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Endgames Statistical Question

Treatment allocation by minimisation

BMJ 2013; 347 doi: https://doi.org/10.1136/bmj.f6569 (Published 01 November 2013) Cite this as: BMJ 2013;347:f6569
  1. Philip Sedgwick, reader in medical statistics and medical education
  1. 1Centre for Medical and Healthcare Education, St George’s, University of London, London, UK
  1. p.sedgwick{at}sgul.ac.uk

Researchers assessed the effectiveness of adenoidectomy in children with recurrent upper respiratory tract infections. An open randomised controlled trial study design was used. The intervention was immediate adenoidectomy, with or without myringotomy. Control treatment was a strategy of initial watchful waiting.1

The trial participants were 111 children aged 1-6 years with recurrent upper respiratory tract infections who had been selected for adenoidectomy. Participants were recruited from 13 sites, including 11 general hospitals and two academic centres. Children were allocated to treatment using minimisation to control for age (<2 and ≥2 years) and site of recruitment. Length of follow-up was a maximum of 24 months.

The primary outcome measure was the number of upper respiratory tract infections per person year during follow-up. No significant difference was seen between treatment groups, with 7.91 episodes of upper respiratory tract infections per person year in the adenoidectomy group and 7.84 in the control group (difference in incidence rate 0.07, 95% confidence interval −0.70 to 0.85). It was concluded that in children selected for adenoidectomy with recurrent upper respiratory tract infections, immediate surgery confers no clinical benefits over a strategy of initial watchful waiting.

Which of the following statements, if any, are true?

  • a) Minimisation was used to achieve a balance in the numbers of participants and baseline characteristics between treatment groups

  • b) Each participant had an equal probability of being allocated to the intervention or control group.

  • c) For each participant recruited to the trial, treatment allocation depended on his or her individual characteristics

Answers

Statements a and c are true, whereas b is false.

The purpose of the trial was to assess the effectiveness of adenoidectomy in children with recurrent upper respiratory tract infections. The control treatment was a strategy of initial watchful waiting. The proposed sample size was small. If simple random allocation (commonly known as random allocation or randomisation) had been used to allocate participants to treatment it would not have guaranteed equal numbers in each group. Treatment groups are more likely to have equal numbers of participants when sample sizes are large. If treatment groups do not have similar numbers of participants, baseline characteristics are unlikely to be comparable and confounding may occur. Therefore, differences between treatment groups in outcome may not be due to differences in treatment but to differences in prognostic factors. Complex statistical analysis will then be needed, and the results of such analysis may not be reliable because it is not always possible to measure and adjust for pertinent prognostic factors.

Treatment allocation by minimisation achieves a balance between treatment groups in the numbers of participants and baseline characteristics (a is true). In the above trial, age and site of recruitment were considered to be important prognostic factors that would affect outcome. These factors were controlled for to ensure a balance between treatment groups at baseline.

With treatment allocation by minimisation, each participant did not have an equal probability of being allocated to the intervention or control group (b is false). The first participant to be recruited was allocated to treatment using simple random allocation. However, each subsequent participant was allocated to treatment so as to minimise the imbalance between treatment groups with respect to age and site of recruitment.

The method is best illustrated by a fictitious example. Consider that 15 participants have already been recruited to the trial and allocated to treatment. The next participant to be allocated to treatment is aged under 2 years and recruited from the first (of 11) general hospitals. To decide which treatment the patient is allocated, the balance of participants already recruited to the trial with the same age and site of recruitment as the next patient to be allocated is compared between treatment groups (c is true). There are various methods for assessing the balance. The most popular is to sum, for each treatment group, the frequencies across each of the prognostic factors for those participants already recruited who have the same characteristics as the next patient to be allocated treatment. In the above trial, this would have involved summing, for each treatment group, the total number of participants aged under 2 years plus the total number recruited from the first (of 11) general hospitals.

Consider that, of the 15 participants recruited to the trial so far, seven have been allocated to adenoidectomy; four of these seven were aged less than 2 years and one was recruited from the first (of 11) general hospitals. Of the eight participants to have been allocated to control, five were aged under 2 and two were recruited from the first (of 11) general hospitals. Therefore, for adenoidectomy, the sum of the frequencies for the characteristics of the next patient to be allocated treatment was: 4 (age) + 1 (site of recruitment)=5, whereas for the control treatment this was 5 (age) + 2 (site of recruitment)=7. For the characteristics of age under 2 years and site of recruitment (first of 11 general hospitals) there is an imbalance in favour of control. The next participant would therefore be allocated to the treatment with the lowest total score—that is, the adenoidectomy treatment group. If the scores had been tied between treatment groups, then treatment allocation would have been chosen purely at random. After the treatment allocation had been determined for the current participant, the frequencies for each category of age and site of recruitment would be updated and the process repeated for subsequent participants.

Treatment allocation by minimisation is sometimes referred to as a dynamic randomisation method because it depends on the characteristics of the next participant to enter the trial, as described above (c is true). However, given that treatment allocation for a patient recruited to the trial depends on the characteristics of participants already recruited to the trial and those of the patient to be allocated, treatment allocation is almost entirely predictable. Therefore, it is recommended that each treatment allocation incorporates a random element. A weighted allocation may be used so that there is a high probability—for example 0.80, that the next participant receives the treatment that minimises the imbalance between treatment groups. By introducing a random element it makes treatment allocation less predictable. This would minimise any potential bias in treatment allocation on behalf of those who are recruiting participants and the patients themselves. Although this is obviously desirable, treatment allocation should be concealed until after allocation. Allocation concealment has been described in a previous question.2 Introduction of this random element will result in a greater imbalance between treatment groups than if it had not been used. However, there will still be a greater balance between treatment groups than if simple random allocation had been used.

Minimisation is referred to as a restricted randomised method because it involves randomisation but does not constitute simple random allocation. Restricted randomisation will ensure a greater balance between treatment groups in sample size and prognostic factors at baseline. Probably the most common type of restricted randomisation is block randomisation, described in a previous question,3 which ensures similar numbers of participants in each treatment group. For each consecutive block of patients, the size of which is a multiple of the number of treatment groups, participants are allocated to treatment in a random order, with an equal number allocated to each treatment in each block.

Other types of restricted randomisation include stratified allocation, described in a previous endgame.4 Stratified randomisation involves the random allocation of patients to treatment within each stratum of a prognostic factor, thereby balancing the characteristics of patients allocated to each treatment group. However, stratified allocation will achieve comparability between treatment groups in baseline characteristics and sample size only if block randomisation is incorporated within the stratum. The method is referred to as stratified block randomisation, or often simply as stratified randomisation.

In the above trial, treatment allocation by minimisation was chosen in preference to stratified block randomisation because it is more effective at balancing the numbers of participants and prognostic factors at baseline between treatment groups when the sample size is small. If there are several variables to be controlled for, stratified block randomisation can lead to large numbers of strata. In the above trial, the prognostic factors of age (<2 and >2 years) and site of recruitment (11 general hospitals and two academic centres) would have resulted in 26 strata in total. It would have been difficult to incorporate block randomisation within each stratum, and it might have led to a large number of incomplete blocks—that is, it might not have been possible to recruit complete blocks of patients into each stratum. Therefore, it is unlikely that the treatment groups would have been balanced with respect to the numbers of participants and baseline characteristics after the allocation of all patients. Treatment allocation by minimisation avoided this problem, and in particular it ensured that there was a balance between treatment groups after the allocation of each participant recruited to the trial.

Notes

Cite this as: BMJ 2013;347:f6569

Footnotes

  • Competing interests: None declared.

References

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