Logic Argument of Research Article s1

Chapter 3-7. Randomize Using Excel

In the last chapter, we practiced taking a random sample.

In this chapter, we practice randomizing subjects into two treatment arms. This is easier to set up in Excel than in Stata.

Simon (1999) presents a simple approach to randomizing subjects to two or more experimental groups, which is the approach we will use.

To give a quick overview of what we are going with this topic, here is a suggestion for describing it to a colleague.

Suggestion for Advising Someone on Randomization

You should use a method called “random permuted blocks”. If you have two groups to assign subjects to, for example, you want the first two subjects to go into group A or group B in a random order. For the next two subjects, this is repeated, by the random order is selected independently of the previous two subjects. This is called a block of size 2. It might look something like: AB, BA, BA, AB, …where each block of size 2 will contain a possible permutation of the group assignments in a random order (thus, “random permuted blocks”). In this way, you achieve balance between the groups as the study progresses, with equal numbers in each group, which insures the groups remain balanced on any possible “learning effect”, such as the study team gets better at the study procedure as the study progresses. This also insures that the sample sizes are equal if the study has to be stopped early. A randomization schedule is created. One column contains the numbers 1 to N, which is the order that the subjects are enrolled. This number is placed on the outside of an envelope. Inside the envelope is the group assignment. When the subject is enrolled, the envelope is opened to discover the group assignment. An improvement over this is called “random permuted blocks with random block size”. In the approach described above, the study coordinator would be able to guess the group assignment of subjects 2, 4, etc., since the subject would be assigned to the opposite group of the previous subject, subject 1, 3, etc. To avoid this, a block size of 2, 4, and perhaps 6, is used, with the order of the block size randomized. This makes it impossible to guess the next subject’s assignment, because the coordinator will never know what block size is currently being used.

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Source: Stoddard GJ. Biostatistics and Epidemiology Using Stata: A Course Manual [unpublished manuscript] University of Utah School of Medicine, 2011. http://www.ccts.utah.edu/biostats/?pageId=5385

Chapter 3-7 (revision 14 Jul 2011) p. 1

Suggested Citation

The random permuted blocks approach, with or without random block sizes, is a well-establish procedure, so there is no need to give a citation for it, particularly in a research paper. However, if you are nervous that a grant reviewer will be unfamiliar with it, a good citation for both approaches is:

Friedman LM, Furberg CD, DeMets DL. Fundamentals of Clinical Trials, 3rd ed., New York, Springer, 1998, pp.64-66.

There is no need to cite the Simon (1999) paper, since that just a paper describing specifically how to do it in Excel, rather than an authoritative description and justification of these randomization methods.

Example: Here is an example of researchers using random permuted blocks for their randomization into study groups (Kuhn et al., N Engl J Med, 2008). In their Randomization subsection of their Methods section, they report,

“At 1 month post partum, participants who were still breast-feeding their infants (whose HIV status had not yet been determined) and were willing to continue with the study were randomly assigned to a study group with the use of a computer algorithm that was designed by the study statistician with a randomized permuted-block design within each site….”

Example: Here is an example of researchers using random permuted blocks with random block size for their randomization into study groups (Kirkley et al., N Engl J Med, 2008). In their Study Treatment subsection of their Methods section, they report,

“The patients were randomly assigned, with the use of a computer-generated schedule, to receive optimized physical and medical therapy alone (control group) or to receive both optimized physical and medical therapy and arthroscopic treatment….To minimize the risk of predicting the treatment assignment of the next eligible patient, randomization was performed in permuted blocks of two or four with random variation of the blocking number.”

Simple Randomization

Suppose we want to randomize 10 subjects to 2 groups (intervention & control), with 5 in each group. The first step is to prepare a randomization list.

