Choosing a Cluster Sampling Design for Lot Quality Assurance Sampling Surveys <s> Cluster sampling in LQAS <s> For a current, practical introduction to the field of sampling that you'll want to keep close at hand, Sharon L. Lohr's SAMPLING: DESIGN AND ANALYSIS, 2ND EDITION, answers the call. Practical and authoritative, the book is listed as a standard reference for training on real-world survey problems by a number of prominent surveying organizations. Lohr concentrates on the statistical aspects of taking and analyzing a sample, incorporating a multitude of applications from a variety of disciplines. The text gives guidance on how to tell when a sample is valid or not, and how to design and analyze many different forms of sample surveys. Recent research on theoretical and applied aspects of sampling is included, as well as technology instructions for using statistical software with survey data. <s> BIB001 </s> Choosing a Cluster Sampling Design for Lot Quality Assurance Sampling Surveys <s> Cluster sampling in LQAS <s> Results Hypothesis tests showed GAM as <10% for the 33 � 6 design and GAM as 510% for the 67 � 3 and Sequential designs. Point estimates for the 33 � 6 and 67 � 3 designs were similar to those of the 30 � 30 cluster-survey for GAM (6.7%, CI ¼ 3.2–10.2%; 8.2%, CI ¼ 4.3–12.1%, 7.4%, CI ¼ 4.8–9.9%) and all other indicators. The CIs for the LQAS designs were only slightly wider than the CIs for the 30 � 30 cluster-survey; yet the LQAS designs required substantially less time to administer. Conclusions The LQAS designs provide statistically appropriate alternatives to the more timeconsuming 30 � 30 cluster-survey. However, additional field-testing is needed using independent samples rather than a nested study design. <s> BIB002 </s> Choosing a Cluster Sampling Design for Lot Quality Assurance Sampling Surveys <s> Cluster sampling in LQAS <s> The conventional method to collect data on the health, nutrition, and food security status of a population affected by an emergency is a 30 × 30 cluster survey. This sampling method can be time and resource intensive and, accordingly, may not be the most appropriate one when data are needed rapidly for decision making. In this study, we compare the precision, time and cost of the 30 × 30 cluster survey with two alternative sampling designs: a 33 × 6 cluster design (33 clusters, 6 observations per cluster) and a 67 × 3 cluster design (67 clusters, 3 observations per cluster). Data for each sampling design were collected concurrently in West Darfur, Sudan in September-October 2005 in an emergency setting. Results of the study show the 30 × 30 design to provide more precise results (i.e. narrower 95% confidence intervals) than the 33 × 6 and 67 × 3 design for most child-level indicators. Exceptions are indicators of immunization and vitamin A capsule supplementation coverage which show a high intra-cluster correlation. Although the 33 × 6 and 67 × 3 designs provide wider confidence intervals than the 30 × 30 design for child anthropometric indicators, the 33 × 6 and 67 × 3 designs provide the opportunity to conduct a LQAS hypothesis test to detect whether or not a critical threshold of global acute malnutrition prevalence has been exceeded, whereas the 30 × 30 design does not. For the household-level indicators tested in this study, the 67 × 3 design provides the most precise results. However, our results show that neither the 33 × 6 nor the 67 × 3 design are appropriate for assessing indicators of mortality. In this field application, data collection for the 33 × 6 and 67 × 3 designs required substantially less time and cost than that required for the 30 × 30 design. The findings of this study suggest the 33 × 6 and 67 × 3 designs can provide useful time- and resource-saving alternatives to the 30 × 30 method of data collection in emergency settings. <s> BIB003 </s> Choosing a Cluster Sampling Design for Lot Quality Assurance Sampling Surveys <s> Cluster sampling in LQAS <s> Traditional lot quality assurance sampling (LQAS) methods require simple random sampling to guarantee valid results. However, cluster sampling has been proposed to reduce the number of random starting points. This study uses simulations to examine the classification error of two such designs, a 67×3 (67 clusters of three observations) and a 33×6 (33 clusters of six observations) sampling scheme to assess the prevalence of global acute malnutrition (GAM). Further, we explore the use of a 67×3 sequential sampling scheme for LQAS classification of GAM prevalence. Results indicate that, for independent clusters with moderate intracluster correlation for