Investigating the relationship between predictability and imbalance in minimisation: a simulation study

BACKGROUND: The use of restricted randomisation methods such as minimisation is increasing. This paper investigates under what conditions it is preferable to use restricted randomisation in order to achieve balance between treatment groups at baseline with regard to important prognostic factors and whether trialists should be concerned that minimisation may be considered deterministic. METHODS: Using minimisation as the randomisation algorithm, treatment allocation was simulated for hypothetical patients entering a theoretical study having values for prognostic factors randomly assigned with a stipulated probability. The number of times the allocation could have been determined with certainty and the imbalances which might occur following randomisation using minimisation were examined. RESULTS: Overall treatment balance is relatively unaffected by reducing the probability of allocation to optimal treatment group (P) but within-variable balance can be affected by any P <1. This effect is magnified by increased numbers of prognostic variables, the number of categories within them and the prevalence of these categories within the study population. CONCLUSIONS: In general, for smaller trials, probability of treatment allocation to the treatment group with fewer numbers requires a larger value P to keep treatment and variable groups balanced. For larger trials probability of allocation values from P = 0.5 to P = 0.8 can be used while still maintaining balance. For one prognostic variable there is no significant benefit in terms of predictability in reducing the value of P. However, for more than one prognostic variable, significant reduction in levels of predictability can be achieved with the appropriate choice of P for the given trial design.