|Example 1. MAMS AD; assumptions and adaptive methods; approach for claiming evidence or informing adaptations; statistical program|
“The primary response (outcome) from each patient is the difference between the baseline HOMA-IR score and their HOMA-IR score at 24 weeks. The sample size calculation is based on a one-sided type I error of 5% and a power of 90%. If there is no difference between the mean response on any treatment and that on control, then a probability of 0.05 is set for the risk of erroneously ending the study with a recommendation that any treatment be tested further. For the power, we adopt a generalisation of this power requirement to multiple active treatments due to Dunnett . Effect sizes are specified as the percentage chance of a patient on active treatment achieving a greater reduction in HOMA-IR score than a patient on control as this specification does not require knowledge of the common SD, σ. The requirement is that, if a patient on the best active dose has a 65% chance of a better response than a patient on control, while patients on the other two active treatments have a 55% chance of showing a better response than a patient on control, then the best active dose should be recommended for further testing with 90% probability. A 55% chance of achieving a better response on active dose relative to control corresponds to a reduction in mean HOMA-IR score of about a sixth of an SD (0.178σ), while the clinically relevant effect of 65% corresponds to a reduction of about half an SD (0.545σ). The critical values for recommending that a treatment is taken to further testing at the interim and final analyses (2.782 and 2.086) have been chosen to guarantee these properties using a method described by Magirr et al. , generalising the approach of Whitehead and Jaki . The maximum sample size of this study is 336 evaluable patients (84 per arm), although the use of the interim analysis may change the required sample size. The study will recruit additional patients to account for an anticipated 10% dropout rate (giving a total sample size of 370). An interim analysis will take place once the primary endpoint is available for at least 42 patients on each arm (i.e., total of 168, half of the planned maximum of 336 patients). Sample size calculation was performed using the MAMS package in R .” 
Example 2. 3-arm 2-stage AD with dose selection; group sequential approach; assumptions; adaptation decision-making criteria; stage 1 and 2 sample sizes; use of simulations
“Sample size calculations are based on the primary efficacy variable (composite of all-cause death or new MI through day 7), with the following assumptions: an event rate in the control group of 5.0%, based on event rates from the phase II study (24); a relative risk reduction (RRR) of 25%; a binomial 1-sided (α = 0.025) superiority test for the comparison of 2 proportions with 88% power; and a 2-stage adaptive design with one interim analysis at the end of stage 1 data (35% information fraction) to select 1 otamixaban dose for continuation of the study at stage 2. Selection of the dose for continuation was based on the composite end point of all-cause death, Myocardial Infarction (MI), thrombotic complication, and the composite of Thrombosis in Myocardial Infarction (TIMI) major bleeding through day 7, with an assumed probability for selecting the “best” dose according to the primary endpoint (r = 0.6), a group sequential approach with futility boundary of relative risk of otamixaban versus UFH plus eptifibatide ≥1.0, and efficacy boundary based on agamma (− 10) α spending function . Based on the above assumptions, simulations (part of item 24b, see supplementary material) showed that 13,220 patients (a total of 5625 per group for the 2 remaining arms for the final analysis) are needed for this study.”  See Fig. 1.