A more powerful test based on ratio distribution for retention noninferiority hypothesis

Rothmann et al. ( 2003 ) proposed a method for the statistical inference of fraction retention noninferiority (NI) hypothesis. A fraction retention hypothesis is defined as a ratio of the new treatment effect verse the control effect in the context of a time to event endpoint. One of the major concerns using this method in the design of an NI trial is that with a limited sample size, the power of the study is usually very low. This makes an NI trial not applicable particularly when using time to event endpoint. To improve power, Wang et al. ( 2006 ) proposed a ratio test based on asymptotic normality theory. Under a strong assumption (equal variance of the NI test statistic under null and alternative hypotheses), the sample size using Wang's test was much smaller than that using Rothmann's test. However, in practice, the assumption of equal variance is generally questionable for an NI trial design. This assumption is removed in the ratio test proposed in this article, which is derived directly from a Cauchy-like ratio distribution. In addition, using this method, the fundamental assumption used in Rothmann's test, that the observed control effect is always positive, that is, the observed hazard ratio for placebo over the control is greater than 1, is no longer necessary. Without assuming equal variance under null and alternative hypotheses, the sample size required for an NI trial can be significantly reduced if using the proposed ratio test for a fraction retention NI hypothesis.