When William of Ockham meets Thomas Bayes: finding a few diagnoses among a great many symptoms

Bayes' formula is a means to estimate disease probability based on the presence of symptoms and the outcome of clinical tests. The probability helps to decide among competing diagnostic options. If, however, several diseases present with similar symptoms, they may appear equally probable, and Bayes' formula will fail as an aid to reach a diagnostic decision. The aim of this study is to show how a merger of Bayes' principle with that of Ockham can help to decide in favour of one diagnosis among multiple, seemingly equally probable diagnostic hypotheses. The hypotheses are compared to each other with respect to those tests and symptoms which they fail to explain. The unexplained tests and symptoms are used to estimate the probabilities for a set of secondary diagnoses that match each one of the primary diagnoses. The more likely a secondary diagnosis appears, the less likely its corresponding primary diagnosis will remain as the sole diagnosis to explain all the clinical findings. Even without a detailed calculation, the proposed concept of using unexplained tests and symptoms to rate competing differential diagnoses could help the clinician to select the most probable diagnosis.