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The authors have declared that no competing interests exist.

Conceived and designed the experiments: CO JJV MP. Performed the experiments: CO MP. Analyzed the data: CO MP. Contributed reagents/materials/analysis tools: CO SJB JJV MP. Wrote the paper: CO SJB JJV MP. Responsible for the primary statistical development of methods and implementation: CO. Provided technical support and advisement of statistical development: MP. Provided data and expert advisement for application to schistosomiasis: SJB. Provided context and expert advisement for LQAS design and implementation: JJV.

Originally a binary classifier, Lot Quality Assurance Sampling (LQAS) has proven to be a useful tool for classification of the prevalence of

We outline MC-LQAS design principles and formulae for operating characteristic curves. In addition, we derive the average sample number for MC-LQAS when utilizing semi-curtailed sampling and introduce curtailed sampling in this setting. We also assess the performance of MC-LQAS designs with maximum sample sizes of

Overall performance of MC-LQAS classification was high (kappa-statistic of 0.87). In three of the studies, the kappa-statistic for a design with

This work provides the needed analytics to understand the properties of MC-LQAS for assessing the prevalance of

The control of schistosomiasis calls for rapid and reliable classification tools. This study evaluates the performance of one such tool, Lot Quality Assurance Sampling (LQAS) for assessing the prevalence of

Schistosomiasis is a tropical disease caused by infection with

The World Health Organization (WHO) recommends a three-way classification (≤10%, >10 and <50%, ≥50%) of the prevalence of schistosome infection to determine appropriate interventions for school-age children

A classification tool, LQAS has been used in a variety of settings to identify program areas as either “acceptable” or “unacceptable” with respect to a preestablished target

The Brooker

The primary aim of the current work is the development of a unified Multiple Category-LQAS tool (MC-LQAS) and the validatation of its use in multiple setting in East Africa. Specifically, we outline the theoretical underpinnings of MC-LQAS system, focusing on classification into one of three categories, and provide guidelines for choosing design parameters. Next, we present the theoretical aspects of sequential sampling as employed by researchers in the field

Traditional LQAS calls for a random sample of

A) Operating Characteristic curve for LQAS design with n = 15,d = 7, and α = β = 0.20; B) Operating Characteristic curves for low (dashed-dotted), medium (dashed), and high (solid) categories for MC-LQAS design with n = 15, d_{1} = 1, d_{2} = 7, and δ_{1} = δ_{1} = δ_{1} = δ_{1} = 0.20; C) Average Sample Number for semi-curtailed (solid) and curtailed (dashed) LQAS with n = 15 and d = 7; D) Average Sample Number for semi-curtailed (solid) and curtailed (dashed) MC-LQAS with n = 15, d_{1} = 1, and d_{2} = 7.

The choice of the sample size and decision rule are critical, as they determine the expected classification error in the procedure. Generally, _{U}_{L}_{U}_{L}_{L} = 0.40_{U} = 0.60_{L}_{U}

Due to the monotonicity of the OC curve, it follows that for any _{L}_{U}_{L}_{U}_{L}<p<p_{U}

The MC-LQAS procedure extends basic LQAS by classifying a sample against multiple decision rules. In the following we develop MC-LQAS for three-way classification although the method is generalizable to more than three categories. For three-way classification, we must choose a total of two decision rules, _{1}_{2}_{1}_{2}

Analogous to the OC curve, for a specific design we can plot the probability of classification into each of the three categories against _{1} = 1, d_{2} = 7

As with LQAS, in practice we choose to control for potential misclassification at predetermined thresholds, which we call _{L1}_{U1}_{L2}_{U2}_{L1}<p_{1}*<p_{U1}_{L2}<p_{2}*<p_{U2}_{1}* = p_{L1}_{2}* = p_{U2}_{1}_{2}_{1}_{2}_{3}_{4}_{L}_{U}_{U1}_{L2}

We note that in the above formulation, we have ignored possible misclassification into the extreme categories. Depending on the distance between thresholds, misclassification into a non-contiguous category can be minimal for even small samples. Hence, for moderate sample sizes, we only worry about four possible misclassifications, which are those misclassifications into contiguous classes.

In certain situations, it is possible to reduce the sample size needed to reach a decision by “sampling to the decision rule”. For example, suppose we define a traditional LQAS plan with a sample size

Indeed, one can benefit even more by adopting a

The notion of curtailed sampling is easily extended to MC-LQAS. For example, MC-LQAS also allows for the potential of early stopping by sampling to the decision rule, or semi-curtailed sampling. For example, when utilizing an MC-LQAS design with _{1} = 1_{2} = 7

The curtailed version of MC-LQAS is slightly different than its traditional counterpart in that it allows for early stopping for low, moderate, or high classifications. Continuing with our example, if the first thirteen observations are failures, then it follows that the lot will be classified as low irrespective of the remaining observations. Likewise, if in the first twelve observations are four successes and eight failures, then sampling can stop with a moderate classification, as neither low nor high classifications are possible at this point. The semi-curtailed and curtailed ASNs for an MC-LQAS design with _{1} = 1_{2} = 7

In the following, we consider

Horizontal lines are 95% exact confidence intervals.

