Article
On the Need of a TOST-Modification in the Setting of Comparability Testing
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Authors
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Alexandra Nießl
- Boehringer Ingelheim Pharma GmbH & Co. KG, Biberach, Germany; Ulm University, Ulm, Germany
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Erich Bluhmki
- Boehringer Ingelheim Pharma GmbH & Co. KG, Biberach, Germany; HBC University of Applied Sciences, Biberach, Germany
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Christian Palmes
- Siemens Healthineers, Marburg, Germany
| Published: | February 26, 2021 |
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Outline
Text
The two one-sided t-tests (TOST) assesses whether the mean-difference of two populations is sufficiently close to zero. Based on a sample of each population, the TOST aims to decide whether the absolute value of this mean-difference is smaller than some predefined upper limit, the acceptance criterion. However, it is often unclear how to choose a proper equivalence margin. One popular approach in the setting of comparability testing is to use a multiple of the standard deviation of one of those two populations (e.g. the reference group) as acceptance criterion.
In the setting of analytical similarity testing for example, it has been suggested to use an equivalence margin of 1.5 times the reference standard deviation. This margin has been established under the assumption that this standard deviation is known and fix. In practice however, the reference standard deviation is typically unknown and has to be estimated from the reference sample. This is prone leading to potential inflation of type I and/or type II error probabilities, as the uncertainty in the estimate of the margin is not considered. That means, on one hand, the type error of the TOST is not controlled at the pre-specified significance level, and on the other hand, the calculated sample size might not be sufficient to show analytical similarity, as the power might be reduced.
To resolve this issue, we propose a new modification of the TOST by taking into account the uncertainty of the margin. More precisely, we calculated the exact cumulative distribution function (CDF) to derive modified TOST quantiles, which ensure that the type I error is controlled.
We conducted several simulations studies to evaluate systematically the performance of our modified TOST compared to the regular TOST in scenarios with estimated equivalence margins. We focused on realistic settings in the field of analytical similarity. In particular, we incorporate power and sample size considerations in our evaluation.
A major benefit of our concept of the modified TOST quantiles is that the overall set-up is the same as for the regular TOST. Thus, we provide a flexible and easy-to-use approach that controls the type I error rate. Moreover, our modified TOST can be applied to any comparability or equivalence test situations with random margins and is not limited to applications of analytical similarity.
The authors declare that they have no competing interests.
The authors declare that an ethics committee vote is not required.
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