Unequal randomisation

All other things being equal, having equal numbers of subjects in the two treatment groups provides the maximum amount of information (the greatest power) with regard to the relative efficacy of the treatments. There may, however, be issues that override statistical efficiency  

Unequal randomisation is sometimes needed as a result of these considerations. To achieve this, the randomisation list will be designed for the second example above with double the number of A and B allocations compared to placebo. 

For unequal randomisation we would choose the block size accordingly. For a 2 1 randomisation to A or P we could randomly choose from the blocks  

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Finally note that in our considerations we have worked with groups of equal size. It is straightforward to adapt the calculations for unequal randomisation schemes and the computer packages mentioned earlier can deal with these. Altman (1991), Section 15.3 provides a simple method for adapting the standard sample size calculation to unequal group sizes as follows. If N is the calculated sample size based in an equal randomisation and k represents the ratio of the number of patients in one group compared to the other group, then the required number of patients for a A to 1 randomisation is ... 

In order to reduce the number of subjects on placebo in a clinical trial, some investigators employ an unequal randomisation technique, whereby fewer subjects receive placebo than receive active comparator. For example, the ratio of 1 2, or 1 3 may be chosen in a large clinical study. Some statisticians, however, insist that if this design is chosen, then all subjects must have an equal chance of receiving all medications. Thus, in a 2 1 randomisation of active versus placebo, the randomisation would actually be 2 1 1. 

Dumville JC, Hahn S, Miles JNV, Torgerson DJ (2006) The use of unequal randomisation ratios in clinical trials A review. Contemporary Clinical Trials 27 1-12. 

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