More powerful exact noninferiority and equivalence tests based on binary matched pairs

Assessing the therapeutic noninferiority or equivalence of one medical treatment compared to another is often based on the difference of response rates from a matched binary pairs design. This paper develops new exact unconditional tests for noninferiority and equivalence that are more powerful than available alternatives. There are three new elements presented in this paper. First we introduce the LR statistic as an alternative to the previously proposed score statistic of Nam (1997). Second, we eliminate the nuisance parameter by estimation followed by maximization as an alternative to the partial maximization of Berger and Boos (1994) or traditional full maximization. Third, for testing equivalence it is standard to combine two one-sided tests (TOST). We point out that even if the one-sided tests are exact and efficient, the TOST will be conservative and requires a further adjustment to remove this conservatism. Based on an extensive numerical study, we recommend tests based on the score statistic, the nuisance parameter being controlled by estimation followed by maximization.