Repeated sampling of different individuals within the same clusters to improve precision of longitudinal estimators: the DISC design

Background: Longitudinal studies often involve repeated cluster sampling of a population at multiple time points, such as in difference-in-differences (DID) studies. Although cohort designs typically lead to more efficient estimators relative to repeated cross-sectional (RCS) designs, they are often impractical.
Methods: We describe the DISC (Different Individuals, Same Clusters) design, a sampling scheme that improves the precision of estimators in these settings. The DISC design represents a hybrid between a cohort and an RCS design, in which the researcher takes a single sample of clusters at baseline, but takes different cross-sectional samples of individuals within clusters at each time point.
Results: We show analytically that the DISC design yields DID estimators with much higher precision relative to an RCS design, particularly if cluster effects are present. For example, for a design with two surveys, 40 clusters, and 25 individuals per cluster, the variance of a commonly-used DID treatment effect estimator is 2.3 times higher in the RCS design for an intraclass correlation coefficient (ICC) of 0.05 and 3.8 times higher for an ICC of 0.1. We also present results of a simulation study comparing the RCS and DISC designs, using both a simple DID estimator and a more complex doubly-robust DID (DRDID) estimator that leverages covariate information, and show gains in precision for both estimators when using the DISC design. Additionally, we illustrate DISC sampling using a household survey dataset from South Africa.
Conclusions: Use of the DISC design can result in estimators that have substantially lower variance than the analogous estimator resulting from an RCS design.