## INTRODUCTION

This JAMA Guide to Statistics and Methods explains the rationale for permuted block randomization and for stratifying randomization in clinical trials.

The most compelling way to establish that an intervention definitively causes a clinical outcome is to randomly allocate patients into treatment groups. Randomization helps to ensure that a certain proportion of patients receive each treatment and that the treatment groups being compared are similar in both measured and unmeasured patient characteristics.1,2 Simple or unrestricted, equal randomization of patients between 2 treatment groups is equivalent to tossing a fair coin for each patient assignment.2,3 As the sample size increases, the 2 groups will become more perfectly balanced. However, this balance is not guaranteed when there are relatively few patients enrolled in a trial. In the coin toss scenario, obtaining several consecutive heads, for example, is more likely than typically perceived.1,4 If a long series of assignments to 1 group occurred when randomizing patients in a clinical trial, imbalances between the groups would occur.

Imbalances between groups can be minimized in small sample–size studies by restricting the randomization procedure. Restricted randomization means that simple randomization is applied within defined groups of patients. Two articles published in JAMA used restrictions on the randomization procedure: Bilecen et al5 used permuted block randomization, a restricted randomization method used to help ensure the balance of the number of patients assigned to each treatment group.3 Kim et al6 used a stratified randomization scheme together with permuted block randomization. Stratified randomization is a restricted randomization method used to balance one or a few prespecified prognostic characteristics between treatment groups.1

## EXPLANATION OF THE CONCEPT

### What Are Permuted Blocks and Stratified Randomization?

The permuted block technique randomizes patients between groups within a set of study participants, called a block. Treatment assignments within blocks are determined so that they are random in order but that the desired allocation proportions are achieved exactly within each block. In a 2-group trial with equal allocation and a block size of 6, 3 patients in each block would be assigned to the control and 3 to the treatment and the ordering of those 6 assignments would be random. For example, with treatment labels A and B, possible blocks might be: ABBABA, BABBAA, and AABABB. As each block is filled, the trial is guaranteed to have the desired allocation to each group.

Stratified randomization requires identification of key prognostic characteristics that are measurable at the time of randomization and are considered to be strongly associated with the primary outcome. The categories of the prognostic characteristics define the strata and the total number of strata for randomization is the product of the number of categories across the selected prognostic characteristics.1,7 Randomization is then performed separately within each stratum.7 For example, if randomization were stratified by sex (men vs women) ...

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