### Introduction

^{1)}, a set of guidelines proposed to improve completeness of the clinical study report, also includes randomization. Randomization plays a crucial role in increasing the quality of evidence-based studies by minimizing the selection bias that could affect the outcomes. In general, randomization places programming for random number generation, random allocation concealment for security, and a separate random code manager. After then, the generated randomization is implemented to the study [2]. Randomization is based on probability theory and hence difficult to understand. Moreover, its reproducibility problem requires the use of computer programming language. This study tries to alleviate these difficulties by enabling even a non-statistician to understand randomization for a comparative RCT design.

### Methods of Randomization

### Simple randomization

^{2)}but it cannot prevent the imbalances in the sample size or prognostic factors that are likely to occur as the number of subjects participating in the study decreases. If the ratio of number of subjects shows an imbalance, that is, it is not 1 : 1, even with the same number of subjects participating, the power of the study will fall. In a study involving a total of 40 subjects in two groups, if 20 subjects are allocated to each group, the power is 80%; this will be 77% for a 25/15 subject allocation and 67% for a 30/10 subject allocation (Fig. 1).

^{3)}In addition, it would be difficult to consider a 25/15 or 30/10 subject allocation as aesthetically balanced.

^{4)}In other words, the balancing of subjects seems plausible to both researchers and readers. Unfortunately, the nature of simple randomization rarely lets the number of subjects in both groups to be equal [6]. Therefore, if it is not out of the range of the assignment ratio (e.g., 45%–55%),

^{5)}it is balanced. As the total number of subjects increases, the probability of departing from the assignment ratio, that is, the probability of imbalance, decreases. In the following, the total number of subjects and the probability of imbalance were examined in the two-group study with an assignment ratio of 45%–55% (Fig. 2). If the total number of subjects is 40, the probability of the imbalance is 52.7% (Fig. 2, point A), but this decreases to 15.7% for 200 subjects (Fig. 2, point B) and 4.6% for 400 subjects (Fig. 2, point C). This is the randomization method recommended for large-scale clinical trials, because the likelihood of imbalance in trials with a small number of subjects is high [6–8].

^{6)}However, as the number of subjects does not always increase, other solutions need to be considered. A block randomization is helpful to resolve the imbalance in number of subjects, while a stratified randomization and an adaptive randomization can help resolve the imbalance in prognostic factors.

### Block randomization

^{7)}When using blocks, we need to apply multiple blocks and randomize within each block. At the end of block randomization, the number of subjects can easily be balanced, and the maximum imbalance in the study can be limited to an appropriate level. That is, block randomization has the advantage of increasing the comparability between groups by keeping the ratio of the number of subjects between groups almost the same. However, if the block size is 2, the allocation result of the second subject in the block can be easily predicted with a high risk of observation bias.

^{8)}Therefore, the block size used should preferably be 4 or more. However, note that even when the block size is large, if the block size is known to the researcher, the risk of selection bias will increase because the treatment of the last subject in the block will be revealed. To reduce the risk of predictability from the use of one block size, the size may be varied.

^{9)}

### Restricted randomization for unbalanced allocation

### Stratified randomization

^{10)}in the number of subjects allocated to the treatment group. To reduce this risk, the prognostic factors should be carefully selected. These prognostic factors should be considered again during the statistical analysis and at the end of the study.

### Adaptive randomization

#### Minimization^{11)}

^{12)}First, the total number of imbalances is calculated after virtually allocating a newly recruited subject to all groups, respectively. Then, each group has its own the total number of imbalances. Here, this subject will be allocated to the group with lowest total number of imbalances.