Enter the column headings Sequence and Group into cells A1 and B1, respectively. To enter the sequence number, enter “1” into cell A2, click on the lower right corner of the cell, hold down the Ctrl-key and drag downward for 10 rows. This will fill up the first column with the numbers 1 to 10. Enter “intervention” into cell B2, click on the cell, and drag down 5 rows (when you do not hold down the Ctrl-key, it simply duplicates the cell contents.) Enter “control” into cell B7, click on the cell, and drag down 5 rows. The spreadsheet should now look like this:

A B 1 Sequence Group 2 1 intervention 3 2 intervention 4 3 intervention 5 4 intervention 6 5 intervention 7 6 control 8 7 control 9 8 control 10 9 control 11 10 control

This has all of the group assignments we need (5 in each group). It simply needs to be put into a random order. To do that, we add a column of random numbers (uniform random numbers, ranging between 0 and 1). Add the heading RandNum into cell C1. Enter =rand() into cell C2. When you hit the Enter key, a random number replaces what you typed. Click on the number in cell C2. Drag down to row 11, which will fill the column with random numbers.

Your spreadsheet will now look like the following (except your random numbers will be different):

A B C 1 Sequence Group RandNum 2 1 intervention 0.131791 3 2 intervention 0.535269 4 3 intervention 0.08444 5 4 intervention 0.495398 6 5 intervention 0.514196 7 6 control 0.132303 8 7 control 0.558167 9 8 control 0.968525 10 9 control 0.098076 11 10 control 0.41867

The problem with what we have so far, is that these random numbers will automatically change each time the spreadsheet is updated (saving the file and opening it again, for example, will change all the random numbers). To fix the numbers so they are just values that cannot change, rather than calls to the function rand(), highlight the entire column of numbers, from cell C2 to C11. Click on Edit - Copy, then Click on Edit - Paste Special, select Paste - Values, and click OK. This makes the numbers permanent.

The best thing to do next is to copy all of these cells and paste them a few columns to the right, in the spreadsheet. That way, you have two tables to compare to make sure the randomization step (discussed next) worked correctly. It also gives you a way to recover easily if you make a mistake or simply want to start over.

Now we will randomize the group assignments. Highlight the the Group and RandNum columns of your second (duplicated) table. [It does not matter whether or not you include the entire column, or include the variable names (Group and RandNum), when you highlight the columns —Excel is clever enough to consider the first row as column headings, and so the first row does not get sorted along with the other cells.] Click on Data - Sort. Enter RandNum in the “Sort by” box, and then click OK.

Your table will now be sorted by the random numbers and the group column will be scrambled (Chaos created from Order).

A B C 1 Sequence Group RandNum 2 1 intervention 0.08444 3 2 control 0.098076 4 3 intervention 0.131791 5 4 control 0.132303 6 5 control 0.41867 7 6 intervention 0.495398 8 7 intervention 0.514196 9 8 intervention 0.535269 10 9 control 0.558167 11 10 control 0.968525

Random Permuted Blocks

The simple randomization approach will work for situations such as randomizing hospital units.

For the clinical trial situation, where subjects enter the study across time, a different approach is required. The problem with the simple randomization approach in this case is that an unequal sample size will accumulate in the two study arms as the study progresses, becoming balanced only at the end.

To assure balance as the data accumulate, which will help to avoid a “learning curve” bias, or any bias introduced by the time of entry into the study, a block randomization is used. We will use a block size of 2, so balance is achieved after every two subjects enter the study. [Any block size, that is a multiple of the number of groups, could be used.]

Beginning with the following columns (our randomization list from above before we sorted),

A B C 1 Sequence Group RandNum 2 1 intervention 0.131791 3 2 intervention 0.535269 4 3 intervention 0.08444 5 4 intervention 0.495398 6 5 intervention 0.514196 7 6 control 0.132303 8 7 control 0.558167 9 8 control 0.968525 10 9 control 0.098076 11 10 control 0.41867

, highlight and copy that into another location on your spreadsheet. Then, add the following Block column to the left of the RandNum column. [To insert a column, highlight the RandNum column, right click the mouse, and click on Insert.]

E F G H 1 Sequence Group Block RandNum 2 1 intervention 1 0.131791 3 2 intervention 2 0.535269 4 3 intervention 3 0.08444 5 4 intervention 4 0.495398 6 5 intervention 5 0.514196 7 6 control 1 0.132303 8 7 control 2 0.558167 9 8 control 3 0.968525 10 9 control 4 0.098076 11 10 control 5 0.41867

Next, highlight the columns F through H, using the mouse.

E F G H 1 Sequence Group Block RandNum 2 1 intervention 1 0.131791 3 2 intervention 2 0.535269 4 3 intervention 3 0.08444 5 4 intervention 4 0.495398 6 5 intervention 5 0.514196 7 6 control 1 0.132303 8 7 control 2 0.558167 9 8 control 3 0.968525 10 9 control 4 0.098076 11 10 control 5 0.41867

Click on the Data icon on the toolbar. Select “Sort”, then Sort by: Block Then by: RandNum OK

Chapter 3-7 (revision 14 Jul 2011) p. 6 which produces,

A B C D 1 Sequence Group Block RandNum 2 1 intervention 1 0.131791 3 2 control 1 0.132303 4 3 intervention 2 0.535269 5 4 control 2 0.558167 6 5 intervention 3 0.08444 7 6 control 3 0.968525 8 7 control 4 0.098076 9 8 intervention 4 0.495398 10 9 control 5 0.41867 11 10 intervention 5 0.514196

Notice that an intervention and a control are used every two rows of the randomization list, creating sample size balance every two study subjects.

This is called “random permuted blocks” because the permutations “AB” and “BA”, or “Intervention-Control” and “Control-Intervention”, are randomized, rather than just A and B.

Random Permuted Blocks With Randomized Block Sizes

If an investigator is attempting to guess what group the next patient will be randomized to, and has noticed that balance appears to be accomplished every two patients in an un-blinded study, the investigator can introduce bias by decided whether or not to enroll the next patient.

One solution is to use a large block size, say 20, instead of 2. It is also a good idea to not inform the investigator that blocks are used in the randomization.

Another approach is to use multiple block sizes. For a two-arm study, you might use block sizes of 2, 4, and 6 in a random order. This would make it particularly difficult for the investigator to keep track.

To illustrate, let’s say the sample size will be 12 in each group, so we can use two each of block sizes 2, 4, and 6.

1) Start by creating the Sequence column, which establishes the sample size and provides an ID number for the order in which patients will enter the study.

A Sequence 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

2) Copy that column and add two new columns, creating one each of the desired block sizes:

C D E Sequence Group BlockSize 1 Intervention 2 2 Control 2 3 Intervention 4 4 Intervention 4 5 Control 4 6 Control 4 7 Intervention 6 8 Intervention 6 9 Intervention 6 10 Control 6 11 Control 6 12 Control 6 13 14 15 16 17 18 19 20 21 22 23 24

3) Copy those columns and add one new column, providing a random number in the first cell of each block, using “=rand()”.

G H I J Sequence Group BlockSize RandNumBlock 1 Intervention 2 0.615181 2 Control 2 3 Intervention 4 0.175673 4 Intervention 4 5 Control 4 6 Control 4 7 Intervention 6 0.427291 8 Intervention 6 9 Intervention 6 10 Control 6 11 Control 6 12 Control 6 13 14 15 16 17 18 19 20 21 22 23 24

4) Copy this to new columns. The, copy the cells in the last three columns and paste just below them. Notice that the random numbers changed, which is fine (they update every time a change is made to the spreadsheet).

L M N O Sequence Group BlockSize RandNumBlock 1 Intervention 2 0.36642 2 Control 2 3 Intervention 4 0.51709 4 Intervention 4 5 Control 4 6 Control 4 7 Intervention 6 0.73186 8 Intervention 6 9 Intervention 6 10 Control 6 11 Control 6 12 Control 6 13 Intervention 2 0.38613 14 Control 2 15 Intervention 4 0.05518 16 Intervention 4 17 Control 4 18 Control 4 19 Intervention 6 0.391385 20 Intervention 6 21 Intervention 6 22 Control 6 23 Control 6 24 Control 6

5) We are now ready to fix the random numbers so they do not change. Copy and paste the RandNum column onto itself, using “Paste Special”, as described on page 2.

6) Copy these into new columns. Then, highlight each RandNum number and drag it into the empty cells just below it, so that each row of a block has an identical random number.