the GAM outcome, the three sampling designs maintain approximate validity for LQAS analysis. Sequential sampling can substantially reduce the average sample size that is required for data collection. The presence of intercluster correlation can impact dramatically the classification error that is associated with LQAS analysis. Copyright (c) 2009 Royal Statistical Society. <s> BIB004 </s> Choosing a Cluster Sampling Design for Lot Quality Assurance Sampling Surveys <s> Cluster sampling in LQAS <s> OBJECTIVE ::: To estimate the yellow fever (YF) vaccine coverage for the endemic and non-endemic areas of Bolivia and to determine whether selected districts had acceptable levels of coverage (>70%). ::: ::: ::: METHODS ::: We conducted two surveys of 600 individuals (25 x 12 clusters) to estimate coverage in the endemic and non-endemic areas. We assessed 11 districts using lot quality assurance sampling (LQAS). The lot (district) sample was 35 individuals with six as decision value (alpha error 6% if true coverage 70%; beta error 6% if true coverage 90%). To increase feasibility, we divided the lots into five clusters of seven individuals; to investigate the effect of clustering, we calculated alpha and beta by conducting simulations where each cluster's true coverage was sampled from a normal distribution with a mean of 70% or 90% and standard deviations of 5% or 10%. ::: ::: ::: RESULTS ::: Estimated coverage was 84.3% (95% CI: 78.9-89.7) in endemic areas, 86.8% (82.5-91.0) in non-endemic and 86.0% (82.8-89.1) nationally. LQAS showed that four lots had unacceptable coverage levels. In six lots, results were inconsistent with the estimated administrative coverage. The simulations suggested that the effect of clustering the lots is unlikely to have significantly increased the risk of making incorrect accept/reject decisions. ::: ::: ::: CONCLUSIONS ::: Estimated YF coverage was high. Discrepancies between administrative coverage and LQAS results may be due to incorrect population data. Even allowing for clustering in LQAS, the statistical errors would remain low. Catch-up campaigns are recommended in districts with unacceptable coverage. <s> BIB005 </s> Choosing a Cluster Sampling Design for Lot Quality Assurance Sampling Surveys <s> Cluster sampling in LQAS <s> OBJECTIVE ::: Vaccination programmes targeting disease elimination aim to achieve very high coverage levels (e.g. 95%). We calculated the precision of different clustered lot quality assurance sampling (LQAS) designs in computer-simulated surveys to provide local health officers in the field with preset LQAS plans to simply and rapidly assess programmes with high coverage targets. ::: ::: ::: METHODS ::: We calculated sample size (N), decision value (d) and misclassification errors (alpha and beta) of several LQAS plans by running 10 000 simulations. We kept the upper coverage threshold (UT) at 90% or 95% and decreased the lower threshold (LT) progressively by 5%. We measured the proportion of simulations with < or =d individuals unvaccinated or lower if the coverage was set at the UT (pUT) to calculate beta (1-pUT) and the proportion of simulations with >d unvaccinated individuals if the coverage was LT% (pLT) to calculate alpha (1-pLT). We divided N in clusters (between 5 and 10) and recalculated the errors hypothesising that the coverage would vary in the clusters according to a binomial distribution with preset standard deviations of 0.05 and 0.1 from the mean lot coverage. We selected the plans fulfilling these criteria: alpha < or = 5% beta < or = 20% in the unclustered design; alpha < or = 10% beta < or = 25% when the lots were divided in five clusters. ::: ::: ::: RESULT ::: When the interval between UT and LT was larger than 10% (e.g. 15%), we were able to select precise LQAS plans dividing the lot in five clusters with N = 50 (5 x 10) and d = 4 to evaluate programmes with 95% coverage target and d = 7 to evaluate programmes with 90% target. ::: ::: ::: CONCLUSION ::: These plans will considerably increase the feasibility and the rapidity of conducting the LQAS in the field. <s> BIB006 </s> Choosing a Cluster Sampling Design for Lot Quality Assurance Sampling Surveys <s> Cluster sampling in LQAS <s> OBJECTIVES ::: To evaluate oral poliovirus vaccine (OPV) coverage of the November 2009 round in five Northern Nigeria states with ongoing wild poliovirus transmission using clustered lot quality assurance sampling (CLQAS). ::: ::: ::: METHODS ::: We selected four local government areas in each pre-selected state and sampled six clusters of 10 children in each Local Government Area, defined as the lot area. We