Practical experience with the design and analysis of a three-armed equivalence study

Abstract

Objective: While there is a lot of experience with the design, conduct and interpretation of bioequivalence studies, the methodology of trials concerning therapeutic equivalence is still at an early stage of development. Two-armed equivalence studies involve special problems of interpretation, which can be partly solved by the introduction of a third (placebo) arm. We describe a trial in which the therapeutic equivalence of horse chestnut seed extract (HCSE) and compression treatment was to be demonstrated in patients with chronic venous insufficiency (CVI). Compression is regarded as the standard therapy in this field. However, the efficacy of compression in terms of the variable of primary interest, namely oedema reduction, has never been demonstrated according to current methodological rules. Thus, the `standard' had to be established in the trial itself. This can be achieved by demonstration of relevant superiority in comparison with placebo.

Methods: Two hypotheses had to be tested: (1) the relevant superiority of compression compared with placebo as a precondition for (2) the at most irrelevant inferiority of HCSE in comparison with compression (`equivalence'). For both corresponding statistical tests, the irrelevance criterion – formulated as standardized difference – was set to 0.5.

Results: Therapeutic equivalence could not be demonstrated following this design, because compression failed to be relevantly superior compared with placebo, even though HCSE was shown to be at most irrelevantly inferior compared with compression. Explorative analyses show that it is not possible to reject simultaneously both null hypotheses with the obtained data when using equal irrelevance limits for both tests.

Conclusion: Although the primary objective of the trial could not be achieved, the results were encouraging. Thus, a new study was planned and started based on the observed data. The concept of a shifted null hypothesis may be applied to `routine' clinical trials too; using `no difference' as the null hypothesis in a trial does not seem to be meaningful when in fact an at least relevant difference is required.