AbstractWe consider delays that occur in the reporting of events such as cases of a reportable disease or insurance claims. Estimation of the number of events that have occurred but not yet been reported (OBNRevents) is then important. Current methods of doing this do not allow random temporal fluctuations in reporting delays, and consequently, confidence or prediction limits on OBNR events tend to be too narrow. We develop an approach that uses recent reporting data and incorporates random effects, thus leading to more reasonable and robust predictions