The effect of clustering on lot quality assurance sampling: a probabilistic model to calculate sample sizes for quality assessments

Abstract

BackgroundTraditional Lot Quality Assurance Sampling (LQAS) designs assume observations are collected using simple random sampling. Alternatively, randomly sampling clusters of observations and then individuals within clusters reduces costs but decreases the precision of the classifications. In this paper, we develop a general framework for designing the cluster(C)-LQAS system and illustrate the method with the design of data quality assessments for the community health worker program in Rwanda.ResultsTo determine sample size and decision rules for C-LQAS, we use the beta-binomial distribution to account for inflated risk of errors introduced by sampling clusters at the first stage. We present general theory and code for sample size calculations.The C-LQAS sample sizes provided in this paper constrain misclassification risks below user-specified limits. Multiple C-LQAS systems meet the specified risk requirements, but numerous considerations, including per-cluster versus per-individual sampling costs, help identify optimal systems for distinct applications.ConclusionsWe show the utility of C-LQAS for data quality assessments, but the method generalizes to numerous applications. This paper provides the necessary technical detail and supplemental code to support the design of C-LQAS for specific programs.

Use of Lot quality assurance sampling surveys to evaluate community health worker performance in rural Zambia: a case of Luangwa district

“…In this study, LQAS demonstrated consistent household visits by CHWs and hence validated its applicability in our settings for monitoring CHW performance. This finding is consistent with previous studies that have used LQAS to monitor CHW performance [18]. Two major additional findings from this study were (1) the confirmed CHW household visitation rate demonstrated a positive trend, increasing over time, and (2) the pattern of topics discussed was consistent with the burden of disease as captured through the OPD attendances at the health facility and common illnesses that were identified in the CHW zones.…”

Estimation after classification using lot quality assurance sampling: corrections for curtailed sampling with application to evaluating polio vaccination campaigns

“…More recently, Hedt‐Gauthier et al . () proposed methods for choosing both the number of clusters and the cluster size under an arbitrary degree of clustering to assure a minimum level of expected classification error under complete sampling. The new approach might also have implications for the amount of variance inflation expected in the data and for confidence interval construction.…”

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 ] propose modeling X j as a beta-binomial random variable with mean p and intraclass correlation ρ : The betabinomial model can also be written as a two-stage model, with X j ∼ Binomial ( m , p j ) and p j ∼ Beta ( p , ρ ) (where the beta distribution is parameterized based on the mean p and intraclass correlation ρ ). The beta distribution has support on (0,1), and this betabinomial model is common for clustered binary data.…”

“…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.…”