Unequal group sizes in randomised trials: guarding against guessing

We cringe at the pervasive notion that a randomised trial needs to yield equal sample sizes in the comparison groups. Unfortunately, that conceptual misunderstanding can lead to bias by investigators who force equality, especially if by non-scientific means. In simple, unrestricted, randomised trials (analogous to repeated coin-tossing), the sizes of groups should indicate random variation. In other words, some discrepancy between the numbers in the comparison groups would be expected. The appeal of equal group sizes in a simple randomised controlled trial is cosmetic, not scientific. Moreover, other randomisation schemes, termed restricted randomisation, force equality by departing from simple randomisation. Forcing equal group sizes, however, potentially harms the unpredictability of treatment assignments, especially when using permuted-block randomisation in non-double-blinded trials. Diminished unpredictability can allow bias to creep into a trial. Overall, investigators underuse simple randomisation and overuse fixed-block randomisation. For non-double-blinded trials larger than 200 participants, investigators should use simple randomisation more often and accept moderate disparities in group sizes. Such unpredictability reflects the essence of randomness. We endorse the generation of mildly unequal group sizes and encourage an appreciation of such Inequalities. For non-double-blinded randomised controlled trials with a sample size of less than 200 overall or within any principal stratum or subgroup, urn randomisation enhances unpredictability compared with blocking. A simpler alternative, our mixed randomisation approach, attains unpredictability within the context of the currently understood simple randomisation and permuted-block methods. Simple randomisation contributes the unpredictability whereas permuted-block randomisation contributes the balance, but avoids the perfect balance that can result in selection bias.