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

Abstract

Achieving accurate, real-time estimates of disease activity is challenged by delays in case reporting. "Nowcast" approaches attempt to estimate the complete case counts for a given reporting date, using a time series of case reports that is known to be incomplete due to reporting delays. Modeling the reporting delay distribution is a common feature of nowcast approaches. However, many nowcast approaches ignore a crucial feature of infectious disease transmission-that future cases are intrinsically linked to past reported cases-and are optimized to one or two applications, which may limit generalizability. Here, we present a Bayesian approach, NobBS (Nowcasting by Bayesian Smoothing) capable of producing smooth and accurate nowcasts in multiple disease settings. We test NobBS on dengue in Puerto Rico and influenza-like illness (ILI) in the United States to examine performance and robustness across settings exhibiting a range of common reporting delay characteristics (from stable to time-varying), and compare this approach with a published nowcasting software package while investigating the features of each approach that contribute to good or poor performance. We show that introducing a temporal relationship between cases considerably improves performance when the reporting delay distribution is time-varying, and we identify trade-offs in the role of moving windows to accurately capture changes in the delay. We present software implementing this new approach (R package "NobBS") for widespread application and provide practical guidance on implementation.

Fig 1. Weekly dengue fever nowcasts for December 23, 1991 through November 29, 2010 using a 2-year moving window.

(A) Weekly NobBS nowcasts along with (B) point estimate and uncertainty accuracy, as measured by the score and the prediction error, are compared to (C) weekly nowcasts by the HH approach with (D) corresponding 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 score (brown line) and the difference between the true and mean estimated number of cases (grey line) are shown as a function of time.

Fig 2. Weekly ILI nowcasts for June 30, 2014 through September 25, 2017 using a 6-month moving window.

(A) Weekly NobBS nowcasts along with (B) point estimate and uncertainty accuracy, as measured by the score and the prediction error, are compared to (C) weekly nowcasts by the HH approach with (D) corresponding 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). For the HH approach, the 95% prediction intervals are very narrow and are thus difficult to see. 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 27-week moving window (grey shade) and used to make nowcasts. The score (brown line) and the difference between the true and mean estimated number of cases (grey line) are shown as a function of time.