Modified replacement randomization

We propose a slight modification of replacement randomization by imposing an imbalance criterion within a restricted range of patient entry numbers. The bound on imbalance is stated most simply in terms of the maximum allowable difference in treatment assignments at the end of the trial. For clinical trials in which two therapies are compared, we study, by means of computer simulations, the dependence of both selection bias and the mean number of randomization list replacements on the parameters defining the procedure.