Three statistical tests for detecting overcounting of individuals in serological test data

In this paper we consider the amount of undetected replication in HIV infection diagnoses as reported to the Public Health Laboratory Service AIDS Centre, Colindale, London. These diagnoses are usually reported with the date of birth of the individual but no names held on the database. The PHLS cannot always tell whether two reports with the same date of birth correspond to the same individual. The number of replications of date of birth recorded in sixteen birth years was provided for investigation. This paper examines statistical methods for deciding whether there is a greater amount of replication of birthdates in the sample than expected by chance alone. Three methods are outlined. The first uses χ2‐tests to compare the observed and expected number of i‐tuples. The second uses a partial ranking scheme for the possible values of the replication vector and the third uses a test based on the number of pairs in a sample. Using a 5 % significance level, these tests reveal that, respectively, five out of the last eleven, one out of the first five and five out of the total sixteen birth years show evidence of more replication than expected by chance alone. © 1998 John Wiley & Sons, Ltd.