Testing noninferiority of response rates for regulatory filings using transformations

When comparing a new treatment to a standard, it is common to analyze with the intent of showing that the response rate of the new treatment is not markedly lower than that of the standard. This requires a definition of noninferiority (how different the response rates can be). One definition proposed for antimicrobial products is an adaptive definition that allows a larger difference in response rates when lower response rates are observed In this paper we discuss some advantages and disadvantages of this adaptive definition and seek alternative analysis methods that preserve the benefits while eliminating some of the drawbacks of the adaptive definition. One potential method is to analyze for equivalence using transformations. Analyzing for equivalence with the angular transformation or the log odds (but not the log) will preserve aspects of the adaptive, definition such as requiring a smaller difference in response rates when currently available products have higher efficacy. Using a transformation has advantages over the adaptive definition, such as allowing for power calculations using standard formulae from the literature.