Response to: Understanding the null hypothesis (H0) in non-inferiority trials

I read with great interest the article by Zhou et al. [1] aiming to test whether a lactate-decreasing resuscitation protocol (lactate strategy), compared with central venous oxygen saturation-oriented resuscitation therapy (ScvO2 strategy), would decrease mortality among septic shock patients. It is not clear why the authors performed a noninferiority trial (NIT) whereas the primary objective of the study was to establish whether the lactate strategy was “superior” to the ScvO2 strategy [1]. Even though evidence of superiority can be claimed from NITs, there are several fundamental differences between superiority trials and NITs [2]. Whereas superiority trials aim to determine whether a new intervention is superior to the best available one, NITs seek to demonstrate that the new intervention is no worse than the comparator by more than a prespecified, small amount. This amount is known as the non-inferiority margin, or delta (Δ). The null hypothesis (H0) of superiority trials asserts that there is no true difference between the interventions, and the alternative hypothesis (H1) states that there is a difference between the interventions. A type I error is the error of rejecting H0 when it is actually true. A type II error is a failure to reject H0 when in fact H1 is true. NITs, by contrast, have a H0 that the new intervention is inferior or worse than the old by more than −Δ (it is inferior). The H1 to be proven is that the new intervention is inferior to the standard intervention by less than − Δ (it is not inferior; Fig. 1) [2]. Thus, the definitions of type I and type II errors are reversed for NIT. In this study, the authors claimed the superiority of the lactate strategy over the ScvO2 strategy because the lactate group had a significantly lower mortality compared with the ScvO2 group (18.3 versus 27.9%, P = 0.033). However, the P value that is calculated in NITs is special and is called the P value for noninferiority, which differs from the P value for superiority [3]. The finding that P value of the difference in mortality was 0.033 means only that H1 is accepted and the lactate strategy is not inferior to the ScvO2 strategy. To be able to claim superiority, the 95% confidence interval of the mortality difference, which is not provided in this study, should exclude zero (Fig. 1). Moreover, the non-inferiority margin in this study was 15% [1]. However, the authors did not provide any justification as to why they chose 15 rather than 10% as used in a previous trial [4].