  In this paper, we propose considering an exact likelihood score (ELS) test
for non-inferiority comparison and we derive its test-based confidence interval
for the difference between two independent binomial proportions. The p-value
for this test is obtained by using exact binomial probabilities with the
nuisance parameter being replaced by its restricted maximum likelihood
estimate. Calculated type I errors revealed that the proposed ELS method has
important advantages for non-inferiority comparisons over popular asymptotic
methods for adequately powered confirmatory clinical trials, at 80% or 90%
statistical power. For unbalanced sample sizes of the compared treatment
groups, the type I errors for the asymptotic score method were shown to be
higher than the nominal level in a systematic pattern over a range of the true
proportions, but the ELS method did not suffer from such a problem. On average,
the true type I error of the ELS method was closer to the nominal level than
all considered methods in the empirical comparisons. Also, in rare cases, the
type I errors of the ELS test exceeded the nominal level, but only by a small
amount. In addition, the p-value and confidence interval using the ELS method
can be obtained in less than 30 seconds of computer time for most confirmatory
trials. The theoretical arguments and the attractive empirical evidence, along
with fast computation time, should make the ELS method very attractive for
consideration in statistical practice.
