Unconditional exact tests for equivalence or noninferiority for paired binary endpoints

Problems of establishing equivalence or noninferiority between two medical diagnostic procedures involve comparisons of the response rates between cor related proportions. When the sample size is small the asymptotic tests may not be reliable. This article proposes an unconditional exact test procedu re to assess equivalence or noninferiority. Two statistics. a sample-based test statistic and a restricted maximum likelihood estimation (RMLE)-based test statistic, to define the rejection region of the exact test are consid ered. We show the p-value of the proposed unconditional exact tests can be attained at the boundary point of the null hypothesis. Assessment of equiva lence is often based on a comparison of the confidence limits with the equi valence limits. We also derive the unconditional exact confidence intervals on the difference of the two proportion means for the two test statistics. A typical data set of comparing two diagnostic procedures is analyzed usin g the proposed unconditional exact and asymptotic methods. The p-value from the unconditional exact tests is generally larger than the p-value from ti le asymptotic tests. In other words, an exact confidence interval is genera lly wider than the confidence interval obtained from an asymptotic test.