We use these data to assess the performance of the MC-LQAS design with _{1} = 1_{2} = 7_{1} = 2_{1} = 1_{2} = 7_{1} = δ_{2} = δ_{3} = δ_{4} = 0.20_{L1} = 0.055_{U1} = 0.188_{L2} = 0.392_{U2} = 0.606_{1} = 2_{2} = 12_{L1} = 0.062_{U1} = 0.164_{L2} = 0.417_{U2} = 0.583

We generate 1000 MC-LQAS classifications of each school in the sample by repeatedly “sampling down” the individual data to 15 or 25 students and classifying each school based on these observations. To compare the classifications resulting from MC-LQAS with those that result from binning the full sample prevalence, we calculate for each simulation the weighted kappa statistic, which measures agreement between classification methods across locations

For simulation with n = 15, d_{1} = 1, and d_{2} = 7, (A) average proportion of correctly classified schools with expected Operating Characteristic curves overlaid (dashed grey), (B) Average Sample Number when utilizing semi-curtailed sampling with expected Average Sample Number overlaid (dashed grey), and (C) Average Sample Number when utilizing curtailed sampling with expected Average Sample Number overlaid (dashed grey).

The results of our simulation study are presented in

n = 15, d_{1} = 1, d_{2} = 7 |
n = 25, d_{1} = 2, d_{2} = 12 |
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SS (# Schools) | κ-statistic | Curtailed ASN | Semi-Curtailed ASN | κ-statistic | Curtailed ASN | Semi-Curtailed ASN | |

All Studies | 25246 (388) | 0.875 (0.864–0.885) | 12.902 (12.871–12.936) | 14.504 (14.487–14.523) | 0.897 (0.888–0.907) | 21.538 (21.486–21.593) | 24.158 (24.137–24.180) |

Brooker et al | 1739 (25) | 0.774 (0.723–0.830) | 12.892 (12.760–13.040) | 14.255 (14.200–14.320) | 0.822 (0.780–0.874) | 21.263 (21.000–21.520) | 23.730 (23.640–23.800) |

Clarke et al | 1093 (21) | 0.459 (0.341–0.576) | 13.371 (13.190–13.571) | 14.991 (15.000–15.000) | 0.518 (0.394–0.615) | 21.859 (21.524–22.202) | 24.997 (25.000–25.000) |

Clements et al | 8617 (143) | 0.763 (0.722–0.808) | 13.119 (13.091–13.147) | 14.909 (14.895–14.923) | 0.808 (0.771–0.844) | 22.100 (22.042–22.161) | 24.847 (24.832–24.860) |

Kabatereine et al | 13797 (199) | 0.901 (0.889–0.912) | 12.698 (12.648–12.749) | 14.196 (14.166–14.231) | 0.920 (0.910–0.931) | 21.139 (21.055–21.216) | 23.631 (23.588–23.678) |

Point estimates are mean and quantities in parentheses represent the inerquartile range over 1000 simulated datasets.

The notable exception was the Clarke

The ASN for a maximum sample size of n = 15 when utilizing curtailed and semi-curtailed sampling was 12.90 (IQR: 12.87–12.94) and 14.50 (IQR: 14.49–14.52), respectively. When the maximum sample size was increased to n = 25, the ASN for curtailed and semi-curtailed sampling increased to 21.54 (IQR: 21.50–21.59) and 24.2 (24.14–24.18), respectively.

This work outlines a unified and systematic approach to designing Multiple Category-LQAS classification systems with application to the prevalence of _{1} = 1_{2} = 7

Our findings resonate with empirical results pointing to the reliability and potential cost-reduction associated with using LQAS for rapid assessment of

A limitation of this study is the lack of consideration for diagnostic sensitivity and specificity. The standard method for diagnosis of

A shortcoming of our study is that we ignore the underlying distribution of prevalence. In the event that prior information on the level or distribution of

A strength of our study is the principled treatment of curtailed and semi-curtailed sampling in LQAS. The ASN is a largely ignored piece of information that program managers can utilize to inform their choice of LQAS design. Note that curtailed sampling plans allow for early stopping with a classification of moderate prevalence, in addition to low and high. This is in contrast to other sequential LQAS designs used for multiple category classification in the literature, such as those used to classify transmitted HIV drug resistance

Further work is required to evaluate the use of MC-LQAS for sampling for several infections; for example the collection of stool samples to diagnose

LQAS as a tool has come to be associated with simplicity and versatility. MC-LQAS maintains these attributes so as to be useful to a wider audience of practitioners. Here we consider the case of

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We thank Archie Clements, Alan Fenwick and Narcis Kabatereine for providing access to their data.