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Cluster Unit Randomized Trials

13. Other Perils

Is fear of contamination in individually randomized trials overrated?

It was mentioned in the beginning of this chapter that the most common reason cited in the literature for adopting a cluster randomization design is

the risk of experimental contamination that might arise under individual randomization.

We now examine this issue in more detail. Suppose for illustrative purposes that an extreme form of contamination occurs under individual randomization where a proportion R of control group subjects “cross over” and actually take up the experimental invention. Then if we assume that these subjects will experience the same event rate as the experimental group subjects, the difference in event rates that can be detected will be reduced by a factor of 1-R.

For example, suppose the investigators enroll enough subjects in the trial to detect a 20 percentage point difference in event rates at a specified probability level. If a proportion R=0.30 of control group subjects are now expected to assume the same event rate as subjects in the experimental group, the trial must be redesigned to detect a difference of 0.70(20)=14 percentage points. However to detect this smaller effect size it can be easily shown (Torgerson, 2001) that the original sample size must be inflated under individual randomization by a factor 1/(1-R)2 =1/(.70)2=2.04. The investigators may believe that this contamination effect can be avoided by alternatively choosing a cluster randomization design. However the variance inflation factor associated with clustering may be much larger than this.

  • Adjusting the trial size by taking into account the anticipated contamination effect may well be the preferred option, at least in terms of required sample size.
  • Nonetheless it must also be recognized that under individual randomization the effect size estimated by the trial data will be attenuated by the resulting contamination.
  • Thus if the main aim of the investigators is to estimate the “uncontaminated” effect size, the cluster randomization design may still be preferable.