Cluster Unit Randomized Trials

8. Factors Influencing Power

Investigators are often advised in the planning stages of a study to err on the conservative side in estimating the size of sample needed to achieve adequate statistical power.

This advice likely carries even more weight for CRTs when one considers some of the unique problems that may arise.

  • Entire clusters of subjects may be lost to follow-up if a physician, mayor, or school administrator withdraws their cooperation partway through a trial.
  • A further problem is that many interventions in CRTs are applied on a group basis with little or no attention given to individual study participants, adding to the risk of subject withdrawal or inadequate compliance.
  • Overoptimistic expectations concerning the expected effect size might also lead to an underpowered trial, particularly since the lengthy developmental phase that usually precedes individually randomized trials is frequently absent in the context of CRTs.

Beginning with the well-known trials intended to reduce the risk of cardiovascular disease that were designed in the 1970s (e.g., Farquhar et al., 1977; Tuomilehto et al., 1980; Jacobs et al., 1986) many CRTs can be characterized as prevention trials. Such trials, also exemplified by Examples A and B, may be particularly susceptible to low power since they tend to recruit relatively healthy, heterogeneous populations of subjects who may exhibit lower than expected compliance levels, and who also must be followed up for lengthy periods of time in order to detect important reductions in (relatively low) event rates. Moreover, as pointed out by Meinert, 2008, data from previous relevant trials may not be easily available at the planning stages, making it difficult to anticipate the event rate in the control group.

There are a number of steps that may be taken to help improve the power of CRTs.

  • One strategy would be to develop cluster-level eligibility criteria that by definition will serve to reduce between-cluster variability, for example by imposing relatively narrow geographical restrictions at the recruiting stage. Although this strategy may lead to some loss of generalizability (external validity), the resulting increase in power can arguably make this an acceptable trade-off.
  • It is also important to ensure at the design stage of the trial that all important prognostic variables are measured. The baseline version of a primary outcome measure is a particularly powerful prognostic variable, and may be incorporated into the analysis using either a change score approach or by including it as a covariate in a multivariable model. The availability of this value also allows the opportunity for the investigators to re-evaluate key sample size parameters, such as the standard deviation and the ICC. If obtained as part of an overall baseline survey, the resulting information may also be helpful in identifying potential stratification factors.
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.