The Logical Description of a Disease Class as a Boolean Function with Special Reference to the Irritable Bowel Syndrome

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Abstract
Although some disease classes can be defined by a single defining characteristic, in terms of traditional logic, one that is both necessary and sufficient, other disease classes, such as the so-called irritable bowel syndrome (IBS), have only a set of symptoms, signs, etc., which are said to characterize it in some undefined way. This characterization might be made definite by using simple Boolean algebra to give a logical description of the disease class. This method can only be used if the individual doctor can be shown to be consistent in his assignment of a set of data to the disease class and also if his assignment agrees independently with that of another doctor. To test such consistency and concordance, 100 case records were collected of supposed IBS and not-IBS; 20 of these were replicated to test consistency, and the total of 120 records was examined by 5 consultants independently, who assigned them either to an IBS or a not-IBS class. From the 1500 pair-wise comparisons, analysis revealed that the disagreement in assignment between doctors was only slightly greater than the disagreement within doctors, suggesting that the group of doctors acted as if there were an implicit description of IBS with which each of them broadly agreed. This implicit description, if made explicit, could form a basis for diagnosis by logical implication.

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