Comparison of tests and sample size formulae for proving therapeutic equivalence based on the difference of binomial probabilities

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Abstract
To prove the hypothesis that a new treatment is as effective as a standard one, a possibility is to test the one‐sided null hypothesis of a clear inferiority of the new treatment against the alternative hypothesis that, if at all, it is only negligibly inferior. Such a problem is of clinical relevance if, for instance, a new treatment with an effectiveness which is comparable to that of the standard one would be preferred if it is less toxic. If the difference between the two treatments is measured by the difference of failure rates, approximate statistical tests and sample size formulae have to be used. This paper reports the results of an extensive empirical investigation comparing the well known calculations proposed by Blackwelder, Rodary, Com‐Nougue and Tournade, which propose a sample size formula for the test of Dunnett and Gent, and Farrington and Manning. The investigation was conducted in order to allow more comprehensive conclusions than those which may be drawn from the limited examples given by the last authors. For the usual settings in clinical trials, the formulae of Farrington and Manning are recommended. However, there are combinations of statistical parameters for which they are not preferred.