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Three-way classification of medical tests
Methods of three-way classification or trichotomization of medical test results tries to replace the popular method of binary classification or dichotomization. The three classes are Positive, Uncertain (or Intermediate) and Negative. Ideally, an Uncertain or Intermediate test result covers a relative large proportion of diagnostic errors, while the Positive and Negative classification allows for a reduced proportion of diagnostic errors in comparison to two-way classification. When this is the case, this allows for a more differentiated response to the test result. A Positive test result provides a stronger indication to go forward in treatment of the disease for which is tested, when compared to a binary Positive result. Similarly, a Negative test result provides a stronger indication to exclude the presence of the disease. An Intermediate or Uncertain test result would indicate a restrained response, typically monitoring further developments of the patients complaints (watchful waiting or active surveillance).

Two-way classification
The most popular method for classification of diagnostic medical test results is two way or binary classification. The two classes are Positive (the patient has the disease for which is tested) and Negative (the patient has NOT the disease). The two classes are determined with a single cut point of the test results. When a higher test score indicates the presence of the disease, a test score equal or higher than this cut point results in a Positive classification and the test scores lower than this cut point results in a negative classification. The most used statistics for the quality of a medical tests are Sensitivity and Specificity. Sensitivity is the proportion of patients who have the disease who have received a Positive classification. Specificity is the proportion of patients who do NOT have the disease and have received a Negative classification. One of the most popular methods for determining such a cut point is the Youden statistic that indicates the highest possible sum of Sensitivity and Specificity for the test. To compare the qualities of different tests, the Receiver Operating Characteristics curve is used. This graphical method shows the trade-off between Sensitivity and Specificity of the different tests and has a sound following in the medical world since World War II.

The theory of three-way classification
When a medical test is developed for a specific disease, its qualities are evaluated with the use of two samples of patients: one sample with patients who do have the disease and the second sample of patients of which is known that they do not have the disease. The test quality is the assessed as Sensitivity: the proportion of patients who do have the disease that has received positive test results and Specificity, the proportion of patients that do not have the disease that have received a negative test result. There are also patients who have received a negative test result, while in reality they do have the disease (False Negatives) and patients who receive a positive test result, while they do not have the disease (False Positives). The false results are test errors, and a test is more accurate when the amount of these errors is smaller. An example of the two distributions of test results is shown in the next figure: True patients are patients who do have the targeted disease, and true non patients are patients in which the disease is absent. In this type of research the presence or absence of the disease is determined with the use of a gold standard.

The optimal cut-point that maximizes the sum of Sensitivity and Specificity is the point of intersection (horizontal line), which is by definition the point where the Youden Index is maximal. . This is also the point where the total sum of errors is minimized. It is easy to see that the errors are concentrated around the point of intersection, while the highest scores indicate true patients without error and the lowest scores indicate true non-patients without error. In this example both Sensitivity and Specificity of the test is .84 which means that this is a test with relatively high proportions of correct scores. Many medical tests are less accurate, some are better. The minimum proportion of errors is therefore 2 * .16 = .32. For any other choice of a cut point this sum of errors would exceed .32. In this example, if we would want to exclude all most all errors we would have to use only scores lower than 4.5 and scores higher than 6.5. In that case, our decisions would offer a large certainty: we would have only 1.2% of erroneous decisions. But we would also have a huge intermediate area, covering about 70% of all true patients and 70% of all true non-patients. The question is therefore if we can find some middle ground for an intermediate range of test scores, where we do catch the test scores that lead to decisions that are most uncertain, and ranges of test scores that would result in positive and negative decisions that are more often correct than when using solely a single cut-point. A gain in certainty is therefore a trade-off with an acceptable size of the range of uncertain test scores. When using a single cut point, there are no intermediate test scores but it is most likely that patients with a test score close to the point of intersection would receive an erroneous decision.