## Antibody tests prior and posterior (By P Wellsby)

A friend asked about the significance of her positive Covid tests. She had suggestive symptoms and an antibody test was positive. What did this mean? False negatives may occur if you test too soon, before antibodies have developed or the test might have been faulty. Counterintuitively, the significance to her of a positive test depends on the local prevalence of infection. False positives are rare but if the infection prevalence is very low then there may be more false positives than true positives (this would be more likely if she had no suggestive symptoms). If the infection prevalence is high then there would be more true positives than false positives. She had had two positive antibody tests (separated by weeks and by provider of the test) and so she almost certainly had had Covid. Whether she was less likely to suffer from another bout of Covid is a separate question. Failure to take note of prevalence rates when screening asymptomatic patients for a disease (women under 40 with mammograms for breast cancer for example) can lead to disproportionate over investigation of women who were at low risk.

This is standard Bayesian thinking about probabilities. There are prior probabilities (hopefully well-informed guesses) that can be (repeatedly) modified by fresh data that influence prior probabilities to produce more accurate probabilities, the posteriors (the updated priors). Bayes theorem can be used to manage probabilities mathematically to produce better assessments that the latest posterior is more likely to be correct or very nearly correct