Matched-pair noninferiority trials using rate ratio: a comparison of current methods and sample size refinement

In this article, we consider the establishment of noninferiority between a reference test and a new test with respect to the ratio of sensitivity and/or specificity. We first review two (one-sided) noninferiority tests, namely the logarithmic transformation test and the Fieller-type test, and their associated sample size formulae proposed for matched-pair designs when the null hypothesis is of a specified nonunity rate ratio. Different methods for implementing these one-sided noninferiority tests are reviewed. They include (1) the sample-based method, (2) the constrained least-squares estimation method, and (3) the constrained maximum likelihood estimation method. We conduct a simple empirical study to evaluate the performance of various tests/methods. In summary, statistics based on constrained maximum likelihood estimation always control the actual type I error rate much better than other statistics. Moreover, the corresponding approximate sample size formulae are valid asymptotically in the sense that the exact powers associated with the approximate sample size formulae are generally close to the prespecified power level. Methods based on constrained maximum likelihood estimation are illustrated with a real example from a clinical laboratory study.