In many trials, it is desirable to try to balance the treatment arms within important prognostic factors (subject characteristics that are known to be correlated with the outcome). Randomisation should ensure this in the long run, but it is advantageous to ensure balance throughout a large trial (to avoid temporal effects being correlated with treatment) and in smaller trials. Stratification is one way of achieving balance. Minimisation is an alternative method.
Say you want to make sure the treatment groups A and B are balanced with respect to a biomarker which is known to be highly prognostic of the outcome in your trial. You use random permuted blocks separately in those who are positive for the biomarker and those who are negative:
|Biomarker–||A A B B A B B A B A B A A B|
|Biomarker+||A B B A B B A A|
This ensures that the treatment groups are balanced 1:1 at the end of each block within biomarker– and biomarker+ subjects.
The FDA has some good advice on what they call some basic tenets of stratification: