multi-micronutrient was based on the digits 0-5 in a computer-generated random sequence by pre-assigned bocks of ... We start with a list of study subjects [with.
Paper 2582-2007
A SAS Algorithm for Blocked Randomization Jimmy T. Efird, Honolulu, HI, Pollie Bith-Melander, Honolulu, HI, Chieko Kimata, Honolulu, HI, Mi-Kyung Hong, San Francisco, CA, Caroline Jiang, Honolulu, HI, and Kathleen Baker, Honoluolu, HI ABSTRACT By chance, a simple random allocation scheme may yield an unbalanced assignment of treatments in a clinical trial, especially when the sample size is small. In this paper, we compare different randomization schemes and present the SAS code for conducting blocked randomization. A clinical trial example is presented to illustrate the potential pitfalls that may be encountered when failing to use blocked randomization.
INTRODUCTION Randomization refers to a process by which each participant has equal likelihood of being assigned to either intervention or control. The purpose of randomization is to create study groups comparable with respect to both known and unknown risk factors, to eliminate bias by the investigator in the allocation of study participants, and to ensure that statistical tests will yield valid significance levels. Biases do occur in randomization. The most common biases that occur in randomization schemes include selection bias and accidental bias. Selection bias occurs when the allocation process is predictable. Accidental bias occurs when the randomization scheme procedure does not achieve balance on risk factors or prognostic covariates. This is particularly important in small studies. By chance, a simple random allocation scheme may yield an unbalanced assignment of treatments in a clinical trial, especially when the sample size is small. In this paper, we compare different randomization schemes and present the SAS code for conducting blocked randomization. A clinical trial example is presented to illustrate the potential pitfalls that may be encountered when failing to use blocked randomization. Various studies have shown the importance of using this procedure. An example illustrating the need for blocked randomization was indicated in a study on the treatment of diabetic patients with picotamide.1) Blocked randomization was performed with a block size of 4 with blinded treatment allocation. Another study utilizing blocked randomization examined the influence of dietary boron insulin metabolism as modified by nutritional stressors.2) A study on the effect of prenatal multi-micronutrient supplementation on gestational length and birth size provides another example of use of blocked randomization, whereby the investigators used blocked randomization to ensure equal distribution of study participants in each treatment arm. The procedure to allocate daily supplementation of multi-micronutrient was based on the digits 0-5 in a computer-generated random sequence by pre-assigned bocks of 3) 4: AABB, ABAB, ABBA, BABA, and BAAB. Containers coded either A or B, in this case, were delivered by the manufacturer with the assigned code in 2 sealed envelopes. In addition, study participants were numbered in consecutive order at the initial recruitment and then each individual was given a number along with instructions to take one tablet with a meal every morning until delivery. This study was double blinded and block randomized. These various studies illustrate the use of blocked randomization to ensure equal distribution of subjects in a clinical trial setting, particularly in study settings with small sample sizes.
RANDOMIZATION Generally, fixed allocation randomization procedures involve assigning the intervention to participants with a prespecified probability and the allocation probability does not change as the study proceeds. Some of the randomization procedures include simple and blocked randomization. Simple randomization refers to the likelihood of selection by unbiased chance with randomization and could be performed by the following techniques:
Tossing an unbiased coin for a randomized trial with two treatments, namely A and B; or Using a random digit table. A randomization list can be generated by using the digits, one for each treatment assignment, beginning with the top row and then proceeding downwards; or Using a random number-producing algorithm, available on most digital computer systems, which is perhaps the most favorable option for simple randomization.
There are some advantages and disadvantages when utilizing these different techniques for simple randomization. One advantage is that each treatment assignment is unpredictable and the assignment of patients to each treatment arm will not be radically different. However, the disadvantage is that there may be an unequal number of individuals by group. For example, one treatment may be assigned more often than another in one treatment arm. Another issue is chronological bias. In this case, one treatment regimen may be given with greater frequency at the beginning of a
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trial and another regimen with greater frequency at the end of the trial. Because of these issues, simple randomization is not ideal to use, even for large studies. Alternatively, blocked randomization (sometimes referred to as permuted block randomization) ensures a high probability of an equal number of individuals in each treatment arm by sequencing patient assignments by block. Blocked randomization is used to eliminate imbalances in the number of participants assigned in each group, imbalances that can occur as described above in simple randomization.4) In blocked randomization, a table of randomization is used; this table contains, in random order, all possible combinations of a small series of figures. Assuming participants are randomly assigned with equal probability to groups A or B, then for each block of even size (such as 4, 6, or 8), half of the participants will be assigned to group A and the other half to group B.5) The order of the interventions that are assigned to each block is randomized. The process is repeated for consecutive blocks until all participants are randomized. This example of blocked randomization is that used for a typical two-arm trial. The advantage to this randomization scheme is that the numeric balance of study subjects in each group is guaranteed during the course of randomization. In other words, the number in each group will not differ by more than b/2 when b is the length of the block. The following example demonstrates the utility of this procedure. We start with a list of study subjects [with 6) certain adjacent positions], which are grouped into blocks. Assuming that the block size is 4, we then assign positions 1-4 to the first block, 5-8 to the second block, 9-12 to the third block, and 13-16 to the fourth block. We also assume a two-arm trial, which results in block numbers being even. In this case, within a block, 50% of subjects will be assigned to the control group and the other 50% will be assigned to the intervention group. Generally, there is no particular block size recommended, as long as a multiple of the number of treatment arms is used.7) However, this theory works in principle only. If the block size is large and recruitment ends midway through a block, all participants in the first part of the final block may be assigned to the same treatment group, thus creating unbalanced group sizes. Hence choosing a smaller block size with only two assignments per block for a two-arm trial is preferable. At the same time, a special case of blocked randomization can be used if the number of subjects are known and identified in advance, and if all are to be randomized at once. All subjects on the list can be put in one block. The list can then be shuffled into random order. Subjects who end up in the top half can be assigned to the intervention group and the remaining individuals assigned to the control group. Blocked randomization is used to ensure that there is a matter of uncertainty when selecting study subjects. There are some disadvantages to using blocked randomization schemes in a clinical trial. One particular disadvantage is that the final analysis may be quite complex. Another contention is that changing block size may cause the randomization to be predictable. Finally, mid block inequality can occur if there is an interim analysis intended.
THE SAS PROC PLAN The SAS Program consists of a series of SAS statements that are used to define, read in, analyze, and manipulate the data. The typical SAS program, therefore, includes three parts: Data Definition and Options; Data Steps; and Procedure(s). Specifically, the Proc Plan procedure constructs, designs, and randomizes plans for factorial experiments. This includes nested and crossed experiments and randomized block designs. The procedure can produce a printed listing, show the assignment of experimental conditions to experimental units, and produce an output data set. The Proc Plan procedure can construct the following types of experimental designs: • • • •
Full factorial with and without randomization; Certain balanced (or partially incomplete) block designs; Generalized cyclic incomplete block designs; and Latin square designs.
The SAS code to perform blocked randomization is the procedure entitled Proc Plan. The Proc Plan is known to be used in the blocked randomization procedure in clinical trials. An example of this procedure was presented by Zhang et al (PharmaSUG 2005). Zhang et al illustrated how to use the SAS/InterNet application.8) In any clinical trial, a randomization list of subjects is required initially. The next step is to produce parameters, which include total sample size, names of treatment arms, number of treatments, ratio of treatments, and block size, study site, number of sites, sample size for each site, and other variables. A computer-generated procedure for blocked randomization will be displayed on a screen that has various line items, which includes fill-in blanks for the total sample size and the 9) number of study treatments (including both placebo and control). Also, there is a category entitled Scenarios, which provides the following information: a) b)
Randomization for the whole study sample with a button to click to select With Blocked Randomization or Without Blocked Randomization; and Randomization by study site and unit with a button to click to select With Blocked Randomization or Without Blocked Randomization.
Similarly, there is a screen for parameters and there is a button to click to submit the information. Proc Plan then generates a randomization sequence. An example of the generated code consists of the following: 2
TABLE 1: BLOCKED RANDOMIZATION USING THE PROC PLAN * randomization within block; %macro ran_block (blockNum); … %if &seed= %then %do; proc plan; factors N=&blocksize / noprint; output data=One out=Two run; %end; %else %do; Proc plan seed=%eval (&seed+blockNum); Factors N=&blockSize / noprint; Output data=One out=Two; Run; %end; … %mend ran_block; Reference: Zhang et al. (2005). A Dynamic SAS/IntrNet Example with Help of ASP and JavaScript: Online Clinical Trial Randomization List Generator. In SAS PharmaSUG Proceedings: Internet and the Web. PharmaSUG 2005, May 22-25, Phoenix, Arizona.
SAS CODE FOR CONDUCTING BLOCKED RANDOMIZATION Blocked randomization also may be programmed directly in SAS using data step coding. For example, the SAS code in Table 2 generates a randomization scheme for 15 blocks of size 6 for 5 sites in a study assigning participants to either an intervention or non-intervention arm.
TABLE 2: SAS CODE FOR CONDUCTING BLOCKED RANDOMIZATION %macro lp1(x); %do i=1 %to 5; %do j=1 %to 15; data six; do j=1 to 6; x=ranuni(0); output; end; proc sort;; by x; data a1; set six; if _n_
