英文标题：
《Binary Classification Tests, Imperfect Standards, and Ambiguous
  Information》
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作者：
Gabriel Ziegler
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最新提交年份：
2021
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英文摘要：
  New binary classification tests are often evaluated relative to a pre-established test. For example, rapid Antigen tests for the detection of SARS-CoV-2 are assessed relative to more established PCR tests. In this paper, I argue that the new test can be described as producing ambiguous information when the pre-established is imperfect. This allows for a phenomenon called dilation -- an extreme form of non-informativeness. As an example, I present hypothetical test data satisfying the WHO\'s minimum quality requirement for rapid Antigen tests which leads to dilation. The ambiguity in the information arises from a missing data problem due to imperfection of the established test: the joint distribution of true infection and test results is not observed. Using results from Copula theory, I construct the (usually non-singleton) set of all these possible joint distributions, which allows me to assess the new test\'s informativeness. This analysis leads to a simple sufficient condition to make sure that a new test is not a dilation. I illustrate my approach with applications to data from three COVID-19 related tests. Two rapid Antigen tests satisfy my sufficient condition easily and are therefore informative. However, less accurate procedures, like chest CT scans, may exhibit dilation.
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中文摘要：
新的二元分类测试通常相对于预先建立的测试进行评估。例如，用于检测SARS-CoV-2的快速抗原试验是相对于更成熟的PCR试验进行评估的。在本文中，我认为新的测试可以被描述为当预先建立的测试不完美时产生模糊信息。这就产生了一种叫做膨胀的现象——一种非信息性的极端形式。作为一个例子，我给出了满足世卫组织快速抗原检测最低质量要求的假设检测数据，这将导致扩张。信息的模糊性源于由于已建立的测试不完善而导致的数据缺失问题：未观察到真实感染和测试结果的联合分布。利用Copula理论的结果，我构造了所有这些可能的联合分布的集合（通常是非单态的），这允许我评估新测试的信息性。该分析得出了一个简单的充分条件，以确保新测试不是一个膨胀。我用三个2019冠状病毒疾病相关测试的数据来说明我的方法。两种快速抗原检测很容易满足我的充分条件，因此信息丰富。然而，不太准确的程序，如胸部CT扫描，可能会出现扩张。
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分类信息：

一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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