Unequal cluster sizes for trials in English and Welsh general practice: implications for sample size calculations

Cluster randomized trials are often used in primary care settings. In the U.K., general practices are usually the unit of allocation. The effect of variability in practice list size on sample size calculations is demonstrated using the General Medical Services Statistics for England and Wales, 1997. Summary statistics and tables are given to help design such trials assuming that a fixed proportion of patients are to be recruited from each cluster. Three different weightings of the cluster means are compared: uniform, cluster size and minimum variance weights. Minimum variance weights are shown to be superior to uniform, particularly when clusters are small, and to cluster size weights, particularly when clusters are large. Where there are large numbers of participants per cluster and cluster size weights are used, the power actually falls as more patients are recruited to large clusters. When minimum variance weights are used the increase in the design effect due to variation in list size is small, regardless of the size of intracluster correlation coefficient or the number of participants per cluster, provided there is no loss of randomized units. When the expected number of participants per practice is low a greater loss in power comes from practices which fail to recruit patients. A method to estimate the likely effect and allow for it is presented.