{"title":"Optimal group testing with heterogeneous risks.","authors":"Nina Bobkova, Ying Chen, Hülya Eraslan","doi":"10.1007/s00199-023-01502-3","DOIUrl":null,"url":null,"abstract":"<p><p>We consider optimal group testing of individuals with heterogeneous risks for an infectious disease. Our algorithm significantly reduces the number of tests needed compared to Dorfman (Ann Math Stat 14(4):436-440, 1943). When both low-risk and high-risk samples have sufficiently low infection probabilities, it is optimal to form heterogeneous groups with exactly one high-risk sample per group. Otherwise, it is not optimal to form heterogeneous groups, but homogeneous group testing may still be optimal. For a range of parameters including the U.S. Covid-19 positivity rate for many weeks during the pandemic, the optimal size of a group test is four. We discuss the implications of our results for team design and task assignment.</p>","PeriodicalId":47982,"journal":{"name":"Economic Theory","volume":" ","pages":"1-32"},"PeriodicalIF":1.2000,"publicationDate":"2023-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10243685/pdf/","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Economic Theory","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1007/s00199-023-01502-3","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
Abstract
We consider optimal group testing of individuals with heterogeneous risks for an infectious disease. Our algorithm significantly reduces the number of tests needed compared to Dorfman (Ann Math Stat 14(4):436-440, 1943). When both low-risk and high-risk samples have sufficiently low infection probabilities, it is optimal to form heterogeneous groups with exactly one high-risk sample per group. Otherwise, it is not optimal to form heterogeneous groups, but homogeneous group testing may still be optimal. For a range of parameters including the U.S. Covid-19 positivity rate for many weeks during the pandemic, the optimal size of a group test is four. We discuss the implications of our results for team design and task assignment.
我们考虑对具有不同传染病风险的个体进行最佳群体检测。与Dorfman相比，我们的算法显著减少了所需的测试次数（Ann Math Stat 14（4）:436-4401943）。当低风险和高风险样本的感染概率都足够低时，最好形成异质组，每组只有一个高风险样本。否则，形成异质组不是最优的，但同质组测试可能仍然是最优的。对于一系列参数，包括美国在大流行期间多周的新冠肺炎阳性率，团体检测的最佳规模为4。我们讨论了我们的结果对团队设计和任务分配的影响。
期刊介绍：
The purpose of Economic Theory is to provide an outlet for research - in all areas of economics based on rigorous theoretical reasoning, and
- on specific topics in mathematics which is motivated by the analysis of economic problems. Economic Theory''s scope encompasses - but is not limited to - the following fields. - classical and modern equilibrium theory
- cooperative and non-cooperative game theory
- macroeconomics
- social choice and welfare
- uncertainty and information, intertemporal economics (including dynamical systems)
- public economics
- international and developmental economics
- financial economics, money and banking
- industrial organization Economic Theory also publishes surveys if they clearly picture the basic ideas at work in some areas, the essential technical apparatus which is used and the central questions which remain open. The development of a productive dialectic between stylized facts and abstract formulations requires that economic relevance be at the forefront. Thus, correct, and innovative, mathematical analysis is not enough; it must be motivated by - and contribute to - the understanding of substantive economic problems.
Officially cited as: Econ Theory
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