Title : The equivalence testing approach: What sort of statistical information on clinical trials should be requested by regulatory agencies
Abstract:
Background: Clinical trials deserve special attention regarding all aspects of their implementation. Specifically, there are statistical subtleties that can be improved but standard use does not take advantage of that. Moreover, failing to overcome these statistical subtleties can have a negative impact on the conclusions of a clinical study. Such subtleties are related with what we could call “The equivalence approach”.
Aims: To argue in favour of the equivalence approach in statistics. To present examples where the equivalence approach has been overlooked, both from real undergone clinical studies, as well as by statistical advices made by regulatory agencies of medical products.
Methods: The equivalence approach refers to an instance of the well-known statistical tool of test of hypothesis, where an attempt is made of proving similarity of multiple outcomes, and the equivalence hypothesis is located in the alternative.
Results: It is found that the equivalence approach is systematically overlooked in clinical trial reports. An example of this phenomenon in the past was the so called “power approach”, Where regulatory agencies suggested this tool for years until the improved statistical tool known as TOST (Two One-Sided Test) procedure appeared. It has been noted, on the other hand, that when fitting a linear regression model, model selection is based on deleting a coefficient if its associated p-value is not less than 0.05, when testing that this coefficient is different from zero; this practice could be replaced by the following better one: Delete a group of coefficients, if the p-value is less than 0.05, when testing that all those coefficients are near zero. Regulatory agencies do not stress this situation in their advices. Another example comes from non-parametric tests. In a phase II clinical trial assessing the effect and safety of the nutritional supplement Viusid on quality of life, we decided to introduce and use a non-inferiority version of the signed ranks test, because we aimed to show that quality of life did not worsen with the use of Viusid. Moreover, for assessing Goodness-of-fit tests, the hypothesis of “good fit” is usually in the null, when it should be located in the alternative. Finally, we recently faced a clinical trial where the aim was to compare three medicines in patients with Dermatophytosis, looking for similarity. The primary outcome was binary, so we were faced with an “equivalence comparison of three binary outcomes”. Failing to find the needed statistical tool in the literature, we developed ourselves the required methodology.
Conclusion: Equivalence testing is in the core of several statistical analysis. Nevertheless, it is frequently inserted into the null hypothesis, instead of the alternative, where it should be. We believe that statisticians should take more care when applying this tool, avoiding the logical flaws that come from “testing a null hypothesis”. Regulatory agencies should revise and stress their advices in this respect.
