Accounting for expected attrition in the planning of community intervention trials

Trials in which intact communities are the units of randomization are increasingly being used to evaluate interventions which are more naturally administered at the community level, or when there is a substantial risk of treatment contamination. In this article we focus on the planning of community intervention trials in which k communities (for example, medical practices, worksites, or villages) are to be randomly allocated to each of an intervention and a control group, and fixed cohorts of m individuals enrolled in each community prior to randomization. Formulas to determine k or m may be obtained by adjusting standard sample size formulas to account for the intracluster correlation coefficient rho. In the presence of individual-level attrition however, observed cohort sizes are likely to vary. We show that conventional approaches of accounting for potential attrition, such as dividing standard sample size formulas by the anticipated follow-up rate pi or using the average anticipated cohort size m pi, may, respectively, overestimate or underestimate the required sample size when cluster follow-up rates are highly variable, and m or rho are large. We present new sample size estimation formulas for the comparison of two means or two proportions, which appropriately account for variation among cluster follow-up rates. These formulas are derived by specifying a model for the binary missingness indicators under the population-averaged approach, assuming an exchangeable intracluster correlation coefficient, denoted by tau. To aid in the planning of future trials, we recommend that estimates for tau be reported in published community intervention trials.