Bayes-LQAS: classifying the prevalence of global acute malnutrition

Abstract

Lot Quality Assurance Sampling (LQAS) applications in health have generally relied on frequentist interpretations for statistical validity. Yet health professionals often seek statements about the probability distribution of unknown parameters to answer questions of interest. The frequentist paradigm does not pretend to yield such information, although a Bayesian formulation might. This is the source of an error made in a recent paper published in this journal. Many applications lend themselves to a Bayesian treatment, and would benefit from such considerations in their design. We discuss Bayes-LQAS (B-LQAS), which allows for incorporation of prior information into the LQAS classification procedure, and thus shows how to correct the aforementioned error. Further, we pay special attention to the formulation of Bayes Operating Characteristic Curves and the use of prior information to improve survey designs. As a motivating example, we discuss the classification of Global Acute Malnutrition prevalence and draw parallels between the Bayes and classical classifications schemes. We also illustrate the impact of informative and non-informative priors on the survey design. Results indicate that using a Bayesian approach allows the incorporation of expert information and/or historical data and is thus potentially a valuable tool for making accurate and precise classifications.

Figure 1

Classical Operating Characteristic Curve with sample size n = 200, decision rule d = 14, upper threshold p_U = 0.10, lower threshold p_L = 0.05, and maximum tolerated errors α = 0.10 and β = 0.20.

Figure 2

Hypothetical prior distribution of acute malnutrition with mean 8.5% (**) and candidate OC curves for LQAS classification with d = 14 (-) and d = 28 (--).

Figure 3

(A) Various Beta distributions to describe a range of potential prior beliefs. We assume that p ~ Beta(a, b). (B) Bayes OC Curves assuming n = 200 and d = 14. The dashed lines (---) represent 1 - BOC_F and the solid lines (-) represent 1 - BOC_P.

Figure 4

(A) The Figure of Merit plotted as a function of d where p ~ Beta(a, b) and assuming n = 200, p_U = 0.1 and both p_L = 0.05 (-) and p_L = 0.1(---). Solid vertical lines indicate the maximum FOM when p_L = 0.05 and dashed vertical lines indicate maximum FOM when p_L = 0.10. (B) Maximum FOM as a function of the precision with p_U = 0.1 and p_L varying from 0.05 to 0.1 for various assumed Beta priors.