Permuted Block Randomization in Clinical Trials
Permuted block randomization (PBR) is a restricted randomization method that ensures close numerical balance between treatment groups throughout a trial by allocating participants in randomly ordered blocks, making it particularly valuable for smaller trials where simple randomization might produce imbalanced groups.
Core Mechanism and Purpose
Blocked randomization ensures that comparison groups are generated according to a predetermined ratio (usually 1:1) and maintains close balance of numbers in each group at any time during the trial. 1 For example, in a block of eight participants, four would be allocated to each arm of the trial, with the order of interventions varying randomly within each block. 1
When to Use Permuted Block Randomization
Trial Size Considerations
In trials of several hundred participants or more, simple randomization can usually be trusted to generate similar numbers in the two trial groups and roughly comparable groups in terms of known and unknown prognostic variables. 1
For smaller trials—and even for trials not intended to be small but that may stop before reaching their target size—restricted randomization procedures like PBR are useful to achieve balance between groups. 1
UK trialists report that simple randomization is suitable for larger trials but carries a high probability of imbalance between treatment groups in small trials. 2
Implementation Requirements
Essential Reporting Elements
When using PBR, authors must provide specific methodological details: 1
- How blocks were generated (e.g., using a permuted block design with a computer random number generator)
- Block size or sizes used
- Whether block size was fixed or randomly varied
- Whether trialists became aware of block sizes (as this knowledge could lead to code breaking)
Stratification Integration
- Stratification requires some form of restriction such as blocking within strata; stratification without blocking is ineffective. 1
- Stratification is particularly useful for smaller trials to ensure good balance of participant characteristics in each group. 1
- Common stratification factors include recruitment site, sex, and disease stage. 1
Critical Limitations and Mitigation Strategies
Predictability Problem
The major drawback of PBR is reduced unpredictability—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 knew the block size. 1 This creates potential for selection bias, particularly in open-label trials. 3
Risk Mitigation Approaches
To address predictability concerns: 1
- Blind the interventions
- Use larger block sizes
- Randomly vary the block size
The preferred method among UK trialists is using permuted blocks of varying random length within strata, which eliminates the problem of predictability while maintaining balance across combinations of factors. 2
Imbalance in Stratified Designs
When there are a large number of strata or block sizes are too large for the number of patients, imbalance can still occur in the trial as a whole despite using PBR within strata. 4 This risk increases with the number of stratification factors used. 1
Comparison with Alternative Methods
Simple Randomization Trade-offs
While simple randomization is "elegantly sophisticated" in being more unpredictable and surpassing the bias prevention levels of all other alternatives, it lacks the balance guarantees of restricted methods. 1
Emerging Alternatives
Newer methods like the block urn design or big stick design can significantly reduce the probability of deterministic assignments while improving covariate balancing capacity compared to traditional stratified PBR. 5
The big stick design (BSD) method can make the allocation process more unpredictable while maintaining the advantages of PBD, though it requires careful implementation to avoid serious imbalance with increasing strata. 3
Merged block randomization offers similar maximum tolerated imbalance as PBR with blocks of size 4 but with added benefit of being less predictable, making it particularly suitable for small clinical trials and multicentre studies. 6
Common Pitfalls
Underreporting is common—many trials show equal or similar group sizes suggesting use of restricted randomization, yet blocking or stratification was not mentioned in publications. 1
Only 9% of trials in specialty journals and 39% in general medical journals reported use of stratification, and only about half mentioned restricted randomization. 1
If trialists become aware of block sizes during the trial, this should be reported as it could compromise allocation concealment. 1