The epistemology of the SARS-CoV-2 test

Abstract

We investigate the epistemological consequences of a positive SARS-CoV-2 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 sole cause of flu-like symptoms in a given patient. We ask two fundamental epistemological questions regarding each hypothesis: First, given a positive SARS-CoV-2 test, what should we believe about the hypothesis and to what degree? Second, how much evidence does a positive test provide for a 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 for realistic assumptions about the base rate of infected individuals, P(V)≲20%, positive tests having low specificity (75%) would not raise the posterior probability for V to more than 50%. Furthermore, if the test specificity is less than 88.1%, even a positive test having 95% sensitivity would only yield weak to moderate evidence for V against ¬V. We also find that in plausible scenarios, positive tests would only provide weak to moderate evidence for C unless the tests have a high specificity. One has thus to be careful in ascribing the symptoms or death of a positively tested patient to SARS-CoV-2, if the possibility exists that the disease has been caused by another pathogen.

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