Quantifying unrecognised replication present in reports of HIV diagnoses

New diagnoses of HIV infection were reported confidentially to the Public Health Laboratory Service AIDS Centre under a national voluntary surveillance scheme. Two sets of data drawn from the national data sets were made available to us for analysis, the first in 1991 and the second in 1994, by which time the replication of reports had been reduced. The data used in the analyses consisted of the numbers of replications of the reported full date of birth in the individual records (one, two, three and so on), for each year of birth. This paper uses a nonparametric maximum likelihood estimation method for quantifying the amount of replication in the data. The estimated amount of replication was 3.37% (95% confidence interval (0.98%, 11.83%)) in the 1991 data set and 0.58% (95% confidence interval (0%, 2.64%)) in the 1994 data set.