An optimization framework for large-scale screening under limited testing capacity with application to COVID-19.

We consider the problem of targeted mass screening of heterogeneous populations under limited testing capacity. Mass screening is an essential tool that arises in various settings, e.g., ensuring a safe supply of blood, reducing prevalence of sexually transmitted diseases, and mitigating the spread of infectious disease outbreaks. The goal of mass screening is to classify whole population groups as positive or negative for an infectious disease as efficiently and accurately as possible. Under limited testing capacity, it is not possible to screen the entire population and hence administrators must reserve testing and target those among the population that are most in need or most susceptible. This paper addresses this decision problem by taking advantage of accessible population-level risk information to identify the optimal set of sub-populations to target for screening. We conduct a comprehensive analysis that considers the two most commonly adopted schemes: Individual testing and Dorfman group testing. For both schemes, we formulate an optimization model that aims to minimize the number of misclassifications under a testing capacity constraint. By analyzing the formulations, we establish key structural properties which we use to construct efficient and accurate solution techniques. We conduct a case study on COVID-19 in the United States using geographic-based data. Our results reveal that the considered proactive targeted schemes outperform commonly adopted practices by substantially reducing misclassifications. Our case study provides important managerial insights with regards to optimal allocation of tests, testing designs, and protocols that dictate the optimality of schemes. Such insights can inform policy-makers with tailored and implementable data-driven recommendations.

A data-driven simulation approach to quantify the effect of group counseling on system performance of college counseling centers.

Objective: To investigate the effectiveness, from a system's perspective, of offering group counseling options in college counseling centers. Methods: We achieve this through a data-driven simulation-based approach with the aim of providing administrators with a quantitative tool that informs their decision-making process. Results: Our simulation experiments reveal that offering group counseling options without resource reallocation does not have the desired positive impact on the system's performance. However, with resource reallocation, our results demonstrate that the introduction of group counseling options can significantly improve the performance of the system by as much as 40%. Conclusions: Group counseling options, coupled with proper resource reallocation strategies, are effective in reducing access time of first-time patients by as much as 40%. The effect of group counseling is highly dependent on both the number of offered groups as well as their scheduling policy. Scheduling policies have to be scrutinized in light of their resulting group waiting time and resource-utilization efficiency.

Screening multi-dimensional heterogeneous populations for infectious diseases under scarce testing resources, with application to COVID-19.

Testing provides essential information for managing infectious disease outbreaks, such as the COVID-19 pandemic. When testing resources are scarce, an important managerial decision is who to test. This decision is compounded by the fact that potential testing subjects are heterogeneous in multiple dimensions that are important to consider, including their likelihood of being disease-positive, and how much potential harm would be averted through testing and the subsequent interventions. To increase testing coverage, pooled testing can be utilized, but this comes at a cost of increased false-negatives when the test is imperfect. Then, the decision problem is to partition the heterogeneous testing population into three mutually exclusive sets: those to be individually tested, those to be pool tested, and those not to be tested. Additionally, the subjects to be pool tested must be further partitioned into testing pools, potentially containing different numbers of subjects. The objectives include the minimization of harm (through detection and mitigation) or maximization of testing coverage. We develop data-driven optimization models and algorithms to design pooled testing strategies, and show, via a COVID-19 contact tracing case study, that the proposed testing strategies can substantially outperform the current practice used for COVID-19 contact tracing (individually testing those contacts with symptoms). Our results demonstrate the substantial benefits of optimizing the testing design, while considering the multiple dimensions of population heterogeneity and the limited testing capacity.

A robust pooled testing approach to expand COVID-19 screening capacity.

Limited testing capacity for COVID-19 has hampered the pandemic response. Pooling is a testing method wherein samples from specimens (e.g., swabs) from multiple subjects are combined into a pool and screened with a single test. If the pool tests positive, then new samples from the collected specimens are individually tested, while if the pool tests negative, the subjects are classified as negative for the disease. Pooling can substantially expand COVID-19 testing capacity and throughput, without requiring additional resources. We develop a mathematical model to determine the best pool size for different risk groups, based on each group's estimated COVID-19 prevalence. Our approach takes into consideration the sensitivity and specificity of the test, and a dynamic and uncertain prevalence, and provides a robust pool size for each group. For practical relevance, we also develop a companion COVID-19 pooling design tool (through a spread sheet). To demonstrate the potential value of pooling, we study COVID-19 screening using testing data from Iceland for the period, February-28-2020 to June-14-2020, for subjects stratified into high- and low-risk groups. We implement the robust pooling strategy within a sequential framework, which updates pool sizes each week, for each risk group, based on prior week's testing data. Robust pooling reduces the number of tests, over individual testing, by 88.5% to 90.2%, and 54.2% to 61.9%, respectively, for the low-risk and high-risk groups (based on test sensitivity values in the range [0.71, 0.98] as reported in the literature). This results in much shorter times, on average, to get the test results compared to individual testing (due to the higher testing throughput), and also allows for expanded screening to cover more individuals. Thus, robust pooling can potentially be a valuable strategy for COVID-19 screening.

