ABSTRACT
This chapter elaborates the choice of the noninferiority (NI) margin as a small fraction (e�g�, 0�2) of the therapeutic effect of the active control as compared to placebo based on the mean difference for a continuous endpoint�
The hypotheses stated in Section 1�7 of Chapter 1 can be shown graphically in Figure 2�1, where the axis is the true mean response, and the treatment gets better as we move to the right and worse if we move to the left� At the boundary, we have T = S – δ� The null hypothesis is to the left of this boundary inclusively, and the alternative hypothesis is to the right of the boundary�
The International Conference on Harmonization (ICH) E9 document (1998) states that the “margin is the largest difference that can be judged as being clinically acceptable and should be smaller than differences observed in superiority trials of the active comparator�” The ICH E10 document (2001) suggests that (1) the NI margin “cannot be greater than the smallest effect size that the active drug would be reliably expected to have compared with placebo in the setting of the planned trial”; and that (2) the margin “usually will be smaller than that suggested by the smallest expected effect size of the active control because of interest in ensuring that some clinically acceptable effect size (or fraction of the control drug effect) is maintained�” Simon (2001) suggests that the NI margin δ must be no greater than the efficacy of S relative to P and will, in general, be a fraction of this quantity�
2.2 Proposed δ How do you choose δ? This is a big question in testing for NI� To claim that the test treatment is not inferior to the standard therapy, we want δ to be small relative to the effect size of the active control, that is, S – P� Mathematically,
δ should be some small ε between 0 and 1, such as 0�2 times the effect size, that is,
(S P)δ = ε − (2�1)
At first sight, such a proposal appears to be useless because the effect size is not known� However, the effect size can and should be estimated from historical data (1) directly, where the active control was compared to the placebo in placebo-controlled trials, or (2) indirectly, where the active control was compared to another active control in a noninferiority trial� If no such data exists, the active control should not be used as a control in the NI trial because it is difficult to justify the NI margin without such data� For simplicity, we consider the situation where the effect size can and should be estimated directly from historical data, where the active control was compared to the placebo in placebo-controlled trials�
In February 2004, the European Agency for the Evaluation of Medicinal Products (EMEA) Committee for Proprietary Medicinal Products (CPMP) issued points to consider on the choice of NI margin for public comments (EMEA/CPMP 2004)� It stated that “ideas such as choosing delta to be a percentage of the expected difference between active and placebo have been advocated, but this is not considered an acceptable justification for the choice�” This is inconsistent with the EMEA/CPMP concept paper (1999)— see item 10 in Section 1�4 of Chapter 1� Seldrup (2004) made the following comments: “This may be too strong� In some situations it may be the ’right’ (or only) choice meaningful to [the] statistician and clinician�” However, no revision was made in response to these comments in the final document (EMEA/CPMP 2005)�
The NI margin given by Equation 2�1 was first proposed by Ng (1993) and was motivated by regulatory considerations (see also Ng 2001)� Although such a proposal does not answer the big question because the effect size is not known, it does reduce it to two smaller questions, which can be handled a lot easier than one big one (Ng 2008):
How do you choose ε?
