Likelihood ratio and score tests to test the non-inferiority (or equivalence) of the odds ratio in a crossover study with binary outcomes.

We consider the non-inferiority (or equivalence) test of the odds ratio (OR) in a crossover study with binary outcomes to evaluate the treatment effects of two drugs. To solve this problem, Lui and Chang (2011) proposed both an asymptotic method and a conditional method based on a random effects logit model. Kenward and Jones (1987) proposed a likelihood ratio test (LRTM ) based on a log linear model. These existing methods are all subject to model misspecification. In this paper, we propose a likelihood ratio test (LRT) and a score test that are independent of model specification. Monte Carlo simulation studies show that, in scenarios considered in this paper, both the LRT and the score test have higher power than the asymptotic and conditional methods for the non-inferiority test; the LRT, score, and asymptotic methods have similar power, and they all have higher power than the conditional method for the equivalence test. When data can be well described by a log linear model, the LRTM has the highest power among all the five methods (LRTM , LRT, score, asymptotic, and conditional) for both non-inferiority and equivalence tests. However, in scenarios for which a log linear model does not describe the data well, the LRTM has the lowest power for the non-inferiority test and has inflated type I error rates for the equivalence test. We provide an example from a clinical trial that illustrates our methods.