Q R S T Sequence Group BlockSize RandNumBlock 1 Intervention 2 0.36642 2 Control 2 0.36642 3 Intervention 4 0.51709 4 Intervention 4 0.51709 5 Control 4 0.51709 6 Control 4 0.51709 7 Intervention 6 0.73186 8 Intervention 6 0.73186 9 Intervention 6 0.73186 10 Control 6 0.73186 11 Control 6 0.73186 12 Control 6 0.73186 13 Intervention 2 0.38613 14 Control 2 0.38613 15 Intervention 4 0.05518 16 Intervention 4 0.05518 17 Control 4 0.05518 18 Control 4 0.05518 19 Intervention 6 0.391385 20 Intervention 6 0.391385 21 Intervention 6 0.391385 22 Control 6 0.391385 23 Control 6 0.391385 24 Control 6 0.391385

This RandNumBlock column will be used later to randomize the order of the blocks.

7) Copy these into new columns. Then, add a second column of random numbers in the first cell and drag it all the way to the bottom, filling in the entire column.

V W X Y Z Sequence Group BlockSize RandNumBlock RandNumGroup 1 Intervention 2 0.36642 0.2407044 2 Control 2 0.36642 0.1607768 3 Intervention 4 0.51709 0.4609201 4 Intervention 4 0.51709 0.1547385 5 Control 4 0.51709 0.8725464 6 Control 4 0.51709 0.1919791 7 Intervention 6 0.73186 0.4904566 8 Intervention 6 0.73186 0.8843401 9 Intervention 6 0.73186 0.8812662 10 Control 6 0.73186 0.7756594 11 Control 6 0.73186 0.6503676 12 Control 6 0.73186 0.7629637 13 Intervention 2 0.38613 0.6910306 14 Control 2 0.38613 0.7458984 15 Intervention 4 0.05518 0.8386934 16 Intervention 4 0.05518 0.807224 17 Control 4 0.05518 0.477761 18 Control 4 0.05518 0.4581632 19 Intervention 6 0.391385 0.8722347 20 Intervention 6 0.391385 0.8057507 21 Intervention 6 0.391385 0.8545892 22 Control 6 0.391385 0.6339632 23 Control 6 0.391385 0.1114622 24 Control 6 0.391385 0.7572725

8) Copy and Paste Special Values this second column of random numbers, making them fixed

9) Copy these into new columns. Highlight all columns but the Sequence column. Then on the menu bar, click on Data, click on Sort, Sort by RandNumBlock, Then by RandNumGroup, OK.

AB AC AD AE AF Sequence Group BlockSize RandNumBlock RandNumGroup 1 Intervention 2 0.36642 0.2407044 2 Control 2 0.36642 0.1607768 3 Intervention 4 0.51709 0.4609201 4 Intervention 4 0.51709 0.1547385 5 Control 4 0.51709 0.8725464 6 Control 4 0.51709 0.1919791 7 Intervention 6 0.73186 0.4904566 8 Intervention 6 0.73186 0.8843401 9 Intervention 6 0.73186 0.8812662 10 Control 6 0.73186 0.7756594 11 Control 6 0.73186 0.6503676 12 Control 6 0.73186 0.7629637 13 Intervention 2 0.38613 0.6910306 14 Control 2 0.38613 0.7458984 15 Intervention 4 0.05518 0.8386934 16 Intervention 4 0.05518 0.807224 17 Control 4 0.05518 0.477761 18 Control 4 0.05518 0.4581632 19 Intervention 6 0.391385 0.8722347 20 Intervention 6 0.391385 0.8057507 21 Intervention 6 0.391385 0.8545892 22 Control 6 0.391385 0.6339632 23 Control 6 0.391385 0.1114622 24 Control 6 0.391385 0.7572725

10) It now looks like this. Notice that the block sizes are jumbled up, as well as the group assignments within each block. This is what we were after.

