Nowcasting the Number of New Symptomatic Cases During Infectious Disease Outbreaks Using Constrained P-spline Smoothing.

During an infectious disease outbreak, timely information on the number of new symptomatic cases is crucial. However, the reporting of new cases is usually subject to delay due to the incubation period, time to seek care, and diagnosis. This results in a downward bias in the numbers of new cases by the times of symptoms onset towards the current day. The real-time assessment of the current situation while correcting for underreporting is called nowcasting. We present a nowcasting method based on bivariate P-spline smoothing of the number of reported cases by time of symptoms onset and delay. Our objective is to predict the number of symptomatic-but-not-yet-reported cases and combine these with the already reported symptomatic cases into a nowcast. We assume the underlying two-dimensional reporting intensity surface to be smooth. We include prior information on the reporting process as additional constraints: the smooth surface is unimodal in the reporting delay dimension, is (almost) zero at a predefined maximum delay and has a prescribed shape at the beginning of the outbreak. Parameter estimation is done efficiently by penalized iterative weighted least squares. We illustrate our method on a large measles outbreak in the Netherlands. We show that even with very limited information the method is able to accurately predict the number of symptomatic-but-not-yet-reported cases. This results in substantially improved monitoring of new symptomatic cases in real time.