Choosing a design to fit the situation: how to improve specificity and positive predictive values using Bayesian lot...

Lot Quality Assurance Sampling (LQAS) is a provably useful tool for monitoring health programmes. Although LQAS ensures acceptable Producer and Consumer risks, the literature alleges that the method suffers from poor specificity and positive predictive values (PPVs). We suggest that poor LQAS performance is due, in part, to variation in the true underlying distribution. However, until now the role of the underlying distribution in expected performance has not been adequately examined.

We present Bayesian-LQAS (B-LQAS), an approach to incorporating prior information into the choice of the LQAS sample size and decision rule, and explore its properties through a numerical study. Additionally, we analyse vaccination coverage data from UNICEF's State of the World's Children in 1968-1989 and 2008 to exemplify the performance of LQAS and B-LQAS.

Results of our numerical study show that the choice of LQAS sample size and decision rule is sensitive to the distribution of prior information, as well as to individual beliefs about the importance of correct classification. Application of the B-LQAS approach to the UNICEF data improves specificity and PPV in both time periods (1968-1989 and 2008) with minimal reductions in sensitivity and negative predictive value.

LQAS is shown to be a robust tool that is not necessarily prone to poor specificity and PPV as previously alleged. In situations where prior or historical data are available, B-LQAS can lead to improvements in expected performance.