You are presented with multiple paper abstracts, alongside the associated literature review and chapter titles. Given the provided information, you are going to do a literature review. Please generate a coherent literature review that synthesizes the content, draws connections between different works, highlights major findings, and identifies any gaps in the existing research.

Literature Review Title: Choosing a Cluster Sampling Design for Lot Quality Assurance Sampling Surveys 
Chapter Title:  Clustering parameterization 
1. Abstract of Cited Paper (BIB001):  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. 
2. Abstract of Cited Paper (BIB002):  BACKGROUND AND PURPOSE ::: Power and sample size calculations for cluster randomized trials require prediction of the degree of correlation that will be realized among outcomes of participants in the same cluster. This correlation is typically quantified as the intraclass correlation coefficient (ICC), defined as the Pearson correlation between two members of the same cluster or proportion of the total variance attributable to variance between clusters. It is widely known but perhaps not fully appreciated that for binary outcomes, the ICC is a function of outcome prevalence. Hence, the ICC and the outcome prevalence are intrinsically related, making the ICC poorly generalizable across study conditions and between studies with different outcome prevalences. ::: ::: ::: METHODS ::: We use a simple parametrization of the ICC that aims to isolate that part of the ICC that measures dependence among responses within a cluster from the outcome prevalence. We incorporate this parametrization into sample size calculations for cluster randomized trials and compare our method to the traditional approach using the ICC. ::: ::: ::: RESULTS ::: Our dependence parameter, R, may be less influenced by outcome prevalence and has an intuitive meaning that facilitates interpretation. Estimates of R from previous studies can be obtained using simple statistics. Comparison of methods showed that the traditional ICC approach to sample size determination tends to overpower studies under many scenarios, calling for more clusters than truly required. ::: ::: ::: LIMITATIONS ::: The methods are developed for equal-sized clusters, whereas cluster size may vary in practice. ::: ::: ::: CONCLUSIONS ::: The dependence parameter R is an alternative measure of dependence among binary outcomes in cluster randomized trials that has a number of advantages over the ICC. 
3. Abstract of Cited Paper (BIB003):  Estimation of vaccination coverage at the local level is essential to identify communities that may require additional support. Cluster surveys can be used in resource-poor settings, when population figures are inaccurate. To be feasible, cluster samples need to be small, without losing robustness of results. The clustered LQAS (CLQAS) approach has been proposed as an alternative, as smaller sample sizes are required. We explored (i) the efficiency of cluster surveys of decreasing sample size through bootstrapping analysis and (ii) the performance of CLQAS under three alternative sampling plans to classify local VC, using data from a survey carried out in Mali after mass vaccination against meningococcal meningitis group A. VC estimates provided by a 10 × 15 cluster survey design were reasonably robust. We used them to classify health areas in three categories and guide mop-up activities: i) health areas not requiring supplemental activities; ii) health areas requiring additional vaccination; iii) health areas requiring further evaluation. As sample size decreased (from 10 × 15 to 10 × 3), standard error of VC and ICC estimates were increasingly unstable. Results of CLQAS simulations were not accurate for most health areas, with an overall risk of misclassification greater than 0.25 in one health area out of three. It was greater than 0.50 in one health area out of two under two of the three sampling plans. Small sample cluster surveys (10 × 15) are acceptably robust for classification of VC at local level. We do not recommend the CLQAS method as currently formulated for evaluating vaccination programmes.

Literature Review:
In Tables 3 and 4 , designs are compared based on the clustering parameterization (fixed σ versus fixed ρ). For the 55-70% and 75-90% couplets, the designs are similar regardless of how clustering is parameterized. For the 90-95% couplet, the sample size is much larger in the Hedt and Hund methods with fixed ρ u versus fixed ρ l ; similarly, the sample size is much larger in the Pezzoli method with fixed σ l versus fixed σ u . Recall that the examples in Tables 3 and 4 assume that m, the sample size within clusters, is fixed and increments the overall sample size by adding additional clusters. As noted above, clustering variance inflation increases as the withincluster sample size increases. Subsequently, discrepancies between the three methods are more pronounced when the number of sampled clusters k is fixed, rather than m. As an example, if we were to fix the number of clusters to k = 6 rather than fixing the within-cluster sample size m = 10, the total sample size n would range between 72 and 150 when σ = .1 (analogous to the 70-90 sample size range in Table 3 with m fixed). Eq 2 helps explain the sensitivity of the sample size to the clustering parameterization when p l and p u are near 0 or 1. The parameters ρ and σ will be similar for both p l and p u when p l (1 − p l ) % p u (1 − p u ). Hence, ρ l and ρ u are negligibly different when σ = .1 for the 55-70% couplet, whereas ρ u is nearly double ρ l for the 75-90% and 90-95% couplets. To illustrate this difference for the 75-90% couplet, we plot beta distributions fixing σ = .1, fixing ρ l , and fixing ρ u in Fig 2. Unlike the distributional assumptions, choice of clustering parameterization can substantially impact the final sample size for the survey when p l and p u are near 0 or 1. Next, we examine whether existing data support one of the two proposed parameterizations. In Figs 3 and 4 ,ŝ andr are plotted as a function ofp for the data in BIB002 and BIB004 , respectively. Bothr andŝ decrease as a function of estimated vaccination coverage (less clustering occurs in more highly vaccinated areas), consistent with BIB003 and BIB001 . Fixing either σ or ρ likely results in some level of misspecification of α and β. The OC curves corresponding to the different clustering specifications are also shown in Figs 3 and 4 . In the example from BIB002 , the α and β risks are substantially higher when the mean versus the lowess smooth estimate of σ and ρ are used. This inflation of the risks occurs because σ and ρ decrease as a function of p but the average coverage across SAs is lower than 75%. The risks are not inflated in the example from BIB004 because the range of vaccination coverages is similar to the 75-90% couplet thresholds.