We investigate the epistemological consequences of a positive polymerase chain reaction SARS-CoV test for two relevant hypotheses: (i) V is the hypothesis that an individual has been infected with SARS-CoV-2; (ii) C is the hypothesis that SARS-CoV-2 is the cause of flu-like symptoms in a given patient. We ask two fundamental epistemological questions regarding each hypothesis: First, how much confirmation does a positive test lend to each hypothesis? Second, how much evidence does a positive test provide for each hypothesis against its negation? We respond to each question within a formal Bayesian framework. We construe degree of confirmation as the difference between the posterior probability of the hypothesis and its prior, and the strength of evidence for a hypothesis against its alternative in terms of their likelihood ratio. We find that test specificity—and coinfection probabilities when making inferences about C—were key determinants of confirmation and evidence. Tests with < 87% specificity could not provide strong evidence (likelihood ratio > 8) for V against ¬V regardless of sensitivity. Accordingly, low specificity tests could not provide strong evidence in favor of C in all plausible scenarios modeled. We also show how a positive influenza A test disconfirms C and provides weak evidence against C in dependence on the probability that the patient is influenza A infected given that his/her symptoms are not caused by SARS-CoV-2. Our analysis points out some caveats that should be considered when attributing symptoms or death of a positively tested patient to SARS-CoV-2.

中文翻译：

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SARS-CoV-2 阳性检测的认识论

我们针对两个相关假设调查了聚合酶链反应阳性 SARS-CoV 测试的认识论后果：（i）V 是个人已感染 SARS-CoV-2 的假设；(ii) C 是假设 SARS-CoV-2 是特定患者出现流感样症状的原因。我们对每个假设提出两个基本的认识论问题：首先，阳性检验对每个假设有多少确认？其次，一个正面检验为每个假设提供了多少证据来反对它的否定？我们在正式的贝叶斯框架内回答每个问题。我们将确认程度解释为假设的后验概率与其先验概率之间的差异，以及一个假设在似然比方面反对其替代方案的证据强度。我们发现测试特异性——以及在推断 C 时的共感染概率——是确认和证据的关键决定因素。无论敏感性如何，具有 < 87% 特异性的测试都无法为 V 与 ¬V 提供强有力的证据（似然比 > 8）。因此，低特异性测试无法在所有模拟的合理场景中提供有利于 C 的有力证据。我们还展示了阳性 A 型流感检测如何否定 C 并根据患者感染 A 型流感的概率提供不利于 C 的弱证据，因为他/她的症状不是由 SARS-CoV-2 引起的。我们的分析指出了在将阳性检测患者的症状或死亡归因于 SARS-CoV-2 时应考虑的一些警告。