Testing Procedures for Claiming Success on at Least k Out of m Hypotheses with an Application to Biosimilar Development

Multiplicity is a common issue in clinical drug development and there exists many proposals for the handling of multiple testing in clinical trials. However, the literature on testing procedures for claiming success on at least k out of m tests and the operating characteristics of these procedures is still sparse. Such testing is very relevant in biosimilar drug development, for example, where products have gained regulatory approval in the past, even though not all hypotheses could be rejected. Obviously, simple adjustments for multiplicity like the Bonferroni-adjustment or the Holm-procedure are valid as well for this testing problem, but can be conservative. In this article, we propose simple testing procedures for claiming success on at least k out of m tests which are more powerful than standard procedures while still providing strong control of the family-wise error rate. We illustrate their applicability in practice using an example from biosimilar drug development. In the supplementary materials, we provide proofs of the properties of our testing procedures and demonstrate the superiority of the proposed methodologies using simulations.