Preclinical studies are usually of modest size but may be larger if the units are (say) blood samples, biopsy specimens or pathology slides. As indicated, if all units are available, or can be recruited as and when needed, then the randomisation allocation process can be completed in advance of any subject being investigated.

In preclinical experiments, the objective of the randomisation is to help ensure balance of the experimental units between the different (two or more) experimental groups in terms of their basic characteristics. This applies whether the experimental units are biopsy specimens or the human subjects themselves. Thus the objective of the randomisation is to make the final comparison of differences between experimental groups as unbiased as possible. We need to be assured that any differences observed between groups are not due to, for example, where the individual biopsy specimens from the two groups are stored in the refrigerator, but rather are due to the different experimental interventions imposed by the design.

Simple randomisation will not guarantee equal numbers in the different intervention groups. To ensure equal numbers, balanced arrangements can be introduced. This is done by first generating the combinations of the intervention possibilities into blocks of an appropriate size.

The block size is taken as a convenient multiple of the number of interventions under investigation. For example, a two-group design may have block sizes 2, 4, 6 or 8, a three-group 3, 6 or 9, while for a 2x2 factorial design comprising four interventions these may be of size 4, 8 or 12. In addition, the actual block size is often also chosen as a convenient divisor of the planned study size, N. For example, if N = 64, and with four interventions planned, a block size of 8 would be preferable to one of 12, since 8 is a divisor of 64 but 12 is not. Blocks are usually chosen as neither too small nor too large so that for two intervention groups block sizes of 4 or 6 are often used.

Suppose that equal numbers are to be allocated to A and B for successive blocks of four subjects. To do this, one can identify amongst all 16 possible combinations or permutations of A and B in blocks of four that contain two As and two Bs. Thus we are ignoring those permutations with unequal allocation, such as AAAA and AAAB. The

Table 4.1 All possible permutations of length 4 for two treatments A and B each occurring only twice

1 AABB 4 BABA

2 ABAB 5 BAAB

acceptable permutations are summarised in Table 4.1. These permutations are then allocated the numbers 1 to 6 and the randomisation table used to generate a sequence of digits. Suppose this sequence was again 53455 42567, then reading from left to right we generate the allocation BAAB ABBA BABA BAAB BAAB and BABA for the first 24 units.

Often, a particular digit for the sequences of Table T3 would not be used a second time until all relevant individual digits had first been used. In this case, the sequence becomes, in effect, 534---2-67. This generates BAAB ABBA BABA as previously but now followed by permutations 2 and 6 of Table 4.1, which are ABAB and BBAA. Finally we note that permutation 1 has not been used so that AABB completes the full 24-unit allocation sequence. Such devices ensure that for every four successive units included, balance between A and B is maintained. In this case we recruit 12 to A and 12 to B. Once again, precise details of the methods to be used have to be defined and documented before the randomisation process begins.

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