Modelling reporting delays for outbreak detection in infectious disease data

The delay that necessarily occurs between the emergence of symptoms and the identification of the cause of those symptoms affects the timeliness of detection of emerging outbreaks of infectious diseases, and hence the ability to take preventive action. We study the delays that are associated with the collection of laboratory surveillance data in England, Wales and Northern Ireland, using 12 infections of contrasting characteristics. We use a continuous time spline-based model for the hazard of the delay distribution, along with an associated proportional hazards model. The delay distributions are found to have extremely long tails, the hazard at longer delays being roughly constant, suggestive of a memoryless process, though some laboratories appear to stop reporting after a certain delay. The hazards are found typically to vary strongly with calendar time, and to a lesser extent with season and recent organism frequency. In consequence, the delay distributions cannot be assumed to be stationary. These findings will inform the development of outbreak detection algorithms that take account of reporting delays.