Restricted Randomization: A Practical Example

Bailey, R. A.

doi:10.1080/01621459.1987.10478487

Cited by 19 publications

(2 citation statements)

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“…Several of our findings echo what was already known [ 14 – 18 , 25 , 33 ]. Firstly, any covariates that are balanced in the randomisation should be adjusted for in the analysis, to ensure correct type I errors and greatest power.…”

Section: Discussionsupporting

confidence: 92%

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Mind the gap: covariate constrained randomisation can protect against substantial power loss in parallel cluster randomised trials

Kristunas

Grayling

Gray

et al. 2022

BMC Med Res Methodol

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Background Cluster randomised trials often randomise a small number of units, putting them at risk of poor balance of covariates across treatment arms. Covariate constrained randomisation aims to reduce this risk by removing the worst balanced allocations from consideration. This is known to provide only a small gain in power over that averaged under simple randomisation and is likely influenced by the number and prognostic effect of the covariates. We investigated the performance of covariate constrained randomisation in comparison to the worst balanced allocations, and considered the impact on the power of the prognostic effect and number of covariates adjusted for in the analysis. Methods Using simulation, we examined the Monte Carlo type I error rate and power of cross-sectional, two-arm parallel cluster-randomised trials with a continuous outcome and four binary cluster-level covariates, using either simple or covariate constrained randomisation. Data were analysed using a small sample corrected linear mixed-effects model, adjusted for some or all of the binary covariates. We varied the number of clusters, intra-cluster correlation, number and prognostic effect of covariates balanced in the randomisation and adjusted in the analysis, and the size of the candidate set from which the allocation was selected. For each scenario, 20,000 simulations were conducted. Results When compared to the worst balanced allocations, covariate constrained randomisation with an adjusted analysis provided gains in power of up to 20 percentage points. Even with analysis-based adjustment for those covariates balanced in the randomisation, the type I error rate was not maintained when the intracluster correlation is very small (0.001). Generally, greater power was achieved when more prognostic covariates are restricted in the randomisation and as the size of the candidate set decreases. However, adjustment for weakly prognostic covariates lead to a loss in power of up to 20 percentage points. Conclusions When compared to the worst balanced allocations, covariate constrained randomisation provides moderate to substantial improvements in power. However, the prognostic effect of the covariates should be carefully considered when selecting them for inclusion in the randomisation.

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Section: Discussionsupporting

confidence: 92%

“…Increasing the candidate set size may be able to eliminate this problem. Several authors have discussed the potential validity of restricted randomisations, and these may prove useful in determining the appropriate size of the candidate set for a particular covariate constrained randomisation [ 15 , 33 , 35 , 36 ].…”

Section: Discussionmentioning

confidence: 99%