Reporting delay occurs frequently in the case surveillance of a disease such as HIV/AIDS. To evaluate the current trend of incidence, it is important to consider incidence estimates adjusted for reporting delays and the uncertainty associated with this adjustment. For a surveillance system in which cases are reported monthly, there is no straightforward method for constructing the confidence interval estimators for annual incidence or incidence for a period longer than a month. This is because the monthly incidence estimators are not independent and the correlations among them are not available. Furthermore, to estimate the incidence for a specific risk, or exposure, group (e.g. men who have sex with men), we also have to consider the uncertainty associated with the counts from cases reported without an identified risk. Cases with no reported risk are assigned proportionally to each risk group on the basis of experience with cases reported initially with no reported risk but reported later with an identified risk. In this article, we introduce a method for combining the uncertainties associated with both reporting delay and risk redistribution. An estimator for the covariance between two incidence estimators is also provided so that we can make pairwise comparisons and discover any significant changes in incidence over time. Results are applied to evaluating the current trends in AIDS incidence among men who have sex with men in the United States.
Published in 2004 by John Wiley & Sons, Ltd.