Non-inferiority

Kullberg BJ, Sobel JD, Ruhnke M, et al. Voriconazole versus a regimen of amphotericin B followed by fluconazole for candidaemia in non-neutropenic patients a randomised non-inferiority trial. Lancet 2005 366 1435-1442. 

There are three possible specific objectives for comparator trials to show superiority, equivalence or non-inferiority of the new active substance. Each is governed by statistical and regulatory guidelines. - 2... 

Non-inferiority trials are more common than equivalence trials in Phase III drug development. In these, the objective is to show that a new treatment is no less effective than existing treatment. It... 

Fig. 6.1 Relationship between significance tests and confidence intervals for the comparison between a new treatment and control. The treatment differences A and B are in favour of the new treatment but superiority is shown only in A. in B, the outcome may meet criteria for equivalence or non-inferiority as defined in the protocol.

Is a difference sought or is equivalence the objective International conference of harmonisation (ICH E9 ) makes it clear that it is vital that the protocol of a trial, designed to demonstrate equivalence or non-inferiority contains a clear statement that this is its explicit intention (ICH E9, Section 3.3.2). In the past if a trial failed to show that a new treatment gave benefit compared to a standard, it was commonplace to claim that the new treatment was therefore as effective as the standard. Such an argument is no longer acceptable as will be discussed in Section 8.5.6. 

If in Figure 8.9 a positive difference between treatments were indicative of a benefit for the test treatment then case (C) would indicate significant superiority of the new treatment. In such circumstances, we would not wish to conclude that only the treatments were not equivalent. In such circumstances, we can use a single boundary and such studies are called non-inferiority studies in which the objective is to show that the new treatment is no more than a small amount worse than the standard. The conduct of the inference remains similar if the confidence interval is to the right of the non-inferiority boundary, we can conclude that the new treatment is non-inferior to the standard. 

There are a number of issues in using such studies to achieve marketing authorisation. First, there needs to be a justification of the boundaries. Flow can we be sure that the choice of S is appropriate Second, has an appropriate choice comparator been made Is the dose of the comparator appropriate Is the population of patients appropriate Third, while for superiority trials it is generally accepted that the appropriate analysis population is an ITT population, it has been argued that for equivalence and non-inferiority studies that the as per protocol population also has a role to play. Finally we need to be sure that an equivalence or non-inferiority study is... 

Finally, in a non-inferiority trial we are trying to demonstrate that we are at least as good as or not worse than some active control reference treatment in some pre-defined sense. 

In therapeutic equivalence trials and in non-inferiority trials we are often looking to demonstrate efficacy of our test treatment indirectly. It may be that for ethical or practical reasons it is not feasible to show efficacy by undertaking a superiority trial against placebo. In such a case we compare our test treatment to a control treatment that is known to be efficacious and demonstrate either strict... 

Alternatively there may be commercial reasons why we want to demonstrate the non-inferiority of our treatment against an active control. Maybe our treatment potentially has fewer side effects than the active control and we are prepared to pay a small price for this safety advantage in relation to efficacy. If this were the case then of course we would need to show advantages in terms of a reduction in side effects but we would also need to demonstrate that we do not lose much with regard to efficacy. 

Non-inferiority trials are becoming more and more common as time goes on. This in part is due to the constraints imposed by the revised Helsinki Declaration (2004) and the increasing concern in some circles regarding the ethics of placebo use. These trials however require very careful design and conduct and we will discuss this whole area in a subsequent chapter. 

It is all too common to see a conclusion that treatments are the same (or similar) simply on the back of a large p-value this is not necessarily the correct conclusion. Presentation of the 95 per cent confidence interval will provide a statement about the possible magnitude of the treatment difference. This can be inspected and only then can a conclusion of similarity be made if this interval is seen to exclude clinically important differences. We will return to a more formal approach to this in Chapter 12 where we will discuss equivalence and non-inferiority. 

