Adjusting confidence intervals under covariate-adaptive randomization in non-inferiority and equivalence trials

Regulatory authorities guide the use of permutation tests or randomization tests so as not to decrease the Type I error rate when applying covariate-adaptive randomization in randomized clinical trials. For non-inferiority and equivalence trials, this paper derives adjusted confidence intervals using permutation and randomization methods, thus controlling the Type I error to be much closer to the pre-specified nominal significance level. We consider three variable types for the outcome of interest, namely normal, binary, and time-to-event variables for the adjusted confidence intervals. For normal variables, we show that the Type I error for the adjusted confidence interval holds the nominal significance level. However, we highlight a unique theoretical challenge for non-inferiority and equivalence trials: binary and time-to-event variables may not hold the nominal significance level when the model parameters are estimated by models that diverge from the data-generating model under the null hypothesis. To clarify these features, we present simulation results and evaluate the performance of the adjusted confidence intervals. In conclusion, this paper highlights that while normal variables can control Type I errors in non-inferiority and equivalence trials, binary and time-to-event variables cannot control Type I errors unless the model is correctly specified.