8.5 - Minimization

Minimization is another, rather complicated type of adaptive randomization. Minimization schemes construct measures of imbalance for each treatment when an eligible patient is ready for randomization. The patient is assigned to the treatment which yields the lowest imbalance score. If the imbalance scores are all equal, then that patient is randomly assigned a treatment. This type of adaptive randomization imposes tight control of balance, but it is more labor-intensive to implement because the imbalance scores must be calculated with each new patient. Some researchers have developed web-based applications and automated 24-hour telephone services that solicit information about the stratifiers and a computer algorithm uses the data to determine the randomization

One popular minimization scheme is based on marginal totals of the stratifying variables. As an example, consider a three-armed clinical trial (treatments A, B, C). Suppose there are four stratifying variables, whereby each stratifier has three levels (low, medium, high), yielding \(3^4 = 81\) strata in this trial. When 200 patients have been randomized and patient #201 is ready for randomization. The observations of the stratifying variables are recorded as follows.

Patient Stratifier #1 Stratifier #2 Stratifier #3 Stratifier #4
001 Low Low Medium Low
002 High Medium Medium High
. . .
200 Low Low Low Medium

Suppose that patient #201 is ready for randomization and that this patient is observed to have the low level of stratifier #1, the medium level of stratifier #2, the high level of stratifier #3, and the high level of stratifier #4. Based on the 200 patients already in the trial, the number of patients with each of these levels is totaled for each treatment group. (Notice that patients may be double counted in this table.)

  Low Stratifier #1 Medium Stratifier #2 High Stratifier #3 High Stratifier #4 Marginal Total
Trt A 27 45 19 12 103
Trt B 31 48 18 15 112
Trt C 30 43 21 15 109

Patient #201 would be assigned to treatment A because it has the lowest marginal total. If two or more treatment arms are tied for the smallest marginal total, then the patient is randomly assigned to one of the tied treatment arms. This is not a perfect scheme but it is a strategy for making sure that the assignments are as balanced within each treatment group with respect to each of the four variables.