Noninferiority testing for matched-pair ordinal data with misclassification.

New treatments that are noninferior or equivalent to-but not necessarily superior to-the reference treatment may still be beneficial to patients because they have fewer side effects, are more convenient, take less time, or cost less. The noninferiority test is widely used in medical research to provide guidance in such situation. In addition, categorical variables are frequently encountered in medical research, such as in studies involving patient-reported outcomes. In this paper, we develop a noninferiority testing procedure for correlated ordinal categorical variables based on a paired design with a latent normal distribution approach. Misclassification is frequently encountered in the collection of ordinal categorical data; therefore, we further extend the procedure to account for misclassification using information in the partially validated data. Simulation studies are conducted to investigate the accuracy of the estimates, the type I error rates, and the power of the proposed procedure. Finally, we analyze one substantive example to demonstrate the utility of the proposed approach.