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

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

We developed a Bayesian approach to nowcast total case numbers using incomplete, timestamped reported case data based on an estimated delay distribution, intrinsic autocorrelation from the transmission process, and historical case data. Generally, the approach learns from historical information on cases reported at multiple delays (e.g. no delay, 1-week delay, 2-week delay, etc.) from the week of case onset to estimate the reporting delay probability at each delay and the relationship between case counts from week-to-week, and uses this relationship to predict the number of not-yet-reported cases in the present. We tested this approach, NobBS, using two different infectious disease surveillance data sources: dengue surveillance in Puerto Rico, and national notifications of influenza-like illness (ILI) in the United States. Using all of the available data on case reporting delays up to the point of prediction, weekly dengue nowcasts were estimated for the time period December 23, 1991 through November 29, 2010 (989 weeks), and weekly ILI nowcasts were produced over the period June 30, 2014 through September 25, 2017 (170 weeks). For comparison, we generated weekly nowcasts over the same periods using an existing Bayesian approach, here referred to as the benchmark approach (9). To leverage a large amount of historical data to fit the nowcast model while also having a large window over which to assess nowcasts, we used a 104-week (approximately 2-y) moving window dengue and a 27-week (approximately 6-mo) moving window for ILI. Our primary outcome metric to assess nowcast performance was the logarithmic score, a proper score that evaluates the probability assigned to the observed outcome rather than error associated with a point prediction. For purposes of discussion, we reported the exponentiated form of the mean logarithmic score (the geometric mean of the assigned probabilities) to provide a metric on the scale of 0 (no certainty of the outcome) to 1 (complete certainty of the outcome). In addition, we estimated other metrics describing the performance of point estimates (mean absolute error (MAE), root mean square error (RMSE), and relative root mean square error (rRMSE)) and the 95% prediction interval (PI) coverage, and of these, focus on comparing the rRMSE and 95% PI coverage across approaches.