Adequate methods of sequence generation

The use of a random component should be sufficient for adequate sequence generation.


Randomization with no constraints to generate an allocation sequence is called simple randomization or unrestricted randomization. In principle, this could be achieved by allocating interventions using methods such as repeated coin-tossing, throwing dice or dealing previously shuffled cards (Schulz 2002c, Schulz 2006).  More usually it is achieved by referring to a published list of random numbers, or to a list of random assignments generated by a computer.  In trials using large samples (usually meaning at least 100 in each randomized group (Schulz 2002c, Schulz 2002d, Schulz 2006), simple randomization generates comparison groups of relatively similar sizes.  In trials using small samples, simple randomization will sometimes result in an allocation sequence leading to groups that differ, by chance, quite substantially in size or in the occurrence of prognostic factors (i.e. ‘case-mix’ variation) (Altman 1999).


Example (of low risk of bias): We generated the two comparison groups using simple randomization, with an equal allocation ratio, by referring to a table of random numbers.


Sometimes restricted randomization is used to generate a sequence to ensure particular allocation ratios to the intervention groups (e.g. 1:1). Blocked randomization (random permuted blocks) is a common form of restricted randomization (Schulz 2002c, Schulz 2006). Blocking ensures that the numbers of participants to be assigned to each of the comparison groups will be balanced within blocks of, for example, five in one group and five in the other for every 10 consecutively entered participants.  The block size may be randomly varied to reduce the likelihood of foreknowledge of intervention assignment.


Example (of low risk of bias): We used blocked randomization to form the allocation list for the two comparison groups. We used a computer random number generator to select random permuted blocks with a block size of eight and an equal allocation ratio. 


Also common is stratified randomization, in which restricted randomization is performed separately within strata. This generates separate randomization schedules for subsets of participants defined by potentially important prognostic factors, such as disease severity and study centres.  If simple (rather than restricted) randomization was used in each stratum, then stratification would have no effect but the randomization would still be valid. Risk of bias may be judged in the same way whether or not a trial claims to have stratified.


Another approach that incorporates both the general concepts of stratification and restricted randomization is minimization, which can be used to make small groups closely similar with respect to several characteristics. The use of minimization should not automatically be considered to put a study at risk of bias. However, some methodologists remain cautious about the acceptability of minimization, particularly when it is used without any random component, while others consider it to be very attractive (Brown 2005).


Other adequate types of randomization that are sometimes used are biased coin or urn randomization, replacement randomization, mixed randomization, and maximal randomization (Schulz 2002c, Schulz 2002d, Berger 2003). If these or other approaches are encountered, consultation with a statistician may be necessary.