**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=42 blocksize = 6 N = 40 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),]

> head(assign,12) block rand envelope arm 1 1 0.76450776 1 Arm 1 2 1 0.62361346 2 Arm 2 3 1 0.14844661 3 Arm 2 4 1 0.08026447 4 Arm 1 5 1 0.46406955 5 Arm 1 6 1 0.77936816 6 Arm 2 7 2 0.73352796 7 Arm 2 8 2 0.81723044 8 Arm 1 9 2 0.17016248 9 Arm 2 10 2 0.94472033 10 Arm 2 11 2 0.29362384 11 Arm 1 12 2 0.14907205 12 Arm 1It'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 0.98189It'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;

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## 3 comments:

Another alternative in SAS is to use PROC PLAN, which also supports more complicated designs. For this example:

proc plan seed=&seed;

factors Block=%sysfunc(ceil(&N/&blocksize)) ordered

Arm =&blocksize;

output out=Blocks;

run;

data Blocks; set Blocks;

Item = mod(_N_-1,&blocksize)+1;

Arm = mod(Arm,2)+1;

run;

The PROC PLAN doc has a related example. PROC PLAN is used extensively by researchers in clinical trials, and there are dozens of SAS Global Forum papers that describe its use in Big Pharma.

Ho to do proc plan in R?

Hi Muhammad-- What exactly are you trying to do? I'll try to work up an example in R.

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