[BostonCard]

A very sensitive test is one that will capture all the people who had the disease. An 80% sensitive test means that for every 5 negatives, one of those patients actually had the disease but has a negative result, though you can't say which of those 5 results is incorrect.



A very specific test is one that will not be positive if you did not have the disease. So a 99% specific test means that 1 out of a hundred people who were told they had the disease, actually did not have it.



Hope this answers your question. I would like to read the paper to see how they arrived at those numbers.

This is not quite right; you are talking about an 80% negative predictive value, not an 80% sensitivity.  How to adjust for false negatives depends a bit on the prevalence.  For example, in the event that you had a disease with 100% prevalence, then all of your negative tests, by definition would be false negatives (since everyone should be positive).  In the event that you had a disease with 0% prevalence, then you would not have any false negatives by definition, since every negative test would reflect a true negative.

You can plug in the numbers in this spreadsheet:
https://docs.google.com/spreadsheets/d/1...edit#gid=0

It turns out that negative predictive value is about 99.4%, driven by the relatively low prevalence.  So for every 1000 negative tests, 994 will be correct (true negatives) and 6 will be false negatives.  The positive predictive value is 95% which means that for every 100 positive test results, 5 will be false positives, and 95 will be true positives.

Given the test performance characteristics, out of the 3330 people they tested, about 94 of them would have had COVID-19.  Of these, 75 would have tested positive and 18 would have tested negative (numbers don't add up to 100 due to rounding).  The vast majority of the patients (3236 would not have had COVID-19, and of those, because of the high specificity, 3239 would have correctly had a negative test and 16 would have had a positive test, so in all they would have seen about 91 positive tests (95% of which would have been true positives) and 3239 negative tests (of which 99.4% would have been true negatives).

BC

[BostonCard]

A very sensitive test is one that will capture all the people who had the disease. An 80% sensitive test means that for every 5 negatives, one of those patients actually had the disease but has a negative result, though you can't say which of those 5 results is incorrect.



A very specific test is one that will not be positive if you did not have the disease. So a 99% specific test means that 1 out of a hundred people who were told they had the disease, actually did not have it.



Hope this answers your question. I would like to read the paper to see how they arrived at those numbers.

This is not quite right; you are talking about an 80% negative predictive value, not an 80% sensitivity.  How to adjust for false negatives depends a bit on the prevalence.  For example, in the event that you had a disease with 100% prevalence, then all of your negative tests, by definition would be false negatives (since everyone should be positive).  In the event that you had a disease with 0% prevalence, then you would not have any false negatives by definition, since every negative test would reflect a true negative.

You can plug in the numbers in this spreadsheet:
https://docs.google.com/spreadsheets/d/1...edit#gid=0

It turns out that negative predictive value is about 99.4%, driven by the relatively low prevalence.  So for every 1000 negative tests, 994 will be correct (true negatives) and 6 will be false negatives.  The positive predictive value is 95% which means that for every 100 positive test results, 5 will be false positives, and 95 will be true positives.

Given the test performance characteristics, out of the 3330 people they tested, about 94 of them would have had COVID-19.  Of these, 75 would have tested positive and 18 would have tested negative (numbers don't add up to 100 due to rounding).  The vast majority of the patients (3236 would not have had COVID-19, and of those, because of the high specificity, 3239 would have correctly had a negative test and 16 would have had a positive test, so in all they would have seen about 91 positive tests (95% of which would have been true positives) and 3239 negative tests (of which 99.4% would have been true negatives).

BC