Cluster Unit Randomized Trials

12. Perils of Subsampling

The Perils of Cluster Subsampling

As alluded to earlier in this chapter, increasing the number of clusters enrolled in a trial has a greater impact on statistical power than increasing the size of the clusters randomized. Moreover the benefit that may be obtained from increasing the number of participants per cluster is inversely proportional to the value of the intracluster correlation coefficient ρ, with the largest gains in power achieved when the number of participants sampled (subsample size) increases from 1 to 1/ ρ (Donner and Klar, 2004). Thus for trials randomizing entire communities, where values of ρ may be as low as 0.001, very little increase in power will be obtained by sampling more than 1000 subjects from each community. On the other hand, if ρ is about 0.01, as in school-based trials or trials randomizing medical practices, any gain in power diminishes rapidly after 100 students per cluster are enrolled.

Nonetheless, it is not uncommon for an investigator to administer an intervention to all members of a cluster even though the resulting gains in statistical power are minimal. This is often because the extra costs and logistical difficulties involved may not be considered onerous. However in some cases, such as in the COMMIT trial (Example E), it may be felt that the entire cluster (community), not just those individuals directly impacted, might benefit as a result of the synergy and interaction that takes place among cluster members. Some investigators might also have ethical qualms about delivering a new intervention to some but not all members of a cluster.

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Example A
450 villages in Indonesia were randomly assigned to either participate in a Vitamin A supplementation scheme or serve as a control. One-year childhood mortality rates were compared in the two groups (Sommer et al., 1986).
Example B
90 families were randomly assigned to receive either treated nasal tissues or standard tissues. 24-week incidence of respiratory illness was compared in the two groups (Farr et al., 1988).
Example C
One member of each pair of 11 matched maternity hospitals in Belarus was randomly assigned to receive a breastfeeding promotion strategy, with the other member of the pair receiving a control condition based on usual practice (PROBIT trial). The rate of breastfeeding at 12 months was compared between the two groups (Kramer et al., 2001).
Example D
207 general practices were randomized to receive either a structured group education program or standard care offered to patients with newly diagnosed type 2 diabetes. A variety of response variables, including biomedical, lifestyle, and psychosocial measurements were collected over a one-year follow-up period (Davies et al., 2008).
Example E
One member of each pair of 11 matched communities was randomly assigned to a city-wide intervention that promoted the hazards of smoking with the other member serving as a control. Five-year smoking cessation rates were compared in the two groups (COMMIT Research Group, 1995).
Diwan V.K., Wahlström R., Tomson G., Beermann B., Sterky G., Eriksson B. (1995). Effects of ‘Group Detailing’ on the prescribing of lipid-lowering drugs: A randomized controlled trial in Swedish primary care. Journal of Clinical Epidemiology, 48: 705-711.
Alexander F., Roberts M.M., Lutz W., Hepburn W. (1989). Randomization by cluster and the problem of social class bias. Journal of Epidemiology and Community Health, 43:29-36.