This article shows how to compute statistical power for testing the main effect of treatment in three-arm cluster randomized trials. Using orthogonal coding, we derive the exact test statistic of the treatment effect and its non-central distribution. The non-centrality parameter in the omnibus test is found to be related to the non-centrality parameters in the contrast tests. A study of physician and pharmacist comanagement of patients’ blood pressure is used as an example to show the power computation in a three-arm cluster randomized trial.
CarterB. L. (2010). Designing quality health services research: Why comparative effectiveness studies are needed and why pharmacists should be involved. Pharmacotherapy, 30, 751–757.
2.
CarterB.ClarkeW.ArderyG.WeberC.JamesP.VanderW. … Collaboration, Among Pharmacists Physicians To Improve Outcomes Now (CAPTION) Trial Investigators. (2010). A cluster-randomized effectiveness trial of a physician-pharmacist collaborative model to improve blood pressure control. Cardiovascular Quality and Outcomes, 3, 418–423.
3.
DeLusignan. S.GallagherH.ChanT.ThomasN.VlymenJ.NationM.…HarrisK. (2009). The QICKD study protocol: A cluster randomized trial to compare quality improvement interventions to lower systolic BP in chronic kidney disease (CKD) in primary care. Implementation Science, 4, 1–15.
4.
DonnerA.KlarN. (2000). Design and analysis of cluster randomization trials in health research. London, England: Arnold.
5.
HsiehF. Y. (1988). Sample size formulae for intervention studies with the cluster as unit of randomization. Statistics in Medicine, 8, 1195–1201.
6.
JohnsonN.KotzS.BalakrishnanN. (1995). Continuous univariate distributions (Vol. 2, 2nd ed.). New York, NY: Wiley.
7.
LenthR. (2001) Some practical guidelines for effective sample size determination. American Statistician, 55, 187–193.
8.
McCullochC. E.SearleS. R. (2001). Generalized, linear and mixed models. New York, NY: Wiley.
9.
MuntnerP.ShimboD.TonelliM.ReynoldsK.ArnettD. K.OparilS. (2011). The relationship between visit-to-visit variability in systolic blood pressure and all-cause mortality in the general population. Hypertension, 57, 160–166.
10.
MurrayD. M. (1998). Design and analysis of group-randomized trials. New York, NY: Oxford University Press.
11.
PerriaC.MandoliniD.GuerreraC.JeffersonT.BilliP.CalziniV.…PasquarellaA. (2007). Implementing a guideline for the treatment of type 2 diabetics: Results of a cluster-randomized controlled trial (C-RCT). BMC Health Services Research, 7, 1–9.
12.
RaudenbushS.BrykA. (2002). Hierarchical linear models: Applications and data analysis methods (2nd ed.). Newbury Park, CA: Sage.
13.
RaudenbushS. W.MartinezA.SpybrookJ. (2007). Strategies for improving precision in grouprandomized experiments. Educational Evaluation and Policy Analysis, 29, 5–29.
14.
RaudenbushS. W.LiuX. (2001). Effects of study duration, frequency of observation, and sample size on power in studies of group differences in polynomial change. Psychological Methods, 6, 387–401.
15.
ZwarN.RichmondR.HalcombE.FurlerJ.SmithJ.HermizO.…BorlandR. (2010). Quit in general practice: a cluster randomised trial of enhanced in-practice support for smoking cessation. BMC Family Practice, 11, 1–8.
