# Example 2014.2: Block randomization

January 22, 2014
By

(This article was first published on SAS and R, and kindly contributed to R-bloggers)

This week I had to block-randomize some units. This is ordinarily the sort of thing I would do in SAS, just because it would be faster for me. But I had already started work on the project R, using knitr/LaTeX to make a PDF, so it made sense to continue the work in R.

R
As is my standard practice now in both languages, I set thing up to make it easy to create a function later. I do this by creating variables with the ingredients to begin with, then call them as variables, rather than as values, in my code. In the example, I assume 40 assignments are required, with a block size of 6.
I generate the blocks themselves with the rep() function, calculating the number of blocks needed to ensure at least N items will be generated. Then I make a data frame with the block numbers and a random variate, as well as the original order of the envelopes. The only possibly confusing part of the sequence is the use of the order() function. What it returns is a vector of integer values with the row numbers of the original data set sorted by the listed variables. So the expression a1[order(a1$block,a1$rand),] translates to "from the a1 data frame, give me the rows ordered by sorting the rand variable within the block variable, and all columns." I assign the arms in a systematic way to the randomly ordered units, then resort them back into their original order.
seed=42blocksize = 6N = 40set.seed(seed)block = rep(1:ceiling(N/blocksize), each = blocksize)a1 = data.frame(block, rand=runif(length(block)), envelope= 1: length(block))a2 = a1[order(a1$block,a1$rand),]a2$arm = rep(c("Arm 1", "Arm 2"),times = length(block)/2)assign = a2[order(a2$envelope),]
> head(assign,12)   block       rand envelope   arm1      1 0.76450776        1 Arm 12      1 0.62361346        2 Arm 23      1 0.14844661        3 Arm 24      1 0.08026447        4 Arm 15      1 0.46406955        5 Arm 16      1 0.77936816        6 Arm 27      2 0.73352796        7 Arm 28      2 0.81723044        8 Arm 19      2 0.17016248        9 Arm 210     2 0.94472033       10 Arm 211     2 0.29362384       11 Arm 112     2 0.14907205       12 Arm 1
It's trivial to convert this to a function-- all I have to do is omit the lines where I assign values to the seed, sample size, and block size, and make the same names into parameters of the function.
blockrand = function(seed,blocksize,N){  set.seed(seed)  block = rep(1:ceiling(N/blocksize), each = blocksize)  a1 = data.frame(block, rand=runif(length(block)), envelope= 1: length(block))  a2 = a1[order(a1$block,a1$rand),]  a2$arm = rep(c("Arm 1", "Arm 2"),times = length(block)/2) assign = a2[order(a2$envelope),]  return(assign)}

SAS
This job is also pretty simple in SAS. I use the do loop, twice, to produce the blocks and items (or units) within block, sssign the arm systematically, and generate the random variate which will provide the sort order within block. Then sort on the random order within block, and use the "Obs" (observation number) that's printed with the data as the envelope number.
%let N = 40;%let blocksize = 6;%let seed = 42;data blocks;call streaminit(&seed);do block = 1 to ceil(&N/&blocksize);  do item = 1 to &blocksize;     if item le &blocksize/2 then arm="Arm 1";    else arm="Arm 2";     rand = rand('UNIFORM');  output;  end;end;run;proc sort data = blocks; by block rand; run;proc print data = blocks (obs = 12) obs="Envelope"; run;
Envelope    block    item     arm       rand    1         1        3     Arm 1    0.13661    2         1        1     Arm 1    0.51339    3         1        5     Arm 2    0.72828    4         1        2     Arm 1    0.74696    5         1        4     Arm 2    0.75284    6         1        6     Arm 2    0.90095    7         2        2     Arm 1    0.04539    8         2        6     Arm 2    0.15949    9         2        4     Arm 2    0.21871   10         2        1     Arm 1    0.66036   11         2        5     Arm 2    0.85673   12         2        3     Arm 1    0.98189
It's also fairly trivial to make this into a macro in SAS.
%macro blockrand(N, blocksize, seed); data blocks;call streaminit(&seed);do block = 1 to ceil(&N/&blocksize);  do item = 1 to &blocksize;     if item le &blocksize/2 then arm="Arm 1";    else arm="Arm 2";     rand = rand('UNIFORM');  output;  end;end;run;proc sort data = blocks; by block rand; run;%mend blockrand;