Two new methods for non-inferiority testing of the ratio in matched-pair setting

Non-inferiority of one treatment to another based on ratio is a common issue in medical research. Nam and Blackwelder derived a Fieller-type statistic from constrained maximum likelihood estimation of nuisance parameters. Although it improved that of Lachenbruch and Lynch, its size still exceeds the claimed nominal level alpha for some cases. This is in accordance with Sidik who has found that the asymptotic tests are inaccurate in testing a hypothesis of a non-zero difference between marginal probabilities. In this paper, we extend Sidik’s exact tests to non-inferiority in ratio, and propose two new methods—one based on the standard <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>p</mi> </math> </EquationSource> </InlineEquation> value and the other from restricted Bayesian estimation using an approximate <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$$p$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <mi>p</mi> </math> </EquationSource> </InlineEquation> value. Our tests are both based on only one point of the two-dimension nuisance parameter space for accuracy improvement and computational purposes. The sizes and powers of our tests are considered. Simulation results suggest that our tests can control the type I error rates well with competitive powers while the Fieller-type statistic cannot for some cases be investigated. Copyright Sociedad de Estadística e Investigación Operativa 2014