In equivalence and non-inferiority trials (see Chapter 12), the full analysis set and the per-protocol set have equal status and are treated as co-primary. The requirement, therefore, is to show significance for each of these analyses. This is another case where significance is needed on all endpoints with both analyses being conducted at the usual 5 per cent significance level. 

In this chapter we will move away from superiority trials to look at methods for the evaluation of equivalence and non-inferiority. The setting in all cases here is the comparison of a new treatment to an active control where we are looking to demonstrate similarity (in some defined sense) between the two treatments. 

As mentioned in Section 1.10, there are essentially two areas where we would want to conduct non-inferiority trials firstly where inclusion of a placebo for either practical or ethical issues is not possible and we are therefore looking to demonstrate the efficacy of the new treatment indirectly by showing similarity to an established active treatment and secondly where it is necessary to show that there is no important loss of efficacy for a new treatment compared to an existing treatment. 

Finally, before we move on to look at statistical methods, it is worth mentioning that many people feel uncomfortable with the term non-inferiority. In a strict sense, any reduction in the mean response is saying that the new treatment is not as good as the existing treatment and so is inferior. We, however, are using the term non-inferiority to denote a non-zero, but clinically irrelevant reduction in efficacy, which we need to define in an appropriate way. Some practitioners use the term one-sided equivalence as an alternative to non-inferiority. 

A good overview of various aspects of non-inferiority trials is provided by Kaul and Diamond (2006). 

For non-inferiority, the first step involves defining a non-inferiority margin. Suppose that we are developing a new treatment for hypertension and potentially the reason why the new treatment is better is that it has fewer side effects, although we are not anticipating any improvement in terms of efficacy. Indeed, suppose that we are prepared to pay a small price for a reduction in the side effects profile say up to 2 mmHg in the mean reduction in diastolic blood pressure. 

In Figure 12.2, and P2 e mean reductions in diastolic blood pressure in the test treatment and active control groups respectively. If the difference in the means is above zero then the test treatment is superior to the active control, if the difference is zero then they are identical. If the difference falls below zero the test treatment is not as good as the active control. This, however, is a price we are prepared to pay, but only up to a mean reduction in efficacy of 2 mmHg beyond that, the price is too great. The non-inferiority margin is therefore set at —2 mmHg. 

Step 2 is then to run the trial and compute the 95 per cent confidence interval for the difference, Pi — P2> in the mean reductions in diastolic blood pressure. In the above example suppose that this 95 per cent confidence interval turns out to be ( — 1.5 mmHg, 1.8 mmHg). As seen in Figure 12.2, all of the values within this interval are compatible with our definition of non-inferiority the non-inferiority of the test treatment has been established. In contrast, had the 95 per cent confidence interval been, say, (—2.3 mmHg,... 

In order to demonstrate non-inferiority, it is only one end of the confidence interval that matters in our example it is simply the lower end that needs to be above —2 mmHg. It is therefore not really necessary to calculate the upper end of the interval and sometimes we leave this unspecified. The resulting confidence interval with just the lower end is called a one-sided 97.5per cent confidence interval the two-sided 95 per cent confidence interval cuts off 2.5 per cent at each of the lower and upper ends, having the upper end undefined leaves just 2.5 per cent cut off at the lower end. The whole of this confidence interval must be entirely to the right of the non-inferiority margin for non-inferiority to be established. 

For non-inferiority a one-sided confidence interval should be used. ... 

The aim of this study reported by Powderly et al. (1992) was to establish the non-inferiority of a test treatment, fluconazole, compared to an established treatment, amphotericin B, in preventing the relapse of cryptococcal meningitis in HIV-infected patients. It was thought that fluconazole would be less effective than amphotericin B, but would offer other advantages in terms of reduced toxicity and ease of administration fluconazole was an oral treatment while amphotericin B was given intravenously. The non-inferiority margin was set at —15 per cent in terms of relapse rates. 

The non-inferiority margin has been set at —15 per cent. Figure 12.4 displays the non-inferiority region and we need the (two-sided) 95 per cent confidence interval, or the one-sided 97.5 per cent confidence interval, to be entirely within this non-inferiority region for non-inferiority to be established. 

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