Testing Non-inferiority (and Equivalence) Between Two Diagnostic Procedures In Paired-sample Ordinal Data

Before adopting a new diagnostic procedure, which is more convenient and less expensive than the standard existing procedure, it is essentially important to assess whether the diagnostic accuracy of the new prodecure is non-inferior (or equivalent) to that of the standard procedure.Recently, a few recent disussions on testing non-inferior or equivalence between two diagnostic test procedures for dichotomous data appear elsewhere. However, all these papers focused discussion on the situlations in which the underlying test responses were binary or had a well-justified cut-off point to designate the responses as positive or negative. When the test responses are on an ordinal scale, such as in the example of comparing the diagnostic accuracy of using the digitized film with that of using the plain flim, all the methods discussed previously are not applicable.In this paper, we propose two definitions of non-inferiority (and equivalence). On the basis of large sample theory, we develop two simple test procedures for detecting non-inferiority. We further conduct Monte Carle simulation to evaluate the finite sample performance of these test procedures. We note that the proposed asymptotic test procedures can perform well in most of situations.Finally, we note that the extension of these results to accomodate the case of detecting (two-sides) equivalence is simply straightforward.