Superiority trials

In the case of equivalence, noninferiority, and bioequivalence trials, the null hypotheses established are different from the null hypothesis established in superiority trials. In addition, the null hypothesis in each case is unique, and hence they all differ from each other. However, they share a basic similarity. The null hypothesis for each of these designs states, in effect, that the test drug and the comparator drug do not have similar efficacy. As in all hypothesis testing, the statistical methodologies used look for compelling evidence to reject the respective null hypothesis in each case. 

It is noteworthy that, while the null hypothesis in each of the trial designs discussed (superiority, equivalence, noninferiority, and equivalence) is different, the hypothesis testing approach in each case is fundamentally similar to that in every other case. In each instance it is hoped that the null hypothesis will be rejected in favor of the research hypothesis. 

Two common statistical techniques that are typically used to analyze efficacy data in superiority trials are f-tests and ANOVA. In parallel group trials, the independent groups Mest and the independent groups ANOVA discussed in Chapter 7 would be used. Another important aspect of the statistical methodology employed in superiority trials, the use of CIs (confidence intervals) to estimate the clinical significance of a treatment effect, was discussed in Chapter 8. These discussions are not repeated here. Instead, some additional aspects of statistical methodology that are relevant to superiority trials are discussed. 

All of the studies that are performed before a therapeutic confirmatory trial is started collect information that facilitates a logical scientific progression from FTIH studies to the point where the therapeutic confirmatory trial is appropriate. In a real sense, all of these studies, and all of the information gained to date, have had one purpose to allow the primary objective in the therapeutic confirmatory trial to be stated as simply as possible. In this context, the word simple is not pejorative. To the contrary, a primary objective that can be stated simply can be tested simply, i.e., in a straightforward and unambiguous manner. This is a highly desirable attribute in a primary objective. 

The number of objectives that should be incorporated in any clinical trial is often a topic of considerable debate among study teams. One argument often propounded is that, while taking all the trouble to conduct the trial, why not collect as much data as possible and ask as many questions as possible This approach leads to a large number of study objectives, sometimes broken down into primary objectives, secondary objectives, and even tertiary objectives. Proponents of this 

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Trials may be designed to determine equivalence or superiority between therapies. An equivalence trial is designed to show that there is no clinically significant difference between therapies, and a superiority trial is intended to show that one therapy is significantly better than another. 

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... 

In a superiority trial our objective is to demonstrate either that our treatment works by demonstrating superiority over placebo or that we are superior to some reference or standard control treatment. 

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... 

Formulate null and alternative hypotheses. In all cases the alternative hypothesis represents the desirable outcome. In a superiority trial this means that the null hypothesis is equality (or no effect/no change/no dependence) of whatever is being compared while the alternative hypothesis is inequality (there is an effect/a change/a dependence). 

In a superiority trial the primary analysis will be based on the full analysis set with the per-protocol set being used as the basis for a supportive secondary analysis, and in this sense there will be no multiplicity issues. The form of the analysis, however, depends in addition on the methods to be used to account for missing data and these should clearly be pre-specified. It is also good practice to explore the robustness of the conclusions to both the choice of the per-protocol set and the methods to be used for missing data. These analyses again will be supportive (or not) of the main conclusions and no multiplicity aspects arise. 

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. 

In superiority trials, the full analysis set is the basis for the primary analysis. As discussed in Section 7.2, the regulators prefer this approach, in part, because it gives a conservative view of the new treatment. In equivalence/non-inferiority trials, however, it is not conservative and will tend to result in the treatments looking more similar than, in reality, they are. This is because the full analysis set will include the patients who have not complied with the medication schedules and who have not followed the study procedures and the inclusion of such patients will tend to weaken treatment differences. 

As with sample size in superiority trials we generally power on the basis of the per-protocol set and increase the sample size to account for the non-evaluable patients. This is particularly important in non-inferiority trials where the full analysis set and the per-protocol set are co-primary analyses. Note also, as before in superiority trials further factoring up may be needed if there are randomised patients who are being systematically excluded from the full analysis set, as is the case, for example, in anti-infective trials. 

Moving in the opposite direction, that is concluding non-inferiority in a superiority trial, is much more difficult, as this would generally require pre-specification of a non-inferiority margin. Such pre-specification would usually not have been considered in a trial designed to demonstrate superiority. However, if a conclusion of non-inferiority would be a useful outcome then it could be appropriate to consider such pre-specification. Switching from superiority to non-inferiority, however, presents further problems. Assay sensitivity may well be one reason why... 

In previous chapters, discussion has focused on superiority trials. These trials are conducted to demonstrate to the satisfaction of regulatory agencies that the investigational drug is superior in efficacy to a placebo, or possibly superior in efficacy to an active comparator. In addition, this chapter also introduces other study designs that are very informative and, in some cases, necessary. 

While the practical details of the statistical approaches employed in equivalence, noninferiority, and bioequivalence trials are different from those employed in superiority trials, all of the approaches employ hypothesis testing. The differences lie in the nature of the hypotheses that are created and then tested. 

The research question in equivalence trials is structured differently from the research question in superiority trials. The hypothesis testing approach that works so well in superiority trials is of little value in an equivalence trial. As Matthews (2006) commented, Failing to establish that one treatment is superior to the other is not the same as establishing their equivalence. ... 

Given that the format of the research question is different from that used in superiority trials, the formats of the research hypothesis and the null hypothesis are also different. As noted in Section 7.3, the research hypothesis and null hypothesis in superiority trials are stated as follows ... 

Obtaining a nonsignificant p-value in a superiority trial does not demonstrate that the two treatments are the same. This is an extremely important concept and one that is widely misunderstood. Again, then, obtaining a nonsignificant p-value in a superiority trial does not demonstrate that the two treatments are the same. Conventional p-values have no role in establishing equivalence. 

Having seen why the hypothesis testing used in superiority trials is inappropriate for equivalence trials, the appropriate approach in this context is now discussed. The first step in this approach is to establish the equivalence margin for the trial. 

The next step in the case of equivalence trials is quite different from the strategy used in superiority trials. Once the treatment effect has been determined,... 

For the sake of this example, let us say that a decrease in mean efficacy of 3 mmHg in SBP is acceptable. (Please note again that this is a hypothetical example.) The resulting value of minus 3 mmHg yields the noninferiority margin. The trial is then conducted. The treatment effect is calculated, as in superiority trials and equivalence trials, as the difference between the treatment group means. 

Superiority trials of one active compound over another provide the second most convincing proof of efficacy after placebo-controlled studies. The reason for selecting this design rather than placebo has been alluded to already, i.e. it is ethically unjustifiable to use a placebo or (less convincingly) marketing requirements. 

The alternate hypothesis reflects the alternate possible outcome of the trial, and therefore the alternate possible answer to the research question The trial was conducted with the specific goal of providing an answer to the research question. In a superiority trial the alternate hypothesis takes the following form ... 

Following the logic of our memory lip, you will see that the alternate hypothesis in this case, just like in the case of a superiority trial, expresses what we are hoping to find, while the null hypothesis states what we are hoping not to find. The actual natures of the null and alternate hypotheses in an equivalence trial are... 

Imagine the following results from a superiority trial ... 

What form do the null and alternate hypotheses take for a superiority trial with a placebo control ... 

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