Abstract
Testing multiple subjects within a group, with a single test applied to the group (i.e., group testing), is an important tool for classifying populations as positive or negative for a specific binary characteristic in an efficient manner. We study the design of easily implementable, static group testing schemes that take into account operational constraints, heterogeneous populations, and uncertainty in subject risk, while considering classification accuracy- and robustness-based objectives. We derive key structural properties of optimal risk-based designs and show that the problem can be formulated as network flow problems. Our reformulation involves computationally expensive high-dimensional integrals. We develop an analytical expression that eliminates the need to compute high-dimensional integrals, drastically improving the tractability of constructing the underlying network. We demonstrate the impact through a case study on chlamydia screening, which leads to the following insights: (1) Risk-based designs are shown to be less expensive, more accurate, and more robust than current practices. (2) The performance of static risk-based schemes comprised of only two group sizes is comparable to those comprised of many group sizes. (3) Static risk-based schemes are an effective alternative to more complicated dynamic schemes. (4) An expectation-based formulation captures almost all benefits of a static risk-based scheme.
Highlights
Introduction and MotivationClassifying subjects within a large population as positive or negative for a certain binary characteristic, through screening, is important in many settings
Our contributions in this paper are as follows: First, we model important aspects of group testing that are often overlooked in the literature, such as the implementability of the testing scheme and the uncertainty in subject risk, and we do so within a classification accuracy maximization framework
We explore novel expectation-based and robust formulations of this decision problem, show that both models reduce to a common form, which can be equivalently formulated as a network flow problem, and use this reformulation to solve the static testing design problem to optimality, expanding the previous result on dynamic testing schemes in Aprahamian et al (2019) to static testing schemes under risk uncertainty
Summary
The tester needs to determine the various group sizes to be used in the first stage of Dorfman testing, along with the assignment of heterogeneous subjects, with different risk (probability of positivity) estimates for the binary characteristic, to the different groups. We study the problem of determining optimal static risk-based Dorfman testing schemes, comprised of a set of group sizes and a policy to assign subjects, with different risk, to the mutually exclusive groups, under uncertainty on both subject characteristics (the estimated risk) and the actual risk. The aforementioned studies have improved our understanding of optimal risk-based Dorfman testing for a heterogeneous population, they leave out other important aspects of the problem, such as implementability of the testing scheme and uncertainty in subject risk estimates Both Aprahamian et al (2019) and Hwang (1975) assume that the decision-maker can construct an optimal dynamic testing scheme, customized for each batch of subjects, and subject risk values are deterministic and perfectly observable by the tester. To improve the presentation and flow of the paper, all proofs and derivations are relegated to the appendix
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