Applying the principle of logical elimination to probabilistic diagnosis

A probability theorem is described which identifies the factors to be considered when applying the principle of logical elimination to probabilistic diagnosis. The proof is based only on the multiplication, addition and universal bound axioms of probability. When new tests are being designed from knowledge of disease mechanisms, criteria based on the theorem can be used to assess their suitability for interpretation in a logical manner. A simple convention is adopted to allow probabilities to be substantiated in terms of observed frequencies.