A methodology for deriving the sensitivity of pooled testing, based on viral load progression and pooling dilution.

BACKGROUND: Pooled testing, in which biological specimens from multiple subjects are combined into a testing pool and tested via a single test, is a common testing method for both surveillance and screening activities. The sensitivity of pooled testing for various pool sizes is an essential input for surveillance and screening optimization, including testing pool design. However, clinical data on test sensitivity values for different pool sizes are limited, and do not provide a functional relationship between test sensitivity and pool size. We develop a novel methodology to accurately compute the sensitivity of pooled testing, while accounting for viral load progression and pooling dilution. We demonstrate our methodology on the nucleic acid amplification testing (NAT) technology for the human immunodeficiency virus (HIV). METHODS: Our methodology integrates mathematical models of viral load progression and pooling dilution to derive test sensitivity values for various pool sizes. This methodology derives the conditional test sensitivity, conditioned on the number of infected specimens in a pool, and uses the law of total probability, along with higher dimensional integrals, to derive pooled test sensitivity values. We also develop a highly accurate and easy-to-compute approximation function for pooled test sensitivity of the HIV ULTRIO Plus NAT Assay. We calibrate model parameters using published efficacy data for the HIV ULTRIO Plus NAT Assay, and clinical data on viral RNA load progression in HIV-infected patients, and use this methodology to derive and validate the sensitivity of the HIV ULTRIO Plus Assay for various pool sizes. RESULTS: We demonstrate the value of this methodology through optimal testing pool design for HIV prevalence estimation in Sub-Saharan Africa. This case study indicates that the optimal testing pool design is highly efficient, and outperforms a benchmark pool design. CONCLUSIONS: The proposed methodology accounts for both viral load progression and pooling dilution, and is computationally tractable. We calibrate this model for the HIV ULTRIO Plus NAT Assay, show that it provides highly accurate sensitivity estimates for various pool sizes, and, thus, yields efficient testing pool design for HIV prevalence estimation. Our model is generic, and can be calibrated for other infections.

Sequential prevalence estimation with pooling and continuous test outcomes.

Prevalence estimation is crucial for controlling the spread of infections and diseases and for planning of health care services. Prevalence estimation is typically conducted via pooled, or group, testing due to limited testing budgets. We study a sequential estimation procedure that uses continuous pool readings and considers the dilution effect of pooling so as to efficiently estimate an unknown prevalence rate. Embedded into the sequential estimation procedure is an optimization model that determines the optimal pooling design (number of pools and pool sizes) under a limited testing budget, considering the trade-off between testing cost and estimation accuracy. Our numerical study indicates that the proposed sequential estimation procedure outperforms single-stage procedures, or procedures that use binary test outcomes. Further, the sequential procedure provides robust prevalence estimates in cases where the initial estimate of the unknown prevalence rate is poor, or the assumed distribution of the biomarker load in infected subjects is inaccurate. Thus, when limited and unreliable information is available about the current status of, or biomarker dynamics related to, an infection, the sequential procedure becomes an attractive estimation strategy, due to its ability to mitigate the initial bias.

Residual risk and waste in donated blood with pooled nucleic acid testing.

An accurate estimation of the residual risk of transfusion-transmittable infections (TTIs), which includes the human immunodeficiency virus (HIV), hepatitis B and C viruses (HBV, HCV), among others, is essential, as it provides the basis for blood screening assay selection. While the highly sensitive nucleic acid testing (NAT) technology has recently become available, it is highly costly. As a result, in most countries, including the United States, the current practice for human immunodeficiency virus, hepatitis B virus, hepatitis C virus screening in donated blood is to use pooled NAT. Pooling substantially reduces the number of tests required, especially for TTIs with low prevalence rates. However, pooling also reduces the test's sensitivity, because the viral load of an infected sample might be diluted by the other samples in the pool to the point that it is not detectable by NAT, leading to potential TTIs. Infection-free blood may also be falsely discarded, resulting in wasted blood. We derive expressions for the residual risk, expected number of tests, and expected amount of blood wasted for various two-stage pooled testing schemes, including Dorfman-type and array-based testing, considering infection progression, infectivity of the blood unit, and imperfect tests under the dilution effect and measurement errors. We then calibrate our model using published data and perform a case study. Our study offers key insights on how pooled NAT, used within different testing schemes, contributes to the safety and cost of blood. Copyright © 2016 John Wiley & Sons, Ltd.