Box 4 Randomisation and minimisation

 

Simple randomisation

Randomisation based solely on a single, constant allocation ratio is known as simple randomisation [324, 334, 335] Simple randomisation with a 1:1 allocation ratio is analogous to an unbiased coin toss, although tossing a coin is not recommended for sequence generation. No other allocation approach, regardless of its real or supposed sophistication, surpasses the bias prevention and unpredictability of simple randomisation [322, 335].

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Restricted randomisation

Any randomised approach that is not simple randomisation is restricted. Blocked randomisation is the most common form. Other forms, used much less frequently, are methods such as replacement randomisation, biased coin, and urn randomisation [322, 335].

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Blocked randomisation

Blocked randomisation (also called permuted block randomisation) assures that study groups of approximately the same size will be generated when an allocation ratio of 1:1 is used. Blocking can also ensure close balance of the numbers in each group. After every block of 8 participants, for example, 4 would have been allocated to each trial group [336] 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 [337]. Blinding the interventions, using larger block sizes, and randomly varying the block size will help to avoid this problem [322]. Fixed blocks of 2 or 4 are most problematic, as allocation may become predictable for a sizeable proportion of trial participants.

 

Biased-coin and urn randomisation

Biased-coin designs attain the similar objective as blocked designs without forcing strict equality. They therefore preserve much of the unpredictability associated with simple randomisation. Biased-coin designs alter the allocation ratio during the course of the trial to rectify imbalances that might be occurring [322, 335]. Adaptive biased-coin designs, such as the urn design, vary allocation ratios based on the magnitude of the imbalance. However, these approaches are used infrequently.

 

Stratified randomisation

Stratification is used to ensure good balance of participant characteristics in each group. Without stratification, study groups may not be well matched for baseline characteristics, such as age and stage of disease, especially in small trials. Such imbalances can be avoided without sacrificing the advantages of randomisation. Stratified randomisation is achieved by performing a separate randomisation procedure within each of two or more strata of participants (e.g., categories of age or baseline disease severity), ensuring that the numbers of participants receiving each intervention are closely balanced within each stratum. Stratification requires some form of restriction (e.g., blocking within strata) to be effective. The number of strata should be limited to avoid over-stratification [338]. Stratification by centre is common in multicentre trials.

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Minimisation

Minimisation assures similar distribution of selected participant factors between study groups [334, 339]. Randomisation lists are not set up in advance. The first participant 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 (for example, with a probability of 0.8) [340]. The use of a random component is generally preferable [341]. Minimisation has the advantage of creating small groups closely similar in terms of specific desirable participant characteristics at all stages of the trial.

 

Minimisation offers the only acceptable alternative to randomisation, and some have argued that it is superior [342]. Conversely, minimisation lacks the theoretical basis for eliminating bias on all known and unknown factors. Nevertheless, in general, trials that use minimisation are usually considered methodologically similar to randomised trials, even when a random element is not incorporated. For SPIRIT, minimisation is considered a restricted randomisation approach without any judgement as to whether it is superior or inferior to other restricted randomisation approaches.