Extending cluster lot quality assurance sampling designs for surveillance programs

Abstract

Lot quality assurance sampling (LQAS) has a long history of applications in industrial quality control. LQAS is frequently used for rapid surveillance in global health settings, with areas classified as poor or acceptable performance based on the binary classification of an indicator. Historically, LQAS surveys have relied on simple random samples from the population; however, implementing two-stage cluster designs for surveillance sampling is often more cost-effective than simple random sampling. By applying survey sampling results to the binary classification procedure, we develop a simple and flexible non-parametric procedure to incorporate clustering effects into the LQAS sample design to appropriately inflate the sample size, accommodating finite numbers of clusters in the population when relevant. We use this framework to then discuss principled selection of survey design parameters in longitudinal surveillance programs. We apply this framework to design surveys to detect rises in malnutrition prevalence in nutrition surveillance programs in Kenya and South Sudan, accounting for clustering within villages. By combining historical information with data from previous surveys, we design surveys to detect spikes in the childhood malnutrition rate.

Choosing a Cluster Sampling Design for Lot Quality Assurance Sampling Surveys

“…In practice, clustering is often not negligible, and visiting many clusters and selecting few individuals per cluster may be less logistically feasible or cost-effective than sampling more individuals per cluster. To address these limitations, three methods have recently been developed to explicitly accommodate clustering sampling at the design-phase in cluster lqas surveys: the Pezzoli [ 10 – 13 ], Hedt [ 14 ], and Hund [ 15 ] methods. In this paper, we compare these three methods (Hund, Hedt, and Pezzoli) for explicitly accounting for the cluster sampling design and do not discuss designs that ignore the cluster sampling design.…”

“…Hedt et. al [ 14 ] provide code for selecting sample sizes and decision rules for this method; the package in [ 15 ] can also be used to calculate sample sizes and decision rules using the Hedt method.…”

“…Hund and Pagano (2014) do not specify a distribution for p j and instead use an overdispersed binomial model for X [ 15 ]: where D is the survey design effect allowing variability in X above that of the binomial distribution. The design effect is the ratio of the variances using cluster sampling compared to srs and is the multiplicative factor by which the sample size should be inflated to achieve the same precision as srs when using cluster sampling [ 23 ].…”

“…Thus, the sample size and decision rule can be calculated under srs and inflated by the design effect to accommodate clustering. The package in [ 15 ] can be used to calculate sample sizes and decision rules for this method. A limitation of the Hund method is that α and β errors are inexact due to rounding error when transforming from the effective sample size scale.…”

“…Recently, three methods have been proposed to adjust lqas sample sizes and decision rules to accommodate cluster sampling. We refer to these methods as the Pezzoli [ 10 – 13 ], Hedt [ 14 ], and Hund [ 15 ] methods. In this paper, we contrast these methods and provide recommendations for choosing a cluster lqas design.…”