# Block randomisation

If we are conducting a study with two treatment groups say A and B we might patients to treatment groups on the basis of randomly selected numbers. Sequences of random numbers often seem to have patterns in them, like long runs of the same number which may lead to an imbalance in the size of treatment groups if sample sizes are relatively small. One method that can keep groups more or less the same size but doesn't depart too far from perfect randomisation is block randomisation. This involves recruiting patients in short blocks. We ensure that half the patients within each block are allocated to treatment A and half to B. Within each block, however the order of patients is random. to illustrate this we will use block randomisation with a block size of four.

First we have to look at the block of four. There are six different ways that four patients can be split evenly between two treatments:

 1. AABB 2. ABAB 3. ABBA 4. BAAB 5. BABA 6. BBAA

The next step is to select randomly amongst these six different blocks for each group of four patients that are recruited. So we consult a list of random numbers:

9795270571964604603256331708242973...

As we only have six different blocks we drop all numbers outside the range 1 to 6:

52516464632563312423...

Blocks are selected according to the above sequence. So the first eighteen subjects would be allocated to treatments as follows:

 5 2 5 1 6 BABA ABAB BABA AABB BB

This is a worst-case scenario, one group has two more subjects than the other; but this small difference doesn't really matter. We have guaranteed almost perfect matching of the size of groups without departing too far from the principle of purely random selection.