help cluster3

Title

cluster3 -- Determination of sample size, power, and minimum detectable effect size for three-level cluster randomized trials with continuous outcomes.

Syntax

cluster3 [, options]

Main
power compute power

mdes compute minimum detectable effect size

obs3 compute number of level-3 clusters

obs2 compute number of level-2 sub-clusters

obs1 compute number of level-1 observations

Options
a(#) the significance level of the test; default is a(0.05)

p(#) the power of the test; default is p(0.8)

r3(#) the level-3 intraclass correlation coefficient; default is r3(0)

r2(#) the level-2 intraclass correlation coefficient, within level-3; default sets r2=r3

rxy(#) the correlation coefficient between the baseline covariate (x) and the outcome (y); default is rxy(0)

d(#) the standardized effect size, delta (b/sd); default is d(1)

n3(#) number of level-3 clusters in each arm; default is n3(1)

n2(#) number of level-2 sub-clusters, per level-3 cluster; default is n2(1)

n1(#) number of level-1 observations, per level-2 sub-cluster; default is n1(1)

Description

cluster3 The program ^cluster3^ conducts a generalized power analysis for three-level cluster-randomized trials with, or without, the inclusion of a baseline pretest/covariate.

Updates

1. Command updated to include power analysis with and without baseline covariate

2. Results interface updated to display baseline/covariate correlation.

3. Options updated to disallow negative sample size inputs for n3, n2, or n1.

4. Inputs and calculations are now saved as return scalars.

Examples

1. Determine power in a 3-level design with no covariates

. cluster3, r3(0.2) r2(0.3) d(0.4) n3(50) n2(5) n1(15) power

2. Determine power in a 3-level design with baseline covariate and correlation(x,y) of 0.6

. cluster3, r3(0.2) r2(0.3) rxy(0.6) d(0.4) n3(50) n2(5) n1(15) power

3. Determine minimum detectable effect size in a 3-level design with no covariates

. cluster3, r3(0.2) r2(0.3) p(0.9) n3(50) n2(5) n1(15) mdes

4. Determine minimum detectable effect size in a 3-level design with baseline covariate and correlation(x,y) of 0.4

. cluster3, r3(0.2) r2(0.3) rxy(.4) p(0.9) n3(50) n2(5) n1(15) mdes

5. Determine number of clusters in a 3-level design with no covariates

. cluster3, n2(2) n1(12) d(0.25) r3(0.15) r2(0.25) obs3

6. Determine number of clusters in a 3-level design with baseline covariate and correlation(x,y) of 0.8

. cluster3, n2(2) n1(12) d(0.25) r3(0.15) r2(0.25) rxy(0.8) obs3

7. Determine number of sub-clusters in a 3-level design with no covariates

. cluster3, n3(50) n1(12) d(0.25) r3(0.15) r2(0.25) obs2

8. Determine number of sub-clusters in a 3-level design with baseline covariate and correlation(x,y) of 0.65

. cluster3, n3(50) n1(12) d(0.25) r3(0.15) r2(0.25) rxy(0.65) obs2

9. Determine number of level-1 observations in a 3-level design with no covariates

. cluster3, n3(50) n2(5) d(0.25) r3(0.15) r2(0.25) obs1

10. Determine number of level-1 observations in a 3-level design with baseline covariate and correlation(x,y) of 0.65

. cluster3, n3(50) n2(5) d(0.25) r3(0.15) r2(0.25) rxy(0.65) obs1

Saved results

cluster3 saves the following in r():

Macros

r(alpha) Alpha

r(rho3) ICC at level-3

r(rho2) ICC at level-2

r(rxy) Correlation(x,y)

r(power) Power

r(delta) Delta, detectable effect size

r(obs3) Number of level-3 observations per treatment arm

r(obs2) Number of level-2 observations

r(obs1) Number of level-1 observations

r(N) Total number of observations (T+C)

Author

Wael Moussa

FHI 360

Washington, DC

wmoussa@fhi360.org

References

Heo, M. and Leon, A.C., 2008. Statistical power and sample size requirements for three level hierarchical cluster randomized trials. Biometrics, 64(4), pp.1256-1262.

Bloom, H.S., Richburg-Hayes, L. and Black, A.R., 2007. Using covariates to improve precision: Empirical guidelines for studies that randomize schools to measure the impacts of educational interventions. Educational Evaluation and Policy Analysis, 29(1), pp.30-59.

Disclaimer

Any errors are the author's alone. Please email wmoussa@fhi360.org to report any issues.