Design Effect for Cluster Sampling and Cluster Randomised Trials

The design effect is the ratio of the total number of subjects required using cluster randomisation to the number required using individual randomisation.

Usage

design_effect(m, ri)

Arguments

m: integer representing cluster size.
ri: intracluster (=intraclass) correlation coefficient.

Value

Numeric value of design effect.

Details

The design effect can be presented neatly in terms of the intracluster correlation and the number in a single cluster: -

$$D = 1 + (m − 1)r_{I}$$

If there is only one observation per cluster, m = 1, the design effect is 1.0 and the two designs are the same. Otherwise, the larger the intracluster correlation — that is, the more important the variation between clusters is — the bigger the design effect and the more subjects we will need to get the same power as a simply randomised study. Even a small intracluster correlation will have an impact if the cluster size is large.

Note

Description and Details taken verbatim from the second reference.

References

Kerry, S.M. & Bland, J.M., 1998. Sample size in cluster randomisation. Brit Med J 316: 5490. doi:10.1136/bmj.316.7130.549 .

Kerry, S.M. & Bland, J.M., 1998. The intracluster correlation coefficient in cluster randomisation. Brit Med J 316: 1455-1460. doi:10.1136/bmj.316.7142.1455 .

Examples

## Example: x-ray guidelines study from second reference.
design_effect(m = 50L, ri = 0.019)
#> [1] 1.931