  Background: Experimental treatments pass through various stages of
development. If a treatment passes through early phase experiments, the
investigators may want to assess it in a late phase randomised controlled
trial. An efficient way to do this is adding it as a new research arm to an
ongoing trial. This allows to add the new treatment while the existing arms
continue. The familywise type I error rate (FWER) is often a key quantity of
interest in any multi-arm trial. We set out to clarify how it should be
calculated 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 be
calculated when a new arm is added to a platform trial. We extend the Dunnett
probability and derive analytical formulae for the correlation between the test
statistics 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 arm
information (i.e. individuals in continuous and binary outcomes and primary
outcome events in time-to-event outcomes) from the common control arm patients
and the allocation ratio. The FWER is driven more by the number of pairwise
comparisons and the corresponding (pairwise) Type I error rates than by the
timing 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 of
pairwise comparisons is less than 0:30.
  Conclusions: The findings we present in this article can be used to design
trials with pre-planned deferred arms or to design new pairwise comparisons
within an ongoing platform trial where control of the pairwise error rate
(PWER) or FWER (for a subset of pairwise comparisons) is required.
