Logical necessity and sufficiency in medicine

Abstract

Methods from many branches of mathematics are used in the analysis of data from medical sources. Of the many techniques used, logical methods have been relatively neglected. It is the purpose of this report to explain one logical relationship and to demonstrate some ways in which it might be useful. The logical relationship of implication is defined, and used to show what is meant by necessary, sufficient, and necessary and sufficient conditions. It is shown that pathogonomonic features are sufficient conditions for the diseases or states they are associated with. Koch's postulates are demonstrated to be a set of necessary and sufficient conditions. An example concerning the features of pulmonary involvement in scleroderma is used to illustrate, how in practice, necessary and/or sufficient conditions are found. The distinction between logical and causal relationships is made using the information from this example. It is pointed out how these conditions can be used to define two properties of information collecting, which are named (a) redundancy and (b) comprehensiveness. Finally, it is shown how these conditions can be used to select tests for screening, selecting, or identifying diseases.