Interpreting Covid-19 Test Results: A Bayesian Approach

bayesian-inferencediagnostic-testingcovid-19sensitivity-specificity

Abstraction: Bayesian pretest-probability framework for interpreting COVID-19 test results

Key points:

Correct test interpretation requires both test characteristics (sensitivity/specificity) and pretest probability (prevalence + symptoms + exposure)
Viral PCR assumed ~70% sensitive, 99.5% specific; a negative test in NYC in March (70% prevalence) still left a 41% chance of infection
Same negative test in San Francisco (15% prevalence, March) reduced post-test probability to 5% — clinically actionable
Antibody test with 80% sensitivity and 99% specificity at 0.5% SF prevalence: 71% of positives are false positives
Sequential Bayesian updating: a prior positive PCR raises pretest probability for subsequent antibody test from 0.5% to ~30%, flipping a positive antibody result from mostly-false to 97% true positive
Loss of taste/smell is the only COVID symptom with meaningful diagnostic specificity; flu symptoms alone don't substantially move pretest probability

Connections: Bayesian Inference · Diagnostic Testing · Sensitivity Specificity