title: Investigating the relationship between predictability and imbalance in minimisation: a simulation study.
abstract: 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.
authors.affiliation: Health Services Research Unit, University of Aberdeen, Health Sciences Building, 3rd Floor Foresterhill, Aberdeen, AB25 2ZD, UK. g.mcpherson@abdn.ac.uk
authors.forename: Gladys C
authors.initials: GC
authors.lastname: McPherson
authors.forename: Marion K
authors.initials: MK
authors.lastname: Campbell
authors.forename: Diana R
authors.initials: DR
authors.lastname: Elbourne
mesh_terms: D000465:Algorithms; D015982:Bias; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D015233:Models, Statistical; D018579:Patient Selection; D011897:Random Allocation; D016032:Randomized Controlled Trials as Topic / Q000379:methods* / Q000706:statistics & numerical data; D012107:Research Design / Q000706:statistics & numerical data; D018401:Sample Size; D016896:Treatment Outcome
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