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 non-inferiority 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 pre-specified, 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.

Fig. 1

Different possible scenarios of the results of a non-inferiority clinical trial. ∆ is the non-inferiority margin

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 non-inferiority, 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].