Choosing a cluster sampling design for lot quality assurance sampling surveys

Lot quality assurance sampling (LQAS) surveys are commonly used for monitoring and evaluation in resource-limited settings. Recently several methods have been proposed to combine LQAS with cluster sampling for more timely and cost-effective data collection. For some of these methods, the standard binomial model can be used for constructing decision rules as the clustering can be ignored. For other designs, considered here, clustering is accommodated in the design phase. In this paper, we compare these latter cluster LQAS methodologies and provide recommendations for choosing a cluster LQAS design. We compare technical differences in the three methods and determine situations in which the choice of method results in a substantively different design. We consider two different aspects of the methods: the distributional assumptions and the clustering parameterization. Further, we provide software tools for implementing each method and clarify misconceptions about these designs in the literature. We illustrate the differences in these methods using vaccination and nutrition cluster LQAS surveys as example designs. The cluster methods are not sensitive to the distributional assumptions but can result in substantially different designs (sample sizes) depending on the clustering parameterization. However, none of the clustering parameterizations used in the existing methods appears to be consistent with the observed data, and, consequently, choice between the cluster LQAS methods is not straightforward. Further research should attempt to characterize clustering patterns in specific applications and provide suggestions for best-practice cluster LQAS designs on a setting-specific basis.