stratification and minimization are two randomization options to achieve balance in terms of covariate baselines in small RCTs. in recent years, researchers seem to have favoured minimization, particularly for sequential allocation designs with a high number of covariates. in short, the method involves the choice of some imbalance criterion and then sequentially allocates each new individual to the study arm leading to the smallest new criterion value. this allocation can be done purely deterministically or involving some element of chance.
our question is if the approach could be simplified when the assignment to study arms takes place only after inclusion of all participants is completed. our idea is to use simple randomization without any constraints to generate a large number, say N = 1000, of complete and fully random allocation schemes. in the next step we would identify the, say, n = 100 schemes with the smallest imbalances (using a similar criterion as for minimization) or, alternatively, all schemes with a criterion value below some prespecified cut-off value. finally, we would choose one of these remaining schemes at random.
the whole process would be carried out by a third person not involved in the study intervention or the collection of study outcomes. the investigators would only receive the last resulting allocation scheme from the person responsible for allocation.
the rationale behind our idea is simplicity and that we would like not to sacrifice too much randomness for balance.
has anyone heard of such an allocation strategy before? what do you think of it? are there any considerations concerning bias? (in some way, we would just be rejecting allocation schemes as long as we don't like them because of intolerably low balance. on the other hand, minimization or even stratification contain similar aspects...) and what about the implications for the statistical analysis? would you still adjust for the covariates using covariance analysis? any other thoughts?
thank you very much for any feedback!
Hello Thomas,
I am not an expert in conducting RCT but the only reason I can think of which would invalidate this methodology is if there is an unmeasured confounder which is actually imbalanced by balancing on all the measured confounders.
For example, if you achieve the closest balance on income that could lead to imbalance on an urban/suburban/rural variable because urban and rural contain both very high and very low income levels while suburban has less variance. It seems like balancing solely on income might lead to having a lot of low income urban customers, say, balanced by low income rural customers while in fact you want to balance on population density as well (you just don't have access to the variable in the dataset).
Just something to think about. A purely randomized sample should not lead to imbalance on unmeasured confounders while there is a potential that balancing on measured confounders could lead to imbalance on unmeasured confounders if an unmeasured variable has a peculiar relationship with a measured variable.
Best,
Aran
thank you very much vor your answer, aran!
you're definitely right that one has to consider imbalance in unmeasured covariates, but on the other hand: if two covariates are independent then balancing the first one should not lead to imbalancing the second, right? and if both variables are highly correlated then wouldn't balancing one variable - in most cases imaginable - kind of "automatically" co-balance the other?
and even if i'm wrong about the latter, isn't the problem inherent in any balancing algorithm or rather in the concept of balancing itself? in fact, i somehow hoped that my suggestion would do better in this respect than deterministic or "half-determinsitic" minimizing since it preserves "full randomization" at least among the sufficiently balanced allocation schemes...
but maybe my intuition is wrong here... ;-)
thanks again for your comment!
thomas
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