Adaptive biased urn randomization in small strata when blinding is impossible

Adaptive biased urn randomization, applied in, e.g., a clinical trial, has certain attractive properties. If stratified randomization is desired, a good balance between group sizes can be guaranteed, even in (very) small strata. Yet treatment assignment may be kept unpredictable, which is necessary to avoid selection bias if blinding is impossible. In the present paper a more flexible urn model is described. The investigator may choose assignment probabilities that strongly depend on the degree of imbalance when the groups are still small, but with a tendency toward complete randomization when the groups become large. It is also possible to keep the difference in group size below a chosen maximum, which is useful if population characteristics may change during the course of a trial. The new urn model includes random permutations and complete randomization as special cases. An extension of the model allows the promotion of unequal group sizes. Some attention is paid to a randomized version of the minimization method.