The WHO Collaborating Centre for International Drug Monitoring in Uppsala, Sweden, maintains and analyses the world's largest database of reports on suspected adverse drug reaction incidents that occur after drugs are introduced on the market. As in other post-marketing drug safety data sets, the presence of duplicate records is an important data quality problem and the detection of all duplicates in the WHO drug safety database remains a formidable challenge, especially since the reports are anonymised before submitted to the database. However, to our knowledge no work has been published on methods for duplicate detection in post-marketing drug safety data. In this paper, we propose a method for probabilistic duplicate detection based on the hit-miss model for statistical record linkage described by Copas & Hilton. We present two new generalisations of the standard hit-miss model: a hit-miss mixture model for errors in numerical record fields and a new method to handle correlated record fields. We demonstrate the effectiveness of the hit-miss model for duplicate detection in the WHO drug safety database both at identifying the most likely duplicate for a given record (94.7% accuracy) and at discriminating duplicates from random matches (63% recall with 71% precision). The proposed method allows for more efficient data cleaning in post-marketing drug safety data sets, and perhaps other applications throughout the KDD community.