Stratified randomization refers to the situation in which strata are constructed based on values of prognostic variables or baseline covariates and a randomization scheme is performed separately within each stratum. One misconception is to think that the stratified randomization is going to require the equal number of subjects for each strata.
For example, suppose that in a two-arm, parallel design study, we would like to stratify the randomization for age group (<18 versus >=18 years old). But we don't know how many subjects in each age group we could enroll. The purpose is to make sure that within each age group, there are equal numbers of subjects assigned to treatment A or treatment B.
After the study, there may be quite different total number of subjects in each age group, but within each age group, there should be approximately equal number of subjects in treatment A or treatment B.
The strata size usually vary (maybe there are relatively fewer young males and young females with the disease of interest). The objective of stratified randomization is to ensure balance of the treatment groups with respect to the various combinations of the prognostic variables. Simple randomization will not ensure that these groups are balanced within these strata so permuted blocks are used within each stratum are used to achieve balance.
When the stratified randomization is utilized, the # of stratification factors is typically limited to 1 or 2. The number of strata is exponentially increased if too many randomization factors are included. For example, if we have 4 stratification factors and each factor has two levels, then the # of strata = 2^4 = 16 strata, which is not practical.
If there are too many strata in relation to the target sample size, then some of the strata will be empty or sparse. This can be taken to the extreme such that each stratum consists of only one patient each, which in effect would yield a similar result as simple randomization. Keep the number of strata used to a minimum for good effect.
I have also seen a trial to require the equal number of subjects for each strata and with each strata, then equal number of subjects assigned to two treatment groups. In a trial to study the IBS (irritable bowel Syndrome), the protocol required the equal number of subjects in two type of IBSs (IBS-C vs. IBS-M). Within IBS-C or IBS-M group, there should be equal number of subjects assigned to treatment A or treatment B. The things turned out not nice because there were a lot of more subjects with IBS-C than IBS-M. During the study, while enrollment target for IBS-C was achieved, there was still a lot of IBS-M subjects to be enrolled.
IBS-C=Irritable Bowel Syndrome (constipation dominant)
IBS-M=Irritable Bowel Syndrome (mixed - constipation and diarrria)