No test is better than a bad test"": Impact of diagnostic uncertainty in mass testing on the spread of Covid-19

Nicholas Gray; Dominic Calleja; Alex Wimbush; Enrique Miralles-Dolz; Ander Gray; Marco De-Angelis; Elfride Derrer-Merk; Bright Uchenna Oparaji; Vladimir Stepanov; Louis Clearkin; Scott Ferson

The prevalence of the disease matters. The P P V can vary drastically for different populations with different prevalence. The idea that prevalence depends on the population may seem counterintuitive to some audiences. For example, if we were to select 100 people from a respiratory ward this week from any hospital in the UK, and 100 people from a street outside the building, what proportion of each population have Covid-19? If one tests both populations with the same test and found positives in each population, which would have the higher P P V ? To illustrate the impact of prevalence on P P V , for a test with σ = τ = 0.95 if prevalence p = 0.05, then the P P V ≈ 0.48. Figure 1 shows why, for 1000 test subjects there will be similar numbers of true and false positives even with high sensitivity and specificity of 95%. In contrast, using the same tests on a sample with a higher prevalence p = 0.5 we find the P P V = 0.8, see Figure 2 . Similarly, the N P V is lower when the prevalence is higher.