Information, discrimination and divergence in cytology. I. Theoretical aspects and definitions

The results of medical tests update the probability of diagnosis (diagnosability) of a patient from the population prevalence of a disease. This paper demonstrates a method of combining several mutually dependent tests as the sum of log odds ratios, and of separating the log odd ratios of the test results and those of prevalences. Extending Kullback's discriminant function between two states to m states (m greater than or equal to 2), it is shown that the information of a test can be measured by discrimination and divergence, which are well-defined measures in information theory and test theory. The performance of diagnostic cytology can then be compared to the results of histopathologic diagnoses or to a peer-reviewed consensus without the use of arbitrarily given scores or without unfounded assumptions about underlying continuous variables. They can also provide a way to optimize the categorization (classification) of Papanicolaou smears and a means of quality control for morphologic tests. These methods can be used to evaluate the performances of cytology laboratories that use two classifications consisting of different numbers of categories (classes) and states.