Fig 1.
The different steps within the 2-stage LQAS framework for population-based decision-making using an imperfect test.
Fig 2.
Program decision-making process based on 2-stage LQAS framework allowing for an imperfect diagnostic test.
Panel A illustrates the risk of making a wrong program decision (εovertreat and εundertreat) for a given true prevalence πi and decision cut-off c = 90 was applied. The vertical straight line indicates the program prevalence threshold T = 50%, whereas the horizontal dotted lines represent the εovertreat and εundertreat for πi = 37.5% and πi = 62.5%, respectively. Panel B represents the decision cut-off c for a choice of grey zone width (lower limit (LL) = 37.5% and upper limit (UL) = 62.5%) and acceptable risk levels (Eovertreat = 25% and εundertreat = 5%) for a particular of range of πi. The solid sigmoid curves (in red and blue) indicate the values of c that satisfy the conditions and
, whereas the dotted sigmoid curves (green and purple) do not satisfy the conditions mentioned above. All graphs are based on the same theoretical diagnostic test D (sed = 80% and spd = 98%), survey design (nclust = 5 and nsub = 50), an intra-cluster correlation ρi = 0.02 and 10,000 Monte Carlo simulations.
Table 1.
Definitions of the parameters that describe the 2-stage LQAS framework.
Table 2.
Definitions of the derived variables that describe the 2-stage LQAS framework.
Fig 3.
Determination of the decision cut-off c based on 2-stage LQAS framework allowing for imperfect tests.
This figure describes the simulation framework to determine the decision cut-off c that allows for adequate (Eovertreat = 25% and Eundertreat = 5%) decision-making at a true underlying prevalence πi at the implementation unit i equal to 37.5% (LL) and 62.5% (UL) when an imperfect theoretical diagnostic test D (sed = 80% and spd = 98%) was deployed to screen nclust = 5 and nsub = 50 subjects per cluster. We fixed the intra-cluster correlation ρi = 0.02 at both limits of the grey zone. The bottom row graphs (Panels A–D) illustrate the process for the lower limit of the grey zone, whereas the bottom row graphs (Panels E–H) show this for the UL of the grey zone. The horizontal dotted line in Panel D represents the Eovertreat, wherein Panel H represents Eundertreat. The dotted vertical lines in these panels represent the decision cut-off c and the bullet the εovertreat (Panel D) and εundertreat (Panel H). All graphs are based on the same set of 10,000 Monte Carlo simulations.
Fig 4.
The required sensitivity and specificity when applying the current WHO study design.
This figure indicates the required sensitivity and specificity when applying the current WHO study design (nclust = 5 and nsub = 50) that allow for adequate ( or ideal (
decision-making around each of the four program prevalence thresholds T (Panel A: 10%; Panel B: 20%; Panel C: 50%). The intra-cluster correlation ρi was fixed at 0.02, and the limits of the grey zone were defined as a proportion of the program prevalence threshold
. The red area indicates that the combination of the survey design (nclust, nsub) and the test performance (sed and spd) was inadequate for decision-making, while the light blue and the dark blue represent combinations that allow for adequate (
and ideal
decision-making, respectively. All graphs are based on the same set of 10,000 Monte Carlo simulations.
Fig 5.
Impact of the width of the grey zone on program decision-making when applying imperfect diagnostics.
This figure illustrates the impact of the width of the grey zone on the number of subjects per cluster (Panel A), the total number of subjects sampled across nclust clusters on the minimum required survey design for adequate program decision-making (Eovertreat = 25% and Eundertreat = 5%) (Panel B), the decision threshold c (Panel C), and the associated total survey cost (Panel D). We considered program prevalence threshold T of 2%, fixed the intra-cluster correlation ρi at 0.02 and assumed a theoretical diagnostic test Dt1 (sedt1 = 80% and spdt1 = 98%). The width of the grey zone is expressed as a proportion of program prevalence threshold T. The black bullet across the four panels indicates the chosen hypothetical reference grey zone width (T±50%), which was chosen to further illustrate the impact of the diagnostic performance (Fig 6) and geographical variation in prevalence between clusters on program decision-making (Fig 7), and the relative change in total survey cost based on newer diagnostic tests (Fig 8). All graphs are based on the same set of 10,000 Monte Carlo simulations.
