I aim to allocate subjects to four different experimental groups by means of Permuted Block Randomization, in order to get equal group sizes.
This, according to Suresh (2011, J Hum Reprod Sci) can result in groups that are not comparable with respect to important covariates. In other words: there may be significant differences between treatments with respect to subject covaraites, e.g. age, gender, education.
I want to achieve comparable groups with respect to these covaraites. This is normally achieved with stratified randomization techniques, which itself seems to be a type of block randomization with blocks being not treatment groups, but the covariate-categories, e.g. low income and high income.
Is a combination of both approaches possible and practically feasible? If there are, e.g. 5 experimental groups and 3 covariates, each with 3 different categories, randomization that aims to achieve groups balanced wrt covariates and equal in size might be complicated.
Is it possible to perform Permuted Block Randomization to treatments for each "covariate-group", e.g. for low income, and high income groups separately, in order to achieve this goal?
Thanks in advance for answers and help.
Basically yes, but you'll need enough patients for that to ensure each category in each group get enough patients, hence block permutation can use more than one block...
You may also choose to use other randomization methods to ensure size equality and groups comparability, without all the additional complexities of stratification, both for randomization and for statistical analysis after that.
Dear Mr. Curis,
what would those "other randomization methods" with less complexity be? I know that covariate adaptive randomization can be used for getting groups that are comparable wrt covariates, but they did not appear to be particularly less complex.
u can do stratified randomlzation only, and use it with score weighting (such as propensity) even without getting equal number of patients in each class
Dear M. Bruns,
Since I am not a specialist of randomization, far from that, it's difficult to give a definitive answer. I would say 1) it depends on the step at which you prefer to accept some complexity and 2) you should probably try by some simulation different randomizations based on the sample size you defined and the covariate you expect to be important and their changes (which is needed for stratification anyway) to check which method are better to avoid unbalance between groups on these covariates.
Note that your question opens an interesting question: by definition, a (good) randomization must balance any covariate between the groups _in average_ (that is, averaging all possible randomizations of the same set of subjects), but I do not think there is a way to prevent that by "bad luck" you have non comparable covariables if you perform a test (but the reason of doing this test is not clear, and the choice of its risk debatable because of multiple comparisons issues). So any permutation method (and a reasonable sample size, of course) should handle the problem of uncomparable values between the groups, and note guarantee that if a constrain is not added.
Because of that, the affirmation by Suresh et al. that you cite deserve more explainations, which do not seem to be present in the original paper - which, by the way, seems to have been retracted (but may be for other, unrelated, reasons).
The only way to have inbalance despite randomization, in a block design, I can imagine is to have the covariate depending for some reason of time in a somehow periodic pattern with a similar period than the block length, which seems quite improbable. But as I said before, I'm not a specialist on these questions, so may be other situations may make the PBR prone of uncomparable covariate between groups.
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