A partial ranking method for identifying repeated inclusion of individuals in anonymized HIV infection reports

Diagnoses of HIV infection are reported to the Public Health Laboratory Service (PHLS) AIDS Centre under a voluntary surveillance scheme. Names are not held in the data set, but the date of birth of the individual concerned is usually available. This paper describes a statistical method for identifying whether there are likely to be individuals repeatedly represented in the resulting data set, which is considered by birth year. A partial ordering method is used that is especially useful for years where the number of birth years in the sample is too small for chi2 tests to be used. At the 5% level, one of the five birth years tested in the data supplied to us by the PHLS shows evidence of more replication than would be expected from independent random sampling from the population. The results are compared with an alternative maximum-likelihood-based test that reaches the same conclusions. Maximum likelihood methods are further used to estimate the percentage of overcounting of individuals in the sample at 2.7%.