Enter the reverend: introduction to and application of Bayes' theorem in clinical ophthalmology

Abstract

Background: Ophthalmic practice utilizes numerous diagnostic tests, some of which are used to screen for disease. Interpretation of test results and many clinical management issues are actually problems in inverse probability that can be solved using Bayes' theorem.

Design: Use two-by-two tables to understand Bayes' theorem and apply it to clinical examples.

Samples: Specific examples of the utility of Bayes' theorem in diagnosis and management.

Methods: Two-by-two tables are used to introduce concepts and understand the theorem. The application in interpretation of diagnostic tests is explained. Clinical examples demonstrate its potential use in making management decisions.

Main outcome measure: Positive predictive value and conditional probability.

Results: The theorem demonstrates the futility of testing when prior probability of disease is low. Application to untreated ocular hypertension demonstrates that the estimate of glaucomatous optic neuropathy is similar to that obtained from the Ocular Hypertension Treatment Study. Similar calculations are used to predict the risk of acute angle closure in a primary angle closure suspect, the risk of pupillary block in a diabetic undergoing cataract surgery, and the probability that an observed decrease in intraocular pressure is due to the medication that has been started. The examples demonstrate how data required for management can at times be easily obtained from available information.

Conclusions: Knowledge of Bayes' theorem helps in interpreting test results and supports the clinical teaching that testing for conditions with a low prevalence has a poor predictive value. In some clinical situations Bayes' theorem can be used to calculate vital data required for patient management.