Statistical analysis of noninferiority trials with a rate ratio in small-sample matched-pair designs

Testing of noninferiority has become increasingly important in modern medicine as a means of comparing a new test procedure to a currently available test procedure. Asymptotic methods have recently been developed for analyzing noninferiority trials using rate ratios under the matched-pair design. In small samples, however, the performance of these asymptotic methods may not be reliable, and they are not recommended. In this article, we investigate alternative methods that are desirable for assessing noninferiority trials, using the rate ratio measure under small-sample matched-pair designs. In particular, we propose an exact and an approximate exact unconditional test, along with the corresponding confidence intervals based on the score statistic. The exact unconditional method guarantees the type I error rate will not exceed the nominal level. It is recommended for when strict control of type I error (protection against any inflated risk of accepting inferior treatments) is required. However, the exact method tends to be overly conservative (thus, less powerful) and computationally demanding. Via empirical studies, we demonstrate that the approximate exact score method, which is computationally simple to implement, controls the type I error rate reasonably well and has high power for hypothesis testing. On balance, the approximate exact method offers a very good alternative for analyzing correlated binary data from matched-pair designs with small sample sizes. We illustrate these methods using two real examples taken from a crossover study of soft lenses and a Pneumocystis carinii pneumonia study. We contrast the methods with a hypothetical example.