LAUSR

Noninferiority trials are increasingly popular in surgical literature. They aim to demonstrate that a new treatment is no worse than an existing treatment but may have added benefits. Their design is, in many ways, counterintuitive and prone to bias. In this article, we will highlight the design features of noninferiority trials by contrasting them to other studies. We will then explore the biases inherent in their design. A key to understanding noninferiority trials is that their null hypothesis is structured differently to other study designs. In most comparative studies, the null hypothesis is that there is no difference between the intervention and control. The purpose of statistical analysis is to search for evidence against the null hypothesis. The strength of this evidence, represented by the P-value, dictates whether we can accept or reject the null hypothesis. A low P-value provides evidence against the null hypothesis whereas a high P-value fails to do so. In most two-sided comparative studies, the result can show either a difference between intervention and control or no difference. If a difference is found, its size and direction indicate whether the intervention is better or worse than control. One-sided studies, in contrast, are more restrictive. We will commence the discussion with superiority trials, which can be twosided, but for the purposes of this explanation, we will restrict our definition of superiority trials to those which are one-sided. In the case of a one-sided superiority trial, the aim is to investigate whether an intervention is superior to control by a specified margin (superiority margin). The null hypothesis is that the intervention is NOT SUPERIOR to control. Not-superior in this case includes equivalence and inferiority (Fig. 1). A two-sided study, on the other hand, would be able to differentiate between equivalence and inferiority. A one-sided superiority trial can only analyse if an intervention is superior or not-superior to control. To continue this line of reasoning we feel it is helpful to conceptualize the opposite of a one-sided superiority study, which would be an inferiority study (never performed). This hypothetical one-sided study would investigate whether an intervention is inferior to control. The null hypothesis is that the intervention is NOT INFERIOR to control. Not-inferior includes equivalence and superiority (Fig. 2). In a noninferiority trial however, there is an important change to the structure of the null hypothesis. The null hypothesis here is that the intervention is INFERIOR to control. Thus, the null hypothesis of a noninferiority trial does not include equivalence, in contrast to the null hypotheses of superiority and inferiority trials where equivalence is included (Fig. 3). If there is evidence against the null hypothesis of a noninferiority trial, then the intervention is NONINFERIOR to control which could either mean the intervention is equivalent or superior to control. A common misconception with a noninferiority trial is that, if the result is not significant (P > 0.05), the intervention is equivalent to control; this is not true. In fact, if there is no evidence against the null hypothesis, the intervention in a noninferiority trial must be inferior to control (Fig. 4). It is important to understand the biases inherent in a noninferiority study design. Failure to reject a null hypothesis when there is a real difference between intervention and control is a Type 2 error. When the difference between treatment groups is small, a large number of patients is required in each group to demonstrate this difference. This is true for any study where the null hypothesis includes equivalence (twosided study, superiority study, inferiority study). In a small noninferiority study where the intervention is truly inferior to control, it may be difficult to demonstrate this difference and equivalence/ superiority is more likely to be found; a false rejection of the null hypothesis. Thus, in small noninferiority studies, an intervention may be found to be equivalent to control when it is, in fact, inferior.