Merged block randomisation

Randomisation in small clinical trials is a delicate matter, due to the tension between the conflicting aims of balanced groups and unpredictable allocations. The commonly used method of permuted block randomisation has been heavily criticised for its high predictability. Merged block randomisation is a novel and conceptually simple restricted randomisation design for small clinical trials (less than 100 patients per stratum). For 1:1 allocation to treatments A and B, first two sequences consisting of building blocks AB and BA are generated, for example:

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Sequence 1 : A B A B B A A B A B

Sequence 2 : A B B A B A B A B A

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Then a series of coin flips is performed, which indicate how the two sequences will be merged, resulting in the final allocation. For each ‘head’, the sequentially first assignment within sequence 1 that has not been selected yet is placed in the final allocation, while for each ‘tail’, the sequentially first unused treatment assignment within sequence 2 is selected. For example, suppose we perform 10 coin flips and the first is a head. Then we take the first 'A' from sequence 1.

 

Sequence 1 (heads) : A B A B B A A B A B

Sequence 2  (tails): A B B A B A B A B A

Coin flips so far: H

Final allocation: A

 

If the second coin flip is a tails, we take the A from sequence 2.

 

Sequence 1 (heads) : A B A B B A A B A B

Sequence 2  (tails): A B B A B A B A B A

Coin flips so far: H T

Final allocation: A A

 

If the third coin flip is a head, we take the B from sequence 1.
 

Sequence 1 (heads) : A B A B B A A B A B

Sequence 2  (tails): A B B A B A B A B A

Coin flips so far: H T H 

Final allocation: A A B

 

And so on. Merged block randomisation is not restricted to 1:1 randomisation, but is readily applied to unequal target allocations and to more than two treatment groups. In the paper, it is shown that merged block randomisation is a good choice for studies where imbalance is a concern, improving on permuted block randomisation, while retaining the conceptual and practical simplicity of permuted block randomisation.

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Software, a tutorial and an online app are available, see Software for more details.