BACKGROUND: Multi-arm multi-stage (MAMS) randomised trial designs have been proposed to evaluate multiple research questions in the confirmatory setting. In designs with several interventions, such as the 8-arm 3-stage ROSSINI-2 trial for preventing surgical wound infection, there are likely to be strict limits on the number of individuals that can be recruited or the funds available to support the protocol. These limitations may mean that not all research treatments can continue to accrue the required sample size for the definitive analysis of the primary outcome measure at the final stage. In these cases, an additional treatment selection rule can be applied at the early stages of the trial to restrict the maximum number of research arms that can progress to the subsequent stage(s). This article provides guidelines on how to implement treatment selection within the MAMS framework. It explores the impact of treatment selection rules, interim lack-of-benefit stopping boundaries and the timing of treatment selection on the operating characteristics of the MAMS selection design.
METHODS: We outline the steps to design a MAMS selection trial. Extensive simulation studies are used to explore the maximum/expected sample sizes, familywise type I error rate (FWER), and overall power of the design under both binding and non-binding interim stopping boundaries for lack-of-benefit.
RESULTS: Pre-specification of a treatment selection rule reduces the maximum sample size by approximately 25% in our simulations. The familywise type I error rate of a MAMS selection design is smaller than that of the standard MAMS design with similar design specifications without the additional treatment selection rule. In designs with strict selection rules - for example, when only one research arm is selected from 7 arms - the final stage significance levels can be relaxed for the primary analyses to ensure that the overall type I error for the trial is not underspent. When conducting treatment selection from several treatment arms, it is important to select a large enough subset of research arms (that is, more than one research arm) at early stages to maintain the overall power at the pre-specified level.
CONCLUSIONS: Multi-arm multi-stage selection designs gain efficiency over the standard MAMS design by reducing the overall sample size. Diligent pre-specification of the treatment selection rule, final stage significance level and interim stopping boundaries for lack-of-benefit are key to controlling the operating characteristics of a MAMS selection design. We provide guidance on these design features to ensure control of the operating characteristics.

Multi-arm multi-stage trials are an efficient, adaptive approach for testing many treatments simultaneously within one protocol. In settings where numbers of patients available to be entered into trials and resources might be limited, such as primary postpartum haemorrhage, it may be necessary to select a pre-specified subset of arms at interim stages even if they are all showing some promise against the control arm. This will put a limit on the maximum number of patients required and reduce the associated costs. Motivated by the World Health Organization Refractory HaEmorrhage Devices trial in postpartum haemorrhage, we explored the properties of such a selection design in a randomised phase III setting and compared it with other alternatives. The objectives are: (1) to investigate how the timing of treatment selection affects the operating characteristics; (2) to explore the use of an information-rich (continuous) intermediate outcome to select the best-performing arm, out of four treatment arms, compared with using the primary (binary) outcome for selection at the interim stage; and (3) to identify factors that can affect the efficiency of the design.
We conducted simulations based on the refractory haemorrhage devices multi-arm multi-stage selection trial to investigate the impact of the timing of treatment selection and applying an adaptive allocation ratio on the probability of correct selection, overall power and familywise type I error rate. Simulations were also conducted to explore how other design parameters will affect both the maximum sample size and trial timelines.
The results indicate that the overall power of the trial is bounded by the probability of \'correct\' selection at the selection stage. The results showed that good operating characteristics are achieved if the treatment selection is conducted at around 17% of information time. Our results also showed that although randomising more patients to research arms before selection will increase the probability of selecting correctly, this will not increase the overall efficiency of the (selection) design compared with the fixed allocation ratio of 1:1 to all arms throughout.
Multi-arm multi-stage selection designs are efficient and flexible with desirable operating characteristics. We give guidance on many aspects of these designs including selecting the intermediate outcome measure, the timing of treatment selection, and choosing the operating characteristics.

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 while the existing research arms continue, a so-called multi-arm platform trial. The familywise type I error rate is often a key quantity of interest in any multi-arm platform 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.
We show how the familywise type I error rate, 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.
Our results indicate that the familywise type I error rate 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 familywise type I error rate 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 familywise type I error rate can be estimated using Šidák\'s correction if the correlation between the test statistics of pairwise comparisons is less than 0.30.
The findings we present in this article can be used to design trials with pre-planned deferred arms or to add new pairwise comparisons within an ongoing platform trial where control of the pairwise error rate or familywise type I error rate (for a subset of pairwise comparisons) is required.