A Hierarchical Framework for Correcting Under-Reporting in Count Data

Accurate and timely data collection on infectious disease incidence is vital for monitoring as well as for decision making such as taking preventative action. Unfortunately, many such data sets are observational with a the data collection mechanism that is flawed, resulting in counts of disease incidence that are under-reported (censored). Here we explore a Bayesian hierarchical framework aimed at correcting the under-reporting, using supplementary information either in the form of covariates or informative priors or even a fully reported sub-sample of data. We investigate the sensitivity of the framework to these various sources of information, as well as other subjective choices such as which covariates to use to inform under-reporting. We illustrate by using the model to correct under-reported tuberculosis incidence data in Brazil.