In clinical trials it is often desirable to test for superiority and non-inferiority simultaneously. The hypotheses are formulated to test whether a new treatment is superior to a control on at least one endpoint, and non-inferior on all endpoints. The simulation studies of \citet{logan2008superiority} shows that most of the current testing methods are very conservative, especially when the non-inferiority margins are close to zero. In this paper we propose a method for the superiority and non-inferiority problem based on the lower one-side confidence intervals. Theoretically, we prove that our testing method can control the type I error at a pre-specified level $\alpha$, such as 0.05, 0.025 or 0.01, which is also demonstrated in our simulation study. Meanwhile, the simulation study show that our method has a higher power than several alternative methods when the non-inferiority margins are close to zero or when both endpoints have a positive value, hence, the proposed method successfully avoid the deficiency of being conservative and has a higher power. A real example about the efficacy and toxicity of an inhaled drug for asthma compared to placebo is used to illustrate the proposed method.

翻译：在临床试验中，通常需要同时检验优效性和非劣效性。所构建的假设用于检验新治疗在至少一个终点上是否优于对照，并在所有终点上均非劣效。\citet{logan2008superiority}的模拟研究表明，现有的大多数检验方法过于保守，尤其是当非劣效界值接近零时。本文提出一种基于单侧置信下界的优效性和非劣效性问题检验方法。理论上，我们证明了该检验方法能够将第一类错误率控制在预设水平$\alpha$（如0.05、0.025或0.01），这一结论在模拟研究中也得到验证。同时，模拟研究表明，当非劣效界值接近零或两个终点均呈现正值时，本方法的检验效能高于若干替代方法，因此有效避免了保守性缺陷且具有更高的检验效能。通过一个关于吸入型哮喘药物与安慰剂对比的有效性和毒性的实际案例，对所提方法进行了说明。