Restricted randomization, stratified randomization, and forced randomization

Randomization is a fundamental aspect of randomized controlled trials (RCT). When we judge a quality of a clinical trial, whether or not it is a randomized trial is a critical point to consider. However, there are different ways in implementing the randomization and some of the terminologies could be very confusing, for example, 'restricted randomization', 'stratified randomization', and 'forced randomization'.

Without any restriction, the randomization is called 'simple randomization' where there is no block, no stratification applied. Simple randomization will usually not be able to achieve the exact balance of the treatment assignments if the # of randomized subjects are small. In contrary, the restricted randomization refer to any procedure used with random assignment to achieve balance between study groups in size or baseline characteristics. The first technique for restricted randomization is to apply the blocks. Blocking or block randomization is used to ensure that comparison groups will be of approximately the same size. Suppose we are planning to randomize 100 subjects to two treatment groups, with simple randomization, if we enroll entire 100 subjects, we may have approximately equal number of subjects in one of the treatment groups. However, if we enroll a small amount of subjects (for example 10 subjects), we may see quite some deviation from equal assignments and there may not be 5 subjects in each treatment arms. With the application of blocking (block size=10), we can ensure that with every 10 subjects, there will be 5 to each treatment arm.

Stratified randomization is used to ensure that equal numbers of subjects with one or more characteristic(s) thought to affect the treatment outcome in efficacy measure will be allocated to each comparison group. The characteristics (stratification factor) could be patient's demographic information (gender, age group,...) or disease characteristics (baseline disease severity, biomarkers,...). If we conduct a randomized, controlled, dose escalation study, the dose cohort itself can be considered as a stratification factor.  With stratification randomization, we essentially generate the randomization within each stratum. # of strata depends on the number stratification factors used in randomization. If we implement 4 randomization factors with each factor having two levels, we will have a total of 16 strata, which means that our overall randomization schema will include a total 16 portions of the randomization with each portion for a stratum. In determining the # of strata used in randomization, the total number of subjects need to be considered. Overstratification could make the study design complicated and might also be prone to the randomization error. For example, in a stratified randomization with gender as one of the stratification factor, a male subject could be mistakenly entered as female subject and a randomization number from female portion instead of male portio nof the randomization schema could be chosen. This may have impact on the overall balance in treatment assignment as we originally planned. A paper by Kernan et al had an excellent discussion on stratified randomization.

One of the misconception about the stratification is that equal number of subjects are required for each stratum. for example, when we talk about randomization stratified by gender (male and female), people will think that we would like to have 50% of male and 50% of female subjects in the trial. This is not true. What we need is to (assuming 1:1 randomization ratio) have 50% of subjects randomized to each treatment arm in male subjects and in female subjects. This issue has been discussed in one of my old articles. 

The forced randomization is another story and it basically to force the random assignment to deviate from the original assignment to deal with some special situation. For example, in a randomized trial with moderate and severe degree of subjects, we may put a cap on the # of severe subjects to be randomized. When the cap is achieved, the severe subjects will not be randomized any more, but the moderate subjects can still be randomized. We could enforce a cap for # of subjects at a specific country/site or limit the number of subjects for a specific treatment arm to be randomized at a particular country/site. The forced randomization is usually required to deal with the operation issues and is implemented through IVRS or IWRS. Too much forced randomization will neutralize the advantages of the randomization.

all three terms (restricted, stratified, and forced randomization) belong to the fixed sample size randomization in contrary to the dynamic randomization in adaptive designs.