting scenarios. We find that different EWS respond to imperfect data differently. The mean, variance and first differenced variance all perform well unless reporting error is highly overdispersed. The autocorrelation, autocovariance and decay time perform well provided that the aggregation period of the data is larger than the serial interval and reporting error is not highly overdispersed. The coefficient of variation, skewness and kurtosis are found to be unreliable indicators of emergence. Overall, we find that seven of ten EWS considered perform well for most realistic reporting scenarios. We conclude that imperfect epidemiological data is not a barrier to using EWS for many potentially emerging diseases.Author summary: Anticipating disease emergence is a challenging problem, however the public health ramifications are clear. A proposed tool to help meet this challenge are early-warning signals (EWS), summary statistics which undergo characteristic changes before dynamical transitions. While previous theoretical studies are promising, and find that epidemic transitions are preceded by detectable trends in EWS, they do not consider the effects of imperfect data. To address this, we developed a simulation study which assesses how case aggregation and reporting error impact on 10 different EWS’s performance. Case report data were simulated by combining a stochastic SIR transmission model with a model of reporting error. Temporal trends in an EWS were used as a method of distinguishing between an emerging disease (R0 approaching 1) and a stationary disease (constant R0). We investigated the robustness of EWS to reporting process parameters, namely the aggregation period, reporting probability and overdispersion of reporting error. Seven of ten EWS perform well for realistic reporting scenarios, and are strong candidates for incorporation in disease emergence monitoring systems.