  Regulatory authorities guide the use of permutation tests or randomization
tests so as not to increase 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.
