title: Estimation after classification using lot quality assurance sampling: corrections for curtailed sampling with application to evaluating polio vaccination campaigns.
abstract: OBJECTIVE
  To assess the bias incurred when curtailment of Lot Quality Assurance Sampling (LQAS) is ignored, to present unbiased estimators, to consider the impact of cluster sampling by simulation and to apply our method to published polio immunization data from Nigeria.
  
  
  METHODS
  We present estimators of coverage when using two kinds of curtailed LQAS strategies: semicurtailed and curtailed. We study the proposed estimators with independent and clustered data using three field-tested LQAS designs for assessing polio vaccination coverage, with samples of size 60 and decision rules of 9, 21 and 33, and compare them to biased maximum likelihood estimators. Lastly, we present estimates of polio vaccination coverage from previously published data in 20 local government authorities (LGAs) from five Nigerian states.
  
  
  RESULTS
  Simulations illustrate substantial bias if one ignores the curtailed sampling design. Proposed estimators show no bias. Clustering does not affect the bias of these estimators. Across simulations, standard errors show signs of inflation as clustering increases. Neither sampling strategy nor LQAS design influences estimates of polio vaccination coverage in 20 Nigerian LGAs. When coverage is low, semicurtailed LQAS strategies considerably reduces the sample size required to make a decision. Curtailed LQAS designs further reduce the sample size when coverage is high.
  
  
  CONCLUSIONS
  Results presented dispel the misconception that curtailed LQAS data are unsuitable for estimation. These findings augment the utility of LQAS as a tool for monitoring vaccination efforts by demonstrating that unbiased estimation using curtailed designs is not only possible but these designs also reduce the sample size.
authors.affiliation: Department of Environmental and Occupational Health Sciences, University of Washington, Seattle, WA, USA.
authors.forename: Casey
authors.initials: C
authors.lastname: Olives
authors.affiliation: Department of International Public Health, Liverpool School of Tropical Medicine, Liverpool, UK.
authors.forename: Joseph J
authors.initials: JJ
authors.lastname: Valadez
authors.affiliation: Department of Biostatistics, Harvard School of Public Health, Boston, MA, USA.
authors.forename: Marcello
authors.initials: M
authors.lastname: Pagano
mesh_terms: D015982:Bias; D002675:Child, Preschool; D016000:Cluster Analysis; D006801:Humans; D007223:Infant; D009111:Local Government; D055810:Lot Quality Assurance Sampling / Q000379:methods*; D032541:Mass Vaccination / Q000706:statistics & numerical data*; D009549:Nigeria / Q000453:epidemiology; D011051:Poliomyelitis / Q000517:prevention & control*; D015397:Program Evaluation / Q000379:methods*; D011785:Quality Assurance, Health Care / Q000379:methods; D018401:Sample Size
keywords: Lot Quality Assurance Sampling; curtailed sampling; estimation; polio vaccination; program evaluation; semi‐curtailed sampling