Reporting delay: a review with a simulation study and application to Spanish AIDS data

To correct for the effect of reporting delay on incidence data relating to AIDS, three methods of estimation have been analysed: Poisson log-linear; log-linear logistic mixed regression (log-logit), and truncation. The first two methods transform the data in a contingency table. The difference between them is the hypothesis of delay stationarity, which is only assumed by the former. A correction is proposed for the first method to improve its asymptotic properties. The truncation method is based on the product-limit estimator. A simulation study was carried out to examine the behaviour (means, variances and mean squared errors) of the three methods. All were applied to data from the National Commission on AIDS (Spain), showing an improvement in reporting efficiency.