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Randomization of Subjects

Subjects are assigned to study groups by a random mechanism not controlled by the patient or the investigator. Randomization increases the likelihood treatment groups are comparable with respect to distribution of measurable and measurable characteristics.

Randomization Schedule

Prior to study start, a randomization schedule is generated by a statistician. Ex. a 2 treatment trial with 1:1 randomization.

Treatment allocation schemes should:

  • Be unpredictable
    • Neither the participant nor the investigator know in advance which treatment will be assigned (reduced observation bias)
  • Promote balance
    • Groups must be alike in all important aspects and only differ in the intervention each group receives
  • Be simple
    • Easy for investigator/staff to implement

Generally, the randomization ratio should be equally allocated (1:1 randomization). Unequal randomization arises in some situations where we want more in one group than another due to costs or other factors.

Methods of Randomization

  • Unrestricted randomization
  • Block randomization
    • Randomized permuted blocks
  • Stratification
  • Adaptive randomization
    • Biased coin, etc
    • Minimization
  • Cluster randomization

Unrestricted Randomization

  • Equivalent to tossing a fair coin for each subject that enters the trial
  • Assign each treatment randomly and independently of previous treatment
  • Also called simple/complete randomization

SAS Code for generating unrestricted random data:

*Method 1;
*RANUNI: generates random numbers between 0 and 1 which have a uniform distribution;
data one;
seed=123;
do id=1 to 8;
r=ranuni(seed);
if r<0.5 then group='A';
if r>=0.5 then group='B';
output;
end;
run;

* Method 2;
data one;
seed=123;
do id=1 to 8;
r=ranuni(seed);
output;
end;
run;
proc sort data=one;
by r;
run;
data two;
set one;
if _n_<=4 then group='A';
if _n_>4 then group='B';
run;
proc sort data=two;
by id; * Sort again by id;
run;

* Method 3;
data three;
seed=123;
do id=1 to 8;
r=ranuni(seed);
output;
end;
run;
proc rank data=three groups=3 out=three;
var r;
ranks group;
run;
data three;
set three;
if group=0 then trt='A';
if group=1 then trt='B';
if group=2 then trt='C';
run

Note that the seed is a number that determines the starting value. The same positive seed will always generate the same result. If we want a different number each run then set the seed <= 0.

The issue with unrestricted randomization is that is can produce imbalance. Ex. Based on the binomial distribution, a study with two groups and 8 patients will produce a 6:2 assignment 28% of the time.

Block Randomization

Also called permuted block, and is the most common form of randomization in clinical trials. Sequence of blocks that contain the assignment in the desired ratio.

Ex. With N = 8 patients and 2 treatments, A and B, with 1:1 randomization and block size 4:

  1. Take the letters AABB, randomly permute them
  2. Assign treatment for the next set of 4 patients, randomly permute AABB again

Block randomization ensures that of the first 4 patients, 2 receive each treatment.

Choosing Block SIze

The block size must be a multiple of the number in the allocation ratio. Block size is not always mentioned in the study's protocol, as no one needs to know except the statistician who generates the schedule.

A block size of 2 is usually not recommended. It creates a "guessable" pattern of AB, BA, AB...

A large block size is also not recommended (especially for small samples). May lead to incomplete blocks at the end of the study. Ex. N = 12 with block size 8 would leave 4 incomplete blocks.

 

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