used three decision thresholds to classify OPV coverage: 75-90%, 55-70% and 35-50%. A full lot was completed, but we also assessed in retrospect the potential time-saving benefits of stopping sampling when a lot had been classified. ::: ::: ::: RESULTS ::: We accepted two local government areas (LGAs) with vaccination coverage above 75%. Of the remaining 18 rejected LGAs, 11 also failed to reach 70% coverage, of which four also failed to reach 50%. The average time taken to complete a lot was 10 h. By stopping sampling when a decision was reached, we could have classified lots in 5.3, 7.7 and 7.3 h on average at the 90%, 70% and 50% coverage targets, respectively. ::: ::: ::: CONCLUSIONS ::: Clustered lot quality assurance sampling was feasible and useful to estimate OPV coverage in Northern Nigeria. The multi-threshold approach provided useful information on the variation of IPD vaccination coverage. CLQAS is a very timely tool, allowing corrective actions to be directly taken in insufficiently covered areas. <s> BIB007 </s> Choosing a Cluster Sampling Design for Lot Quality Assurance Sampling Surveys <s> Cluster sampling in LQAS <s> In November 2009, Sierra Leone conducted a preventive yellow fever (YF) vaccination campaign targeting individuals aged nine months and older in six health districts. The campaign was integrated with a measles follow-up campaign throughout the country targeting children aged 9–59 months. For both campaigns, the operational objective was to reach 95% of the target population. During the campaign, we used clustered lot quality assurance sampling (C-LQAS) to identify areas of low coverage to recommend timely mop-up actions. We divided the country in 20 non-overlapping lots. Twelve lots were targeted by both vaccinations, while eight only by measles. In each lot, five clusters of ten eligible individuals were selected for each vaccine. The upper threshold (UT) was set at 90% and the lower threshold (LT) at 75%. A lot was rejected for low vaccination coverage if more than 7 unvaccinated individuals (not presenting vaccination card) were found. After the campaign, we plotted the C-LQAS results against the post-campaign coverage estimations to assess if early interventions were successful enough to increase coverage in the lots that were at the level of rejection before the end of the campaign. During the last two days of campaign, based on card-confirmed vaccination status, five lots out of 20 (25.0%) failed for having low measles vaccination coverage and three lots out of 12 (25.0%) for low YF coverage. In one district, estimated post-campaign vaccination coverage for both vaccines was still not significantly above the minimum acceptable level (LT = 75%) even after vaccination mop-up activities. C-LQAS during the vaccination campaign was informative to identify areas requiring mop-up activities to reach the coverage target prior to leaving the region. The only district where mop-up activities seemed to be unsuccessful might have had logistical difficulties that should be further investigated and resolved. <s> BIB008 </s> Choosing a Cluster Sampling Design for Lot Quality Assurance Sampling Surveys <s> Cluster sampling in LQAS <s> BACKGROUND ::: The Uzbekistan 1996 Demographic Health Survey reported 60.4% of women of reproductive age (WRA) had low hemoglobin concentrations (<120 g/L), and anemia was an important public health problem. Fortification of wheat flour was identified as an appropriate intervention to address anemia due to the ubiquitous consumption of wheat flour. A National Flour Fortification Program (NFFP) was implemented in 2005. ::: ::: ::: METHODOLOGY/PRINCIPAL FINDINGS ::: After 3-years of the NFFP, a national survey using large country-lot quality assurance sampling was carried out to assess iron, folate, hemoglobin and inflammation status of WRA; the coverage and knowledge of the fortified first grade UzDonMakhsulot (UDM) flour/grey loaf program; and consumption habits of women to investigate the dietary factors associated with anemia. Estimated anemia prevalence was 34.4% (95% CI: 32.0, 36.7), iron depletion 47.5% (95% CI: 45.1, 49.9) and folate deficiency 28.8% (95% CI: 26.8, 30.8); the effect of inflammation was minimal (4% with CRP >5 mg/L). Severe anemia was more prevalent among folate deficient than iron depleted WRA. Presence of UDM first grade flour or the grey loaf was reported in 71.3% of households. Among WRA, 32.1% were aware of UDM fortification; only 3.7% mentioned the benefits of fortification and 12.5% understood causes of anemia. Consumption of heme iron-containing food (91%) and iron absorption enhancers (97%) was high, as was the consumption of iron absorption inhibitors (95%). ::: ::: ::: CONCLUSIONS/SIGNIFICANCE ::: The NFFP coincided with a substantial decline in the prevalence of anemia. Folate deficiency was a stronger predictor of severe anemia than iron depletion. However, the prevalence of iron depletion was high, suggesting that women are not eating enough iron or iron absorption is inhibited. Fortified products were prevalent throughout Uzbekistan, though UDM flour must be adequately fortified and monitored in the future. Knowledge of fortification and anemia was low, suggesting consumer education should be prioritized. <s> BIB009 </s> Choosing a Cluster Sampling Design for Lot Quality Assurance Sampling Surveys <s> Cluster sampling in LQAS <s> Traditional 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. To 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. We 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. <s> BIB010 </s> Choosing a Cluster Sampling Design for Lot Quality Assurance Sampling Surveys <s> Cluster sampling in LQAS <s> 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 on the basis of 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 nonparametric 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. <s> BIB011
Initially, cluster sampling LQAS surveys were designed to minimize the amount of variance inflation due to clustering without directly inflating the sample size for clustering. For instance, within-cluster sample sizes of m = 1 have been used in LQAS surveys (e.g.  ; BIB009 ) to achieve the same precision as a SRS survey. In 67 × 3 and 33 × 6 LQAS nutrition surveys, small withincluster sample sizes were selected to minimize cluster sampling variance inflation BIB002 BIB003 BIB004 . Stroh and Birmingham (2009) use cluster sampling for LQAS neonatal tetanus elimination surveys and ignore the cluster sampling design, noting that cluster sampling approximates SRS 'when an attribute to be measured in a population is rare or is homogeneously distributed'  . The common theme between these approaches is that the cluster sampling design can be ignored if the within cluster sample size is small or if clustering is negligible. In these situations, the LQAS sample size and decision rule can be calculated using the standard binomial model with no adjustments required to accommodate the use of cluster sampling. 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 BIB005 BIB006 BIB007 BIB008 , Hedt BIB010 , and Hund BIB011 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. We describe these methods below. Pezzoli method. Pezzoli et. al BIB005 proposed the first cluster LQAS method, developed to assess vaccination coverage. The mathematical representation of the Pezzoli model described in BIB006 BIB007 is: We refer to this model as a binomial-scaled model, because p j is modeled as a binomial random variable scaled by η to ensure that p j 2 (0,1). Clustering is incorporated through specifying a value for σ, the standard deviation of the cluster level coverages. To apply the Pezzoli design, η is selected such that σ 2 = p(1 − p)/η. Using the relationship between σ and ρ, it follows that η = 1/ρ. This method is subject to some rounding error, since η is rounded to an integer. To select designs, the authors choose p = {p l , p u } and σ 2 (0,.1) and determine decision rules via simulation based on the distribution of X = ∑ j X j . There is currently no user-friendly software for implementing the Pezzoli method that allows users to select their own design, though Stata simulation code is available from the authors of BIB006 . We have written R functions for designing these surveys and provide examples using this code at https://github.com/lbhund/ ClusterLQAS_PLOS. Hedt method. Hedt et. al BIB010 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. The final decision rule is based on the distribution of X = ∑ j X j . Hedt et. al BIB010 provide R code for selecting sample sizes and decision rules for this method; the R package in BIB011 can also be used to calculate sample sizes and decision rules using the Hedt method. 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 BIB001 . For the two-stage cluster sample with large K, the design effect is D = 1 + (m − 1)ρ. The Hund method can also be written in terms of the 'effective sample size' as X Ã * Binomial(n Ã , p), where X Ã = X/D and n Ã = n/D is the effective sample size. Thus, the sample size and decision rule can be calculated under SRS and inflated by the design effect to accommodate clustering. The R package in BIB011 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.