Fig 6.
Impact of the diagnostic performance on program decision-making.
The contour lines illustrate the relationship between specificity (x-axis), the sensitivity (y-axis), and the minimum number of subjects per cluster nsub (contour lines) for adequate program decision-making (Eovertreat = 25% and Eundertreat = 5%) around a 2% program prevalence threshold for the number of clusters nclust equal to 5, 10, 15 and 20. We fixed the intra-cluster correlation ρi at 0.02 and the limits of the grey zone at 1% and 3%. All graphs are based on the same set of 10,000 Monte Carlo simulations.
Fig 7.
Impact of geographical variation in prevalence between clusters on program decision-making.
This figure illustrates the impact of the geographical variation in prevalence (expressed as intra-cluster correlation, which ranged from 0.012 to 0.032) on the number of subjects per cluster (nsub; Panel A), the total number of subjects sampled across nclust (ntot; Panel B), the corresponding decision cut-off c (Panel C), and the associated total survey costs (Ctot; Panel D) required for adequate program decision-making (Eovertreat = 25% and Eundertreat = 5%) around a 2% program prevalence threshold. In this figure, the sensitivity and specificity were set at 80% and 98%, respectively. The limits of the grey zone at 1% and 3%. All graphs are based on the same set of 10,000 Monte Carlo simulations.
Fig 8.
The relative total survey cost of imperfect diagnostic tests with varying sample throughput and reagent costs.
The contour lines illustrate the total survey cost when applying imperfect diagnostic tests with varying sample throughput and reagent cost to test one sample relative to the total cost of a survey based on the hypothetical reference diagnostic test with the sample throughput (9 samples per hour per person) and cost characteristics (1.38 US$ reagent test cost) of single Kato-Katz thick smear. We considered three hypothetical diagnostic tests Dt3 (reference diagnostic test; Panel A), Dt2 (Panel B), and Dt3 (Panel C), each with a different diagnostic performance (). The intra-cluster correlation ρi was set at 0.02 and the number of clusters at 10. The number of subjects per cluster and the total survey cost was defined as the minimum required number of subjects per cluster and minimal cost required for adequate decision-making (Eovertreat = 25% and Eundertreat = 5%) around a program prevalence threshold of 2%, with the grey zone defined as T±50% (LL = 1% and UL = 3%). All three panels were based on 10,000 Monte Carlo simulations.
Table 3.
The use of the 2-stage LQAS framework to develop guidelines and strategic choices in R&D.
Fig 9.
The relative total survey cost of Kato-Katz thick smear with improved specificity.
The contour lines illustrate the total survey cost when applying a Kato-Katz thick smear with improved specificity KKsp(sekksp = 55%, and spkksp = 99%) with varying sample throughput and reagent cost to test one sample relative to the total cost of a survey based on the soil-transmitted helminths target product profiles diagnostic performance Dtpp1 (setpp1 = 60% and sptpp1 = 99%) with sample throughput (7 samples per hour per person) and cost characteristics (3 US$ reagent test cost). The dotted line indicates the maximum reagent cost per test for the improved Kato-Katz thick smear (1.85 US$) when the sample throughput was set at 7. The intra-cluster correlation ρi was set at 0.02 and the number of clusters at 10. The number of subjects per cluster was estimated as the required minimum number of subjects for adequate decision-making (Eovertreat = 25% and Eundertreat = 5%) around a program prevalence threshold of 2%, with the grey zone defined as T±50% (LL = 1%and UL = 3%). The total survey cost was defined as the minimal cost required. The graph was based on 10,000 Monte Carlo simulations.