Open Science
Introduction
Methods
Results
Discussion
Randomisation: Sequence generation
Item 17b: Type of randomisation and details of any restriction (eg, stratification, blocking, and block size)
Examples
“Treatment assignment was generated using a simple randomization scheme . . . given the open-label nature of the intervention to limit the potential bias due to predictable treatment assignment [280]."
“Randomization (1:1) was performed by an independent researcher using computer generated random table numbers, with a block size of 20 and stratified for the indication of the IUI [intrauterine insemination] (mild male factor or unexplained subfertility) [281]."
“Participants were randomized at an individual-level (1:1 ratio) and were stratified by recruitment location (VU [Vrije University] and UvA [University of Amsterdam]). Block randomization was applied with randomly varied block sizes (6–12 allocations per block) [262]."
“Randomization was stratified by treatment centre, clinical severity (<4 vs >4 on a Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) pain subscale standardized to range from 0 to 10), and by whether patients had previously received TENS [transcutaneous electrical nerve stimulation] with randomly varied block sizes of 2, 4, and 6 [282]."
“Randomization sequence was created using Stata 9.0 (StataCorp., College Station, TX) statistical software and was stratified by center with a 1:1 allocation using random block sizes of 2,4, and 6 [283]."
Explanation
In trials of several hundred participants or more, simple randomisation can usually be trusted to generate similar numbers in the two trial groups [284] and to generate groups that are roughly comparable in terms of known and unknown prognostic variables [285]. For smaller trials of fewer than around 200 participants [286], which are common, some form of restricted randomisation procedure to help achieve balance between groups in size or characteristics may be useful (box 6). However, larger trials of greater than approximately 200 participants may also benefit from registration. For example, they may stop before reaching their target size, they may need more power at interim analyses, or they may benefit from stratification with restriction.
Box start
Box 6: Randomisation and minimisation
Simple randomisation
Pure randomisation based on a single allocation ratio is known as simple randomisation. Simple randomisation with a 1:1 allocation ratio is analogous to a coin toss, although we do not advocate coin tossing for randomisation in a randomised trial. The term “simple” is somewhat of a misnomer. While other randomisation schemes sound complex and more sophisticated, in reality, simple randomisation is elegantly sophisticated in that it is more unpredictable and could surpass the bias prevention levels of all other alternatives.
Restricted randomisation
Restricted randomisation specifies any randomised approach that is not simple randomisation. Blocked randomisation is the most common form. Other means of restricted randomisation include replacement, biased coin, and urn randomisation, although these are used much less frequently [286].
Blocked randomisation
Blocking can be used to ensure close balance of the numbers in each group at any time during the trial. After a block of every eight participants was assigned, for example, four would be allocated to each arm of the trial [287]. Improved balance comes at the cost of reducing the unpredictability of the sequence. Although the order of interventions varies randomly within each block, a person running the trial could deduce some of the next treatment allocations if they discovered the block size [288]. Blinding the interventions, using larger block sizes, and randomly varying the block size can ameliorate this problem.
Stratified randomisation
Stratification is used to ensure a good balance of participant characteristics in each group. By chance, particularly in small trials, trial groups may not be well matched for baseline characteristics, such as age and stage of disease. This weakens the trial’s credibility [289]. Such imbalances can be avoided without sacrificing the advantages of randomisation. Stratification ensures that the numbers of participants receiving each intervention are closely balanced within each stratum. Stratified randomisation is achieved by performing a separate randomisation procedure within each of two or more subsets of participants (eg, those defining each centre, age, or disease severity). Stratification by centre is common in multicentre trials. Stratification requires some form of restriction, such as blocking within strata. Stratification without some form of restriction is ineffective.
Minimisation
Minimisation improves balance between intervention groups for several selected patient factors (eg, age) [271, 290]. The first patient is truly randomly allocated; for each subsequent participant, the treatment allocation that minimises the imbalance on the selected factors between groups at that time is identified. That allocation may then be used, or a choice may be made at random with a heavy weighting in favour of the intervention that would minimise imbalance (eg, with a probability of 0.8). The use of a random component is generally preferable. Minimisation has the advantage of creating small groups closely similar in terms of measurable participant characteristics at all stages of the trial.
Minimisation offers the only acceptable alternative to randomisation, and some have argued that it is superior [291]. Conversely, minimisation lacks the theoretical basis for eliminating bias on all known and unknown factors. Nevertheless, in general, trials that use minimisation are considered methodologically equivalent to randomised trials, even when a random element is not incorporated.
Box end
It is important to indicate whether no restriction was used by stating such or by stating that simple randomisation was done. Otherwise, the methods used to restrict the randomisation, along with the method used for random selection, should be specified. For blocked randomisation, authors should provide details on how the blocks were generated (eg, by using a permuted block design with a computer random number generator), the block size or sizes, and whether the block size was fixed or randomly varied. If the trialists became aware of the block size(s), that information should also be reported as such knowledge could lead to them correctly deciphering future treatment assignments. Authors should specify whether stratification was used and, if so, which factors (eg, recruitment site, sex, disease stage) were involved; the categorisation cut-off thresholds within stratums; and the method used for restriction. Although stratification is a useful technique, especially for smaller trials, it can be complicated to implement and may not perform as well as expected if many stratifying factors are used. If minimisation (box 6) was used, it should be explicitly identified, as should the variables incorporated into the scheme; whether a random element was used should also be stated.
With blocking, although the order of interventions varies randomly within each block, individuals running the trial could deduce some of the future treatment allocations if they discovered the block size [288]. Discovering block sizes is much more likely in unblinded trials, where treatment allocations become known after assignment (box 6). Certain techniques, such as large block sizes and randomly varying block sizes, can help prevent the deciphering of future treatment allocations. Unfortunately, particularly with unblinded trials, a review “found that very few trials used techniques that would eliminate the risk of selection bias,” and that “These findings indicate that a substantial proportion of unblinded trials are at risk of selection bias [292]. Indeed, in a recent study of 179 open, unblinded randomised trials, small block sizes were associated with subversion [293].
Only 9% of 206 reports of trials in specialty journals [269] and 39% of 80 trials in general medical journals reported use of stratification [294]. In each case, only about half of the reports mentioned the use of restricted randomisation. Those studies and that of Adetugbo and Williams [295] found that the sizes of the treatment groups in many trials were very often the same or quite similar, yet blocking or stratification had not been mentioned. One of a few possible causes of this close balance in numbers is under-reporting of the use of restricted randomisation, although non-random manipulation of treatment assignments is also suspected. A more recent study of 298 reports of trials in general medical journals found 69% reported the use of a stratified block method [296].