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

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 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.

Methods: 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.

Results: 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.

Conclusions: 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.

Keywords: MAMS; Platform trials; STAMPEDE trial; adaptive trial designs; familywise type I error rate; multi-arm multi-stage; pairwise error rate; survival time.

Figure 1.

Schematic representation of the control and experimental arm timelines in the STAMPEDE trial. Bottom section: the thick horizontal bars represent the accrual period, and the following solid lines represent the follow-up period. Top section: the striped bars represent the period when the recruited control arm patients overlap during this period between different pairwise comparisons. The colours of the stripes represent the colours of each pairwise comparison. For example, the striped bar that is labelled as $S(1,2,4;6)$ represents the period when the recruited control arm patients are shared between the original pairwise comparisons $1,2,$ and 4 and the sixth newly added comparison during this period.

Figure 2.

Strategies to control type I error rate when adding new experimental arms. Key: (1) allocation ratio for either of the new or ongoing comparisons; (2) for example, $<60\%$ of information time when $A=1$; (3) correlation between the test statistics of pairwise comparisons; (4) K is the total number of pairwise comparisons, including the added arms.