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

## TL;DR

This paper investigates how adding new experimental arms to ongoing randomized clinical trials affects error rates, providing analytical formulas and simulations to guide trial design and error control.

## Contribution

It derives analytical formulas for FWER when new arms are added to platform trials, extending Dunnett's probability and analyzing correlation effects.

## Key findings

- FWER depends on shared control information and allocation ratio.
- FWER is influenced more by the number of comparisons than timing of addition.
- Sidák's correction is applicable when correlation is below 0.30.

## Abstract

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.