Stratified randomisation

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.

How it works

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

Stratification results in perfect balance:

A B Total
Biomarker– 7 7 14
Biomarker+ 4 4 8
Total 11 11 22

This ensures that the treatment groups are balanced 1:1 at the end of each block within biomarker– and biomarker+ subjects. It means we don't end up by chance with more of the biomarker+ subjects getting treatment A for instance. This can happen if we don't use stratification, even with blocks:

All subjects A A B B A B B A B A B A A B A B B A B B A A
Biomarker + + – – + – – – – – + – + – + + – – – – + –

Lack of stratification results in more biomarker– subjects being allocated to B by chance and more biomarker+ subjects being allocated to A:

A B Total
Biomarker– 5 9 14
Biomarker+ 6 2 8
Total 11 11 22

This could skew the unadjusted trial results by making treatment A look good since biomarker+ subjects have a better outcome than biomarker– subjects.

Choosing stratification factors

The FDA has some good advice on what they call some basic tenets of stratification [pdf]:

  • Only variables that can be observed before randomisation can be a basis for stratification.
  • It is impractical to control for more than a few sources of variation by stratification.
  • Variables that are subject to major sources of error because of differing interpretations will not be helpful stratification variables.
  • It is unreasonable to expect that all important sources of baseline variation will be controlled by stratified randomisation.
  • Multicentre trials with plans to enroll substantial numbers of subjects at each centre generally should stratify by centre (i.e., randomised within centres). Stratification for this variable controls for differences in the trial population because of environmental, social, demographic, and other factors and differences in management. In multicentre trials in which only small numbers of subjects are entered at each centre, stratification by centre generally is not practical.
  • Stratification should be limited to those variables that are considered potentially correlated with treatment effect.