|Australian soldiers playing the two-coin toss game "two up".|
Two up requires balance prior to randomization.
According to a 2010 report by the National Research Council (National Academies), the "primary benefit from randomizing clinical trial participants into treatment and control groups comes from balancing the distributions of known and unknown characteristics among these groups prior to study treatments."
It is a simple matter to see that this is not true and that randomization does not imply balancing.
Remember back to gym class and those times where the teams were chosen at random and how mad you got because Bobby and Sue were on the other team and you only got Steve and how unfair that was (and there is no way Jesse was as good as Sue). Or the time where the gym teacher made an effort to balance the two teams by carefully pairing people of equal ability and assigning them to different teams.
Random assignment does not imply balancing and balancing implies non-random assignment.
Of course the authors of the report, who are highly respected statisticians, know this. The authors are more careful in some other parts of the report - putting "probabilistically" in parenthesis before "balances" in another similar paragraph. Moreover, when the authors do discuss the technical reason for randomized control trials they cite the arguments by Rubin (discussed in an earlier post).
The problem with perpetuating the myth that balancing is implied by randomization, is that lay people and regulators may look askance at unbalanced studies, mistaking "unbalance" for "non-random". Worse, we may see reporting bias and publication bias because studies with unbalanced populations or unbalanced treatment arms are held back. Worse still, we may see (or not see) efforts to "balance" the trial through non-random assignment of patients to treatment arms.
So next time you see a well-balanced study. Beware. It may not be random and the results may be baised.