Statistical diagnosis and the influence of diagnostic error

The optimal class of rules for allocating subjects, on the basis of an observable symptom profile, to sick or well states is based on the likelihood-ratio scale. This scale is estimated from a training set where the symptoms and true disease status are simultaneously measured. In the important case where true disease status is unavailable and only a "noisy" diagnosis can be performed, it is shown that exactly the same optimal class of allocation rules is obtained. This is true under very general assumptions of diagnostic error. Special cases are examined, providing insight into the dynamics of such diagnostic error. In particular, the conditions under which sensitivity, specificity, and the overall correct classification rate are underestimates of the true quantities are investigated.