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

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

Figs. 1-2 show weekly dengue and ILI nowcasts for NobBS and the benchmark approach over multiple seasons for both diseases. Table 1 summarizes the point and probability-based accuracy metrics for each, where higher accuracy is indicated by higher average scores, lower MAE, RMSE, and rRMSE, and lower distance from 0.95 for the 95% PI coverage. Because the NobBS model accounts for both under-reporting and the autocorrelated progression of transmission across successive weeks, it makes predictions even in weeks when there are no cases reported for the week. Conversely, the benchmark model does not make nowcasts for weeks in which there are no initial case reports (common in the dengue Puerto Rico data), hence the nowcasts in Figs. 1C and 2C appear as discontinuous lines. To compare models despite these differences, we report accuracy metrics between NobBS and the benchmark approach for both (1) the full time series of the data and (2) weeks when at least one case was reported in the first week, i.e. the subset of weeks for which both models could make predictions (Table 1) . We also computed error metrics for the benchmark model for the full time series by assigning point estimates of 0 cases for nowcasts in weeks without predictions. accuracy, as measured by the log score and the prediction error, are compared to (C) nowcasts by the benchmark approach with (D) corresponding log scores and prediction errors. For nowcasting, the number of newly-reported cases each week (blue line) are the only data available in real-time for that week, and help inform the estimate of the total number of cases that will be eventually reported (red line), shown with 95% prediction intervals (pink bands). The true number of cases eventually reported (black line) is known only in hindsight and is the nowcast target. Historical information on reporting is available within a 104-week moving window (grey shade) and used to make nowcasts. The log score (brown line) and the difference between the true and mean estimated number of cases (grey line) are shown as a function of time.