Table 1 – Overview of the re-randomisation design

 1) Patients are entered into the trial as usual, randomised to a treatment arm, and followed up until all primary and secondary outcomes have been collected;

 2) If a patient requires further treatment after completing their initial follow up period, they may be entered into the trial again, and re-randomised;

 3) This is repeated until the target sample size is met.

Requirements for the re-randomisation design to give unbiased estimates of treatment effect and correct type I error rates

 1) Patients are only re-randomised when they have completed the follow-up period from their previous randomisation;

 2) Randomisations for the same patient are performed independently;

 3) The treatment effect is constant across all randomisation periods.

Asymptotic properties of different analytical approaches

Unadjusted analysis (ignoring patient effects)

 1) Unbiased estimate of treatment effect;

 2) Correct type I error rate;

 3) Equivalent power to a parallel group trial with the same number of observations in certain conditions (details provided in the text).

Adjusted analysis (accounting for patient effects)

 1) Unbiased estimate of treatment effect (requires adjustment for number of previous allocations to both the intervention and control respectively when treatment effects carry over into subsequent randomisation periods);

 2) Correct type I error rates;

 3) Increased power compared to a parallel group trial with the same number of observations in most scenarios.