Bayesian nowcasting during the STEC O104:H4 outbreak in Germany, 2011

Abstract

A Bayesian approach to the prediction of occurred-but-not-yet-reported events is developed for application in real-time public health surveillance. The motivation was the prediction of the daily number of hospitalizations for the haemolytic-uremic syndrome during the large May-July 2011 outbreak of Shiga toxin-producing Escherichia coli (STEC) O104:H4 in Germany. Our novel Bayesian approach addresses the count data nature of the problem using negative binomial sampling and shows that right-truncation of the reporting delay distribution under an assumption of time-homogeneity can be handled in a conjugate prior-posterior framework using the generalized Dirichlet distribution. Since, in retrospect, the true number of hospitalizations is available, proper scoring rules for count data are used to evaluate and compare the predictive quality of the procedures during the outbreak. The results show that it is important to take the count nature of the time series into account and that changes in the delay distribution occurred due to intervention measures. As a consequence, we extend the Bayesian analysis to a hierarchical model, which combines a discrete time survival regression model for the delay distribution with a penalized spline for the dynamics of the epidemic curve. Altogether, we conclude that in emerging and time-critical outbreaks, nowcasting approaches are a valuable tool to gain information about current trends.

A Bayesian Approach to Real-Time Monitoring and Forecasting of Chinese Foodborne Diseases

“…In this section, three different nowcasting procedures will be compared: the Lawless [18] frequency (LF) method with the consideration of the right-truncated nature and two Bayesian procedures, one is BNT method proposed in this paper and Bayesian nowcasting with no truncation (BNnT) method by Hohle and Heiden [20] ignoring the right truncation.…”

“…This is the delay in phase 2. References [19,20,21] used the number of patients reported in the hospital to predict the number of occurred cases. The cycle is very long from the onset to the diagnosis reported, which couldn’t predict the number of cases, or grasp the trends of the disease in a timely way.…”

“…The cycle is very long from the onset to the diagnosis reported, which couldn’t predict the number of cases, or grasp the trends of the disease in a timely way. Therefore, in view of this, our model has the following advantages: First, when the data is complete and there is hospital-confirmed report data in hand, our model uses the number of confirmed patients to predict the number of occurred cases, a procedure similar to that of [20,21]. Then, if the data is incomplete, for example, we only have the visiting data till today, we could use the number of visiting patients to predict the occurred cases, which may lead to a very small overestimation of the number of occurred cases, but least not underestimate them.…”

“…Recently, it has been regarded as a useful tool to real-time monitor the disease surveillance data [19,20], personal pro-health outdoor activities [22], and forecast the epidemics in public health settings [23]. In this paper, we develop a Bayesian nowcasting with truncation (BNT) approach to forecast the daily total number of cases in the presence of reporting delays, which can correct the current number of cases, thus to provide more accurate daily information on current epidemic trends.…”

“…Later, a robust algorithm to perform tracking procedures called “nowcasts” was used to correct for reporting delays [19]. Based on such concept, Hohle and Heiden [20] proposed a Bayesian nowcasting algorithm to deal with the short-term forecasting of the daily number of reported cases. Salmon et al [21] improved the outbreak detection algorithms by taking reporting delays into account.…”