Sequence generation

Explanation

Trial protocols must address the type of randomisation planned (Box 4), as this is the defining feature of a randomised trial. If stratification will be used, the stratification categories (including relevant cut-off boundaries) should be reported (e.g., recruitment site, sex, disease stage).

When restricted randomisation is planned, details on restriction (including minimisation) should not appear in the main body of the protocol in order to reduce predictability of the random sequence (Box 5). The details should instead be described in a separate document that is unavailable to trial implementers, such as recruiters, screeners, enrolers, and assigners. For blocked randomisation, this information would include details on how the blocks will be generated (e.g., permuted blocks by a computer random number generator), the block size(s), and whether the block size will be fixed or randomly varied.

Simple randomisation (unrestricted randomisation) can be specified in the main body of the protocol because it is perfectly unpredictable. Its use does not require a separate document.

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)

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)

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.

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.

Box 5 Need for a separate document to describe restricted randomisation

If   some type of restricted randomisation approach is to be used, in particular   blocked randomisation or minimisation, then knowledge of the specific details   could lead to bias.(343, 344) For example, if the   trial protocol for a two-arm, parallel group trial with a 1:1 allocation   ratio states that blocked randomisation will be used and the block size will   be 6, then trial implementers know that the intervention assignments will   balance every 6 participants. Thus, if intervention assignments become known   after assignment, knowing the block size will allow trial implementers to   anticipate when equality of the sample sizes will arise. A sequence can be   discerned from the pattern of past assignments and then some future   assignments could be accurately predicted. For example, if part of a sequence   contained two “As” and three “Bs”, trial implementers would know the last   assignment in the sequence would be an “A”. If the first three assignments in   a sequence contained three “As,” trial implementers would know the last three   assignments in that sequence would be three “Bs.” Selection bias could   result, regardless of the effectiveness of allocation concealment (Item 22).

This   is mainly a problem in open-label trials where everyone becomes aware of the   intervention after assignment. It can also be a problem in trials where   everyone is supposedly blinded (masked), but the blinding is ineffective, or   the intervention harms provide clues such that treatments can be guessed.

We   recommend that trial investigators do not provide full details of a   restricted randomisation scheme (including minimisation) in the trial   protocol. Knowledge of these details might undermine randomisation by   facilitating deciphering of the allocation sequence. Instead, this specific   information should be provided in a separate document with restricted access.   However, simple randomisation procedures could be reported in detail in the   protocol because simple randomisation is perfectly unpredictable.

Summary of key elements to address

● Type of randomisation: simple versus restricted (e.g., blocked); fixed versus adaptive (e.g., minimisation); and where relevant, the reasons for such choices

● If applicable, factors (e.g., recruitment site, sex, disease stage) to be used for stratification, including categories and relevant cut-off boundaries

● For restricted randomisation, aside from the above: all other details on restriction (including minimisation) should be provided in a separate document in order to reduce predictability of the random sequence