Optimality of Equal vs. Unequal Cluster Sizes in Multilevel Intervention Studies: A Monte Carlo Study for Small Sample Sizes

Optimality of equal versus unequal cluster sizes in the context of multilevel intervention studies is examined. A Monte Carlo study is done to examine to what degree asymptotic results on the optimality hold for realistic sample sizes and for different estimation methods. The relative D-criterion, comparing equal versus unequal cluster sizes, almost always exceeded 85%, implying that loss of information due to unequal cluster sizes can be compensated for by increasing the number of clusters by 18%. The simulation results are in line with asymptotic results, showing that, for realistic sample sizes and various estimation methods, the asymptotic results can be used in planning multilevel intervention studies.

[1]  Bruce E. Ankenman,et al.  OPTIMAL DESIGNS FOR MIXED-EFFECTS MODELS WITH TWO RANDOM NESTED FACTORS , 2003 .

[2]  Ana Ivelisse Avilés,et al.  Linear Mixed Models for Longitudinal Data , 2001, Technometrics.

[3]  Mark Von Tress,et al.  Generalized, Linear, and Mixed Models , 2003, Technometrics.

[4]  Karl J. Friston,et al.  Variance Components , 2003 .

[5]  Gerard J P van Breukelen,et al.  Relative efficiency of unequal versus equal cluster sizes in cluster randomized and multicentre trials , 2007, Statistics in medicine.

[6]  J. Wolfowitz,et al.  An Introduction to the Theory of Statistics , 1951, Nature.

[7]  D. Harville.  Matrix Algebra From a Statistician's Perspective , 1998 .

[8]  Paola Sebastiani,et al.  Experimental designs for mean and variance estimation in variance components models , 1989 .

[9]  X. Liu,et al.  Statistical Power and Optimum Sample Allocation Ratio for Treatment and Control Having Unequal Costs per Unit of Randomization , 2003 .

[10]  S. Raudenbush.  Statistical analysis and optimal design for cluster randomized trials , 1997 .

[11]  Todd C. Headrick,et al.  ON OPTIMIZING MULTI‐LEVEL DESIGNS: POWER UNDER BUDGET CONSTRAINTS , 2005 .

[12]  Martijn P. F. Berger,et al.  OPTIMAL EXPERIMENTAL DESIGNS FOR MULTILEVEL MODELS WITH COVARIATES , 2001 .

[13]  Anthony C. Atkinson,et al.  Optimum Experimental Designs , 1992 .

[14]  Liam Smeeth,et al.  Intraclass correlation coefficients for cluster randomized trials in primary care: data from the MRC Trial of the Assessment and Management of Older People in the Community. , 2002, Controlled clinical trials.

[15]  S. Raudenbush,et al.  Statistical power and optimal design for multisite randomized trials. , 2000, Psychological methods.