A tweetorial in the guise of a story.
A woman is hoping to have her elderly mother visit from out of town. She and her husband are asymptomatic and have been very careful about contacts. The mother, who is driving from Maine, is well, and has had no risk contacts.
The husband suggests that he and his wife get tested to assure that it is safe for his mother-in-law to visit. Is he being thoughtful or is he trying to get out of having her visit?
It is hard to get good numbers for the test characteristics for NP, PCR test for COVID-19. But here are some numbers I have seen (bear with me, if you don't like the numbers, change them, doesn't much matter).
Sensitivity: 95%
Specificity: 85%
LR+: 6.33
LR-: 0.58
What is the husband and wife’s pretest probability for having COVID-19?
We don’t know. The cumulative positive test rate in Chicago is ~ 5% but this depends on the availability of testing, allowed indications for testing, general anxiety in the community…
The case rate in Chicago is 13/100,000 (0.013%).
So, for the sake of this tweetorial, let’s go with a 1% risk for our socially distanced, asymptomatic couple.
Pretest probability is 1%
If he tests positive (and we use the LR+ of 6.33)
His post test probability is 6%. Meaning that the chance the test is a false positive is 94%.
Seems like his recommendation to get tested was self interest rather than altruism.
...and because my numbers appropriately irritated people who know more than me, if we go with 95% sens and 99% spec we get a post test probability of ~ 49%. (I still think he is trying to keep his MIL in Maine! 😉)