Multivariate hierarchical frameworks for modeling delayed reporting in count data

In many fields and applications, count data can be subject to delayed reporting. This is where the total count, such as the number of disease cases contracted in a given week, may not be immediately available, instead arriving in parts over time. For short-term decision making, the statistical challenge lies in predicting the total count based on any observed partial counts, along with a robust quantification of uncertainty. We discuss previous approaches to modeling delayed reporting and present a multivariate hierarchical framework where the count generating process and delay mechanism are modeled simultaneously in a flexible way. This framework can also be easily adapted to allow for the presence of underreporting in the final observed count. To illustrate our approach and to compare it with existing frameworks, we present a case study of reported dengue fever cases in Rio de Janeiro. Based on both within-sample and out-of-sample posterior predictive model checking and arguments of interpretability, adaptability, and computational efficiency, we discuss the relative merits of different approaches.