Statistical inference for equivalence trials with ordinal responses: A latent normal distribution approach

Testing of equivalence/non-inferiority has become an essential component in modern drug and treatment assessment. Before a newly developed treatment is introduced and applied to its target population, it is necessary to compare it to an existing (reference/standard) treatment. Unlike the traditional trial of testing the equality between two treatments, an equivalence trial, for instance, attempts to demonstrate that the responses to two treatments differ by an amount which is clinically insignificant. In many applications, the outcome measures of interest are usually recorded in ordinal scale (e.g., very good; good; moderate; poor). This paper presents a simple approach to the problem of equivalence testing in the presence of ordered categorical data. The proposed methodology operates on the assumption that the observed ordinal variable is governed by an underlying normally distributed trait. The new approach can be readily adopted for (i) commonly used equivalence limits such as difference and the ratio of treatment means and (ii) both one-sided non-inferiority and two-sided equivalence trials. We illustrate our methodology with two medical examples and demonstrate how test results and confidence interval estimates can be obtained from a freely available computer program.