Imbalance properties of centre-stratified permuted-block and complete randomisation for several treatments in a clinical trial

Randomisation schemes are rules that assign patients to treatments in a clinical trial. Many of these schemes have the common aim of maintaining balance in the numbers of patients across treatment groups. The properties of imbalance that have been investigated in the literature are based on two treatment groups. In this paper, their properties for K > 2 treatments are studied for two randomisation schemes: centre-stratified permuted-block and complete randomisation. For both randomisation schemes, analytical approaches are investigated assuming that the patient recruitment process follows a Poisson–gamma model. When the number of centres involved in a trial is large, the imbalance for both schemes is approximated by a multivariate normal distribution. The accuracy of the approximations is assessed by simulation. A test for treatment differences is also considered for normal responses, and numerical values for its power are presented for centre-stratified permuted-block randomisation. To speed up the calculations, a combined analytical/approximate approach is used.