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Background: Experimental treatments pass through various stages ofdevelopment. If a treatment passes through early phase experiments, theinvestigators may want to assess it in a late phase randomised controlledtrial. An efficient way to do this is adding it as a new research arm to anongoing trial. This allows to add the new treatment while the existing armscontinue. The familywise type I error rate (FWER) is often a key quantity ofinterest in any multi-arm trial. We set out to clarify how it should becalculated when new arms are added to a trial some time after it has started.  Methods: We show how the FWER, any-pair and all-pairs powers can becalculated when a new arm is added to a platform trial. We extend the Dunnettprobability and derive analytical formulae for the correlation between the teststatistics of the existing pairwise comparison and that of the newly added arm.We also verify our analytical derivation via simulations.  Results: Our results indicate that the FWER depends on the shared control arminformation (i.e. individuals in continuous and binary outcomes and primaryoutcome events in time-to-event outcomes) from the common control arm patientsand the allocation ratio. The FWER is driven more by the number of pairwisecomparisons and the corresponding (pairwise) Type I error rates than by thetiming of the addition of the new arms. The FWER can be estimated using\v{S}id\'{a}k's correction if the correlation between the test statistics ofpairwise comparisons is less than 0:30.  Conclusions: The findings we present in this article can be used to designtrials with pre-planned deferred arms or to design new pairwise comparisonswithin an ongoing platform trial where control of the pairwise error rate(PWER) or FWER (for a subset of pairwise comparisons) is required.

Adding new experimental arms to randomised clinical trials: impact on error rates