Abstract
Lot Quality Assurance Sampling (LQAS) surveys have become increasingly popular in global health care applications. Incorporating Bayesian ideas into LQAS survey design, such as using reasonable prior beliefs about the distribution of an indicator, can improve the selection of design parameters and decision rules. In this paper, a joint frequentist and Bayesian framework is proposed for evaluating LQAS classification accuracy and informing survey design parameters. Simple software tools are provided for calculating the positive and negative predictive value of a design with respect to an underlying coverage distribution and the selected design parameters. These tools are illustrated using a data example from two consecutive LQAS surveys measuring Oral Rehydration Solution (ORS) preparation. Using the survey tools, the dependence of classification accuracy on benchmark selection and the width of the ‘grey region’ are clarified in the context of ORS preparation across seven supervision areas. Following the completion of an LQAS survey, estimation of the distribution of coverage across areas facilitates quantifying classification accuracy and can help guide intervention decisions.
Highlights
Lot Quality Assurance Sampling (LQAS), referred to as sampling for attributes and acceptance sampling, has a long history of applications in industrial quality control [1,2]
This paper addresses merging Bayesian and frequentist ideas when designing LQAS surveys to provide perspective on LQAS classification accuracy
Positive predictive value (PPV) and negative predictive value (NPV), which quantify the probability of correct diagnosis conditional on the test result, help the patient understand the likelihood of having the disease
Summary
Lot Quality Assurance Sampling (LQAS), referred to as sampling for attributes and acceptance sampling, has a long history of applications in industrial quality control [1,2]. To understand the root of this bias, note that the risks αB and βB for a classification procedure are a function of the specified prior π (); the collected data naturally does not inform the survey design or decision rules, whereas the prior selection does. This prior π () (the estimate of the underlying distribution of coverage in the population) is not utilized in the same manner as standard Bayesian analyses, where prior information is updated using collected data to construct a posterior distribution. Proportion of SAs could have true coverages in the grey region
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