Dynamic Balancing Randomisation: a tree-based method of randomisation and its properties

                 Stephane Heritier, Avinesh Pillai and Val Gebski, 

                NHMRC Clinical Trial Centre, University of Sydney


In the design of randomised clinical trials, balancing of treatment allocation across important 
prognostic factors (strata) improves the efficiency of the final comparisons. Whilst 
randomisation methods exist which attempt to balance treatments across the strata 
(permuted blocks, minimisation), these approaches assign equal importance for all the strata. 
Dynamic Balancing Randomisation (DBR) is a tree-based method proposed by Signorini 
et al. (1995) allowing different levels of imbalance in different strata ensuring a balance for 
each level of prognostic risk factors (conditional balance) whilst at the same time preserving 
randomness. We present a modification to the original approach to maintain a marginal 
balance over important strata and examine the properties of this modification. Two important 
measures of performance are used: a loss function,  which can be interpreted as the 
squared norm of the imbalance vector,  and a forcing index which conveys the degree of 
randomness.  A comparison of the DBR with minimisation (a common randomisation 
procedure for clinical trials) is used to illustrate the advantages of the new method. A 
comparison to the biased coin approach for which the asymptotical behaviour has been 
studied but is not necessarily well known is also made.