Nowcasting by Bayesian Smoothing: A flexible, generalizable model for real-time epidemic tracking

Sarah F. McGough; Michael A. Johansson; Marc Lipsitch; Nicolas A. Menzies

Nowcasting, or "predicting the present," is an approach to mitigate the impact of reporting delays. With origins in the insurance claims and actuarial literature (4, 5) , nowcast models aim to estimate the number of occurred-but-not-yet-reported events (e.g. insurance claims, disease cases) at any given time based on an incomplete set of reports. In public health settings, nowcasting approaches have been explored for AIDS in the 1980s and 1990s (6) (7) (8) as a consequence of the long incubation period from HIV infection until development of AIDS. More recently, nowcasting has been applied to infectious disease outbreaks such as foodborne illness outbreaks (9, 10) . These studies draw principally on survival analysis and actuarial techniques to model the reporting delay and draw inferences based on historical patterns. A majority of studies have strictly focused on modeling the reporting delay distribution-a legacy of the actuarial techniques giving rise to many of these approaches-and generally neglect a key feature of outbreaks: that future cases are intrinsically linked to past reported cases, a fact that creates potentially strong autocorrelation in the true number of cases over short time intervals. In other words, the infectious disease transmission process provides an additional signal of the number of cases to be expected in the near future that has not been included in common methods such as the reverse-time hazard model (11, 12) and the chain ladder method (13). However, proposals to extend the latter approach to state-space models that account for temporal relationships in reporting have existed in the literature since the development of these techniques(13-15) and have been applied in at least one infectious disease context (16) . These developments are promising for disease surveillance, but it is critical to demonstrate performance in a diversity of settings as infectious disease nowcast models to date have largely focused on specific applications, not the common challenges that exist across many different diseases. In this investigation, we find that nowcasting is especially challenging when the proportion of cases reported the week they occur (delay 0) is low and reporting delays are highly variable; we know of no investigations that specifically identify models that perform well in these commonly occurring circumstances. As a result, the characteristics of robust and broadlyapplicable models are difficult to identify. Additionally, several previous models have largely focused on providing point estimates of the number of cases. Point estimates may be helpful, but quantifying the uncertainty in those estimates is even more important in the context of infectious disease outbreaks because uncertainty is intrinsic, and accounting for plausible outcomes apart from the point prediction is critical.