# An ontological analysis of medical Bayesian indicators of performance

### Barton Adrien, Ethier Jean-Francois, Duvauferrier Regis, Burgun Anita

Background: Biomedical ontologies aim at providing the most exhaustive and rigorous representation of reality as described by biomedical sciences. A large part of medical reasoning deals with diagnosis and is essentially probabilistic. It would be an asset for biomedical ontologies to be able to support such a probabilistic reasoning and formalize Bayesian indicators of performance: sensitivity, specificity, positive predictive value and negative predictive value. In doing so, one has to consider that not only the positive and negative predictive values, but also sensitivity and specificity depend upon the group under consideration: this is the “spectrum effect”. Methods: The sensitivity value of an index test IT for a disease M in a group g is identified with the proportion of people in g who have M who would get a positive result to IT if the test IT was realized on them. This value can be estimated by selecting a reference test RT for M and a sample s of g, and measuring the proportion, among members of s having a positive result to RT, of those who got a positive result to IT. Similar approximation strategies hold for prevalence, specificity, PPV and NPV. Indicators of diagnostic performances and their estimations are formalized in the context of the OBO Foundry, built on the realist upper ontology Basic Formal Ontology (BFO). Results: Entities and relations from the Ontology for Biomedical investigations (OBI) and the Information Artifact Ontology (IAO) are used and complemented to represent reference tests and index tests, tests executions, tests results and the relations involving those entities, as well as the values of indicators of performance and their estimates. The computations taking as input several estimates of an indicator of performance to produce a finer estimate are also represented. The value of e.g. sensitivity estimates should be dissociated from the real sensitivity value - which involves possible, non-actual conditions, namely the result a person would get if a medical test would be performed on her. Such conditions could not be directly represented in a realist ontology, but a representation is proposed that introduces only actual entities by considering a disposition whose probability value is the real sensitivity value. A sensitivity estimate is a data item which is about such a disposition. Conclusions: This model provides theoretical basis for the representation of entities supporting Bayesian reasoning in ontologies.