Sequence Group BlockSize RandNumBlock RandNumGroup 1 Control 4 0.05518 0.458163 2 Control 4 0.05518 0.477761 3 Intervention 4 0.05518 0.807224 4 Intervention 4 0.05518 0.838693 5 Control 2 0.36642 0.160777 6 Intervention 2 0.36642 0.240704 7 Intervention 2 0.38613 0.691031 8 Control 2 0.38613 0.745898 9 Control 6 0.391385 0.757272 10 Control 6 0.391385 0.111462 11 Control 6 0.391385 0.633963 12 Intervention 6 0.391385 0.805751 13 Intervention 6 0.391385 0.854589 14 Intervention 6 0.391385 0.872235 15 Intervention 4 0.51709 0.154739 16 Control 4 0.51709 0.191979 17 Intervention 4 0.51709 0.46092 18 Control 4 0.51709 0.872546 19 Intervention 6 0.73186 0.490457 20 Control 6 0.73186 0.650368 21 Control 6 0.73186 0.762964 22 Control 6 0.73186 0.775659 23 Intervention 6 0.73186 0.881266 24 Intervention 6 0.73186 0.88434

11) Finally, copy and paste the Sequence and Group columns onto a new worksheet. Do this by clicking on the Sheet2 tab, and then pasting it there.

A B Sequence Group 1 Control 2 Control 3 Intervention 4 Intervention 5 Control 6 Intervention 7 Intervention 8 Control 9 Control 10 Control 11 Control 12 Intervention 13 Intervention 14 Intervention 15 Intervention 16 Control 17 Intervention 18 Control 19 Intervention 20 Control 21 Control 22 Control 23 Intervention 24 Intervention

Right click on the Sheet2 tab and rename it to “Randomization List”. Right click on the Sheet1 tab and rename it “Setting up Randomization”. You keep this Excel File.

After you have saved your file, which has both sheets, you right click on the “Setting up Randomization” tab, and select “Delete”. You then give a spreadsheet with just the Randomization List sheet to the person responsible for the randomization.

One way the randomization can be carried out is having a piece of paper that contains just “Intervention” or “Control” placed inside envelopes. On the outside of the envelopes put the sequence number. After a patient has been enrolled into the study and consented, the next envelope on the stack is opened and that is the group the study subject goes into.

Not giving anyone else the worksheets that contain the block size guards against the possibility that someone will include the Blocksize column in the envelopes.

Part way into the study, and at the end, you can audit the randomization process by making sure the group assignment order that goes with the enrollment date and time that is recorded on the data collection form (case report form) or in the database, corresponds with your randomization list.

References

Friedman LM, Furberg CD, DeMets DL. (1998). Fundamentals of Clinical Trials, 3rd ed., New York, Springer, pp.64-66.

Kirkley A, Birmingham TB, Litchfield RB, et al. (2008). A randomized trial of arthroscopic surgery for osteoarthritis of the knee. N Engl J Med 359(11):1097-107.

Kuhn L, Aldrovandi GM, Sinkala M., et al. (2008). Effect of early, abrupt weaning on HIV-free survival of children in Zambia. N Engl J Med 359(2):130-41.

Simon, S. (1999). A simple approach for randomisation. [Electronic Rapid Response] 17 Sep 1999. Response to Altman DG, Bland JM. Statistics notes: How to randomise. BMJ 319:703-704.

This paper is not printed in BMJ, but it can be obtained from BMJ’s website. To get it, follow these steps: 1) Go to the Internet website: www.bmj.com 2) click on the Advanced Search link 3) Fill in the following with Year: 1999, Volume: 319, First Page: 703

Specify Year Volume First page/elocator Citation

4) Under Limit Results, select “Articles and electronic communications”

Jan 1994 Jul 2008 Limit From through Include: Results Articles only Articles and electronic communications (eg, rapid responses, Q&A)

5) That finds the paper. Click on Full text.

Journal Home EDUCATION AND DEBATE: Douglas G Altman and J Martin Bland Extract Full text Statistics notes: How to randomise PDF BMJ Sep 1999; 319: 703 - 704

why? Chapter 3-7 (revision 14 Jul 2011) p. 17

6) When the article appears, click on the Read responses to this article link, which brings up Simon’s response.