Test results, part 2: how about negative results?

Ideal case

If you know nothing else besides the test result, then it’s very reliable: 99.9898%, which is basically 100%.

In the real world

Turns out, the negative result remains very robustly trustworthy even when the infection rate grows very large (or you’re in a cohort with a large infection rate).

  • at 10% infection rate, the test is still 99.9% reliable
  • at 50% infection rate, it’s 99% reliable
  • at 90% infection rate, it’s 91.7% reliable
  • at 99% infection rate, it finally drops to 50% reliability (coin toss)
reliability of a negative result as a function of infection rate
healthy.chance <- function(inf.rate, test.rel = 0.99, tot.pop = 10000) {
sick.pop <- tot.pop * inf.rate
healthy.pop <- tot.pop - sick.pop
pos.sick <- sick.pop * test.rel
neg.sick <- sick.pop - pos.sick
neg.healthy <- healthy.pop * test.rel
neg.total <- neg.sick + neg.healthy
chance <- neg.healthy / neg.total
return(chance)
}
infection.rate <- 1:100 / 100
chances <- lapply(infection.rate, healthy.chance)
plot(infection.rate, chances, col = 'blue'); grid()

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Florin Andrei

Florin Andrei

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Graduated Physics. Engineer in the computer industry. Working on my Master’s degree in Data Science.