Does my patient have SARS-CoV-2 infection? A reminder of clinical probability formulas.

Around the world, people are wondering, ‘Do I have SARS-CoV-2?’. Determining a person’s probability of illness is central to the practice and teaching of evidence-based medicine (EBM). Probabilities can be calculated through mathematical formulas, but studies find that many clinicians have difficulty with the calculations.1–4 For many conditions in medicine, clinicians can rely on experience and/or established algorithms. However, with SARS-CoV-2 infection, clinicians lack experience and, given the rapidly changing prevalence of the illness, algorithms are difficult to establish. In this manuscript, we use the example of SARS-CoV-2 as an educational reminder of how clinicians can roughly gauge the probability of illness in different contexts and to highlight some conceptual issues in the estimates needed for the formulas. Broadly speaking, the diagnostic process involves a sequence of estimating the probability of an illness and then adjusting this estimate with each new piece of information. Clinicians are generally taught to calculate the probability of illness given new information through either the use of Bayes probability theorem or the use of a 2×2 contingency table. Mathematically, Bayes theorem and the 2×2 table are the same calculation. The 2×2 table calculation appears less complex than Bayes theorem, because it converts conditional probabilities into numbers that are entered into the cells of the table.2 ### Bayes probability theorem In writing formulas, the term ‘given’ is symbolised as a straight vertical line. Letting ‘P’=probability, ‘A’=SARS-CoV-2 and ‘B’=new information, Bayes probability theorem is: P(A I B)=[P(A) × P(B I A)] / P(B).5 Imagine that B, the new information, is the symptom of a cough. Then the probability of SARS-CoV-2 for a patient given the presence of cough, P(A I B), is equal to the probability of SARS-CoV-2 in the patient’s community, P(A), multiplied by the probability of cough given that the patient has SARS-CoV-2, P(B I A), …