A statistical model of COVID-19 testing in populations: effects of sampling bias and testing errors

Böttcher, Lucas; D’Orsogna, Maria R.; Chou, Tom

doi:10.1101/2021.05.22.21257643

Cited by 5 publications

(8 citation statements)

References 17 publications

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“…Early on, this shortcoming was attributed to low prevalence, which made it difficult to distinguish true and false positives (Bond et al (2020)). However, it soon became clear that there were deeper issues related to statistical interpretation of raw data, suggesting the need to revisit the underlying theory of diagnostic classification (Bermingham et al (2020), Patrone & Kearsley (2021), Böttcher et al (2022)).…”

Section: Introductionmentioning

confidence: 99%

Optimal Decision Theory for Diagnostic Testing: Minimizing Indeterminate Classes with Applications to Saliva-Based SARS-CoV-2 Antibody Assays

Patrone¹,

Prajakta²,

Pisanic³

et al. 2022

Preprint

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In diagnostic testing, establishing an indeterminate class is an effective way to identify samples that cannot be accurately classified. However, such approaches also make testing less efficient and must be balanced against overall assay performance. We address this problem by reformulating data classification in terms of a constrained optimization problem that (i) minimizes the probability of labeling samples as indeterminate while (ii) ensuring that the remaining ones are classified with an average target accuracy X. We show that the solution to this problem is expressed in terms of a bathtub principle that holds out those samples with the lowest local accuracy up to an Xdependent threshold. To illustrate the usefulness of this analysis, we apply it to a multiplex, saliva-based SARS-CoV-2 antibody assay and demonstrate up to a 30 % reduction in the number of indeterminate samples relative to more traditional approaches.

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Section: Introductionmentioning

confidence: 99%

Optimal Decision Theory for Diagnostic Testing: Minimizing Indeterminate Classes with Applications to Saliva-Based SARS-CoV-2 Antibody Assays

Patrone¹,

Prajakta²,

Pisanic³

et al. 2022

Preprint

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“…Estimating prevalence -the proportion of a population that has been infected by a disease -is a fundamental problem in epidemiology. Nonetheless, many core mathematical issues associated with this task have only been recently discovered and understood [1,2]. For example, it has long been assumed that classification of samples as positive or negative is necessary to compute the prevalence.…”

Section: Introductionmentioning

confidence: 99%

Minimizing Uncertainty in Prevalence Estimates

Patrone¹,

Kearsley²

2022

Preprint

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Estimating prevalence, the fraction of a population with a certain medical condition, is fundamental to epidemiology. Traditional methods rely on classification of test samples taken at random from a population. Such approaches to estimating prevalence are biased and have uncontrolled uncertainty. Here, we construct a new, unbiased, minimum variance estimator for prevalence. Recent result show that prevalence can be estimated from counting arguments that compare the fraction of samples in an arbitrary subset of the measurement space to what is expected from conditional probability models of the diagnostic test. The variance of this estimator depends on both the choice of subset and the fraction of samples falling in it. We employ a bathtub principle to recast variance minimization as a one-dimensional optimization problem. Using symmetry properties, we show that the resulting objective function is well-behaved and can be numerically minimized.

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“…Probability models can be formulated to quantify phenomena, such as: (i) the degree to which positive samples have higher antibody levels than negatives; (ii) statistical correlation of data; and (iii) the outline of data described in terms of shapes like spheres or cones. Several previous works have used mathematical modeling in diagnostic classification [6,7]. A recent approach applied a combination of modeling and optimal decision theory to antibody testing and proved optimality for binary classification [6]; [see 8, Chapter 3].…”

Section: Introductionmentioning

confidence: 99%

“…A recent approach applied a combination of modeling and optimal decision theory to antibody testing and proved optimality for binary classification [6]; [see 8, Chapter 3]. Another study built a statistical model for binary classification that accounted for sample bias and used either antibody or viral-load tests [7].…”

Section: Introductionmentioning

confidence: 99%

Modeling in higher dimensions to improve diagnostic testing accuracy: theory and examples for multiplex saliva-based SARS-CoV-2 antibody assays

Luke¹,

Kearsley²,

Pisanic³

et al. 2022

Preprint

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The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic has emphasized the importance and challenges of correctly interpreting antibody test results. Identification of positive and negative samples requires a classification strategy with low error rates, which is hard to achieve when the corresponding measurement values overlap. Additional uncertainty arises when classification schemes fail to account for complicated structure in data. We address these problems through a mathematical framework that combines high dimensional data modeling and optimal decision theory. Specifically, we show that appropriately increasing the dimension of data better separates positive and negative populations and reveals nuanced structure that can be described in terms of mathematical models. We combine these models with optimal decision theory to yield a classification scheme that better separates positive and negative samples relative to traditional methods such as confidence intervals (CIs) and receiver operating characteristics. We validate the usefulness of this approach in the context of a multiplex salivary SARS-CoV-2 immunoglobulin G assay dataset. This example illustrates how our analysis: (i) improves the assay accuracy (e.g. lowers classification errors by up to 35 % compared to CI methods); (ii) reduces the number of indeterminate samples when an inconclusive class is permissible (e.g. by 40 % compared to the original analysis of the example multiplex dataset); and (iii) decreases the number of antigens needed to classify samples. Our work showcases the power of mathematical modeling in diagnostic classification and highlights a method that can be adopted broadly in public health and clinical settings.

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A statistical model of COVID-19 testing in populations: effects of sampling bias and testing errors

Cited by 5 publications

References 17 publications

Optimal Decision Theory for Diagnostic Testing: Minimizing Indeterminate Classes with Applications to Saliva-Based SARS-CoV-2 Antibody Assays

Optimal Decision Theory for Diagnostic Testing: Minimizing Indeterminate Classes with Applications to Saliva-Based SARS-CoV-2 Antibody Assays

Minimizing Uncertainty in Prevalence Estimates

Modeling in higher dimensions to improve diagnostic testing accuracy: theory and examples for multiplex saliva-based SARS-CoV-2 antibody assays

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