Relative efficiency of unequal cluster sizes for variance component estimation in cluster randomized and multicentre trials

Cluster randomized and multicentre trials evaluate the effect of a treatment on persons nested within clusters, for instance patients within clinics or pupils within schools. Although equal sample sizes per cluster are generally optimal for parameter estimation, they are rarely feasible. This paper addresses the relative efficiency (RE) of unequal versus equal cluster sizes for estimating variance components in cluster randomized trials and in multicentre trials with person randomization within centres, assuming a quantitative outcome. Starting from maximum likelihood estimation, the RE is investigated numerically for a range of cluster size distributions. An approximate formula is presented for computing the RE as a function of the mean and variance of cluster sizes and the intraclass correlation. The accuracy of this approximation is checked and found to be good. It is concluded that the loss of efficiency for variance component estimation due to variation of cluster sizes rarely exceeds 20% and can be compensated by sampling 25% more clusters.

[1]  S Senn,et al.  Some controversies in planning and analysing multi-centre trials. , 1998, Statistics in medicine.

[2]  Evangelos Evangelou,et al.  Intraclass correlation coefficients for cluster randomized trials in primary care: the cholesterol education and research trial (CEART). , 2005, Contemporary clinical trials.

[3]  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.

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

[5]  Mirjam Moerbeek,et al.  A comparison between traditional methods and multilevel regression for the analysis of multicenter intervention studies. , 2003, Journal of clinical epidemiology.

[6]  R. J. Hayes,et al.  Design and analysis issues in cluster-randomized trials of interventions against infectious diseases , 2000, Statistical methods in medical research.

[7]  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.

[8]  A. Khuri.  A method for determining the effect of imbalance , 1996 .

[9]  P. Laycock,et al.  Optimum Experimental Designs , 1995 .

[10]  Ilse Mesters,et al.  Short-term effects of a randomized computer-based out-of-school smoking prevention trial aimed at elementary schoolchildren. , 2002, Preventive medicine.

[11]  Mirjam Moerbeek,et al.  Multiple-objective optimal designs for the hierarchical linear model , 2002 .

[12]  S M Kerry,et al.  Unequal cluster sizes for trials in English and Welsh general practice: implications for sample size calculations. , 2001, Statistics in medicine.

[13]  M. Bartelink,et al.  How do we compare with our colleagues? Quality of general practitioner performance in consultations for non-acute abdominal complaints. , 1999, International journal for quality in health care : journal of the International Society for Quality in Health Care.

[14]  M O Roland,et al.  Identifying predictors of high quality care in English general practice: observational study , 2001, BMJ : British Medical Journal.

[15]  Franklin A. Graybill,et al.  Introduction to The theory , 1974 .

[16]  M J Campbell,et al.  Cluster randomized trials in general (family) practice research , 2000, Statistical methods in medical research.

[17]  S. Silvey.  Optimal Design: An Introduction to the Theory for Parameter Estimation , 1980 .

[18]  Martijn P. F. Berger,et al.  Design Issues for Experiments in Multilevel Populations , 2000 .

[19]  V. Fedorov,et al.  The design of multicentre trials , 2005, Statistical methods in medical research.

[20]  Amita K. Manatunga,et al.  Sample Size Estimation in Cluster Randomized Studies with Varying Cluster Size , 2001 .