This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

When planning a randomized clinical trial, careful consideration must be given to how participants are selected for various arms of a study. Selection and accidental bias may occur when participants are not assigned to study groups with equal probability. A simple random allocation scheme is a process by which each participant has equal likelihood of being assigned to treatment versus referent groups. However, by chance an unequal number of individuals may be assigned to each arm of the study and thus decrease the power to detect statistically significant differences between groups. Block randomization is a commonly used technique in clinical trial design to reduce bias and achieve balance in the allocation of participants to treatment arms, especially when the sample size is small. This method increases the probability that each arm will contain an equal number of individuals by sequencing participant assignments by block. Yet still, the allocation process may be predictable, for example, when the investigator is not blind and the block size is fixed. This paper provides an overview of blocked randomization and illustrates how to avoid selection bias by using random block sizes.

The purpose of randomization is to achieve balance with respect to known and unknown risk factors in the allocation of participants to treatment arms in a study [

By probability, a simple randomization scheme may allocate a different number of participants to each study group. This may reduce the power of a statistical procedure to reject the null hypothesis as statistical power is maximized for equal sample sizes [

Block randomization works by randomizing participants within blocks such that an equal number are assigned to each treatment. For example, given a block size of 4, there are 6 possible ways to equally assign participants to a block. Allocation proceeds by randomly selecting one of the orderings and assigning the next block of participants to study groups according to the specified sequence. Note that repeat blocks may occur when the total sample size is greater than the block size times the number of possible orderings. Furthermore, the block size must be divisible by the number of study groups.

A disadvantage of block randomization is that the allocation of participants may be predictable and result in selection bias when the study groups are unmasked. That is, the treatment assignment that has so far occurred least often in the block likely will be the next chosen [

An investigator wishes to compare a family-based educational intervention for childhood weight loss with a standard individual-base program. A planned enrollment of 250 participants, 50 per study site, is to be randomly assigned to the two intervention arms. Below, a computer algorithm written in SAS^{®} (Cary, NC) is presented for performing a block randomization with randomly selected block sizes of 4, 8 and 12 (

The macro works by invoking the ranuni function to equally partition the number of blocks according to a uniform distribution. When the number within the parenthesis of the ranuni function equals zero the seed is determined by the computer system clock. Thus, a different set of block allocations occur each time the macro is executed. Changing the number to a positive integer will assure that the same block allocation is generated during subsequent use of the macro. After the block size is randomly determined the macro efficiently allocates treatment assignment equally within blocks by sorting on the looping index variable. Although the macro only generates 3 randomly selected block sizes the code may be easily modified to increase this number by further partitioning the uniform assignment space. Similarly, the number of study sites and blocks may be increased or decreased by changing the upper range of the two program do-loops. The output of the SAS algorithm corresponding to the first 3 blocks for Site 1 is shown in

A key advantage of blocked randomization is that treatment groups will be equal in size and will tend to be uniformly distributed by key outcome-related characteristics. Typically, smaller block sizes will lead to more balanced groups by time than larger block sizes. However, a small block size increases the risk that the allocation process may be predictable, especially if the assignment is open or there is a chance for unmasking of the treatment assignment. For example, certain immunosuppressive agents change color when exposed to light. This may inadvertently expose the identity of the compound in a clinical trial if the comparator compound is not light sensitive. Unmasking also may be intentional in the case of a physician chemically analyzing a patient’s blood to determine the identity of the randomized drug.

Using a large block size will help protect against the investigator predicting the treatment sequence. However, if one treatment occurs with greater frequency at the beginning of a block, a mid-block inequality can occur if there is an interim analysis or the study is terminated midway through a block. Alternatively, keeping block sizes small and using random sequences of block sizes can ameliorate this problem. Another option is to use larger random block sizes but offset the chance of initial treatment runs within a block by allocating participants using a biased coin approach [

The number of participants assigned to each treatment group will be equal when all the blocks are the same size and the overall study sample size is a multiple of the block size. Furthermore, in the case of unequal block sizes, balance is guaranteed if all treatment assignments are made within the final block [

The advantage of using random block sizes to reduce selection bias is only observed when assignments can be determined with certainty [

The necessity to take into account blocking in the statistical analysis of the data, including when the block sizes are randomly chosen, depends on whether an intrablock correlation exists [

Significant treatment imbalances and accidental bias typically do not occur in large blinded trials, especially if randomization can be performed at the onset of the study. However, when treatment assignment is open and sample size is small than a block randomization procedure with randomly chosen block sizes may help maintain balance of treatment assignment and reduce the potential for selection bias.

The author thanks Katherine T. Jones for valuable comments during the writing of this manuscript and her knowledge and insight are greatly appreciated. The contents of this publication are solely the responsibility of the author and do not necessarily represent the views of any institution or funding agency.

SAS algorithm to perform blocked randomization with random block sizes.

Example output from the SAS algorithm.