Estimation of the design effect in community intervention studies

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Abstract
This paper considers the estimation of the variance of a mortality rate in community intervention studies with little or no replication of intervention regimens. Our approach in estimation of this cluster sampling variance is to determine the variance for simple random sampling and multiply it by a design effect which we calculate with use of information obtained from other sources. When the county is the unit of randomization and the outcome is mortality, we calculate the design effect as the ratio of the age adjusted mortality rates for single stage cluster sampling relative to simple random sampling; we use information from all counties in a state in the calculations. We apply this approach empirically for breast cancer mortality. We found that these design effects were dependent on length of time for accumulation of deaths (1.1 for one year up to 3.5 for eight years) and were quite consistent for the three states and nine years considered in the investigation. We present a model that accounts for the time dependence of the design effect and we show it provides a good representation of the observed relationship.