As of March 13, 45/301 people have tested positive/negative for COVID-19 in Florida. What is the expected false positives/negatives here?
UPDATE (March 14): 71/478 from what I consider the best source.
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See long answer for How accurate are coronavirus tests?
With the "worst-case numbers" from there which I take from the minimum performance requirements the FDA currently uses with an emergency validation to allow labs to quickly implement Covid-19 tests without undergoing the full validation procedure they normally take, we have LR+ ≈ 11 and LR- ≈ 1/20.
The tests may be (and probably are) actually much better.
If we take 71 positive : 478 negative tests as a surrogate for the prevalence of Covid-19 infected among the tested population (14.5 %), the post-test probabilities of having Covid-19 are
71 : 478 * 11 = 781 : 478 ≈ 5 : 3 for those who tested positive, i.e. ≈ 62 % PPV or post-test probability of having Covid-19.
Thus, as many as 38 % of the 71 or 27 could be false positives.
71 : 478 * 1/20 = 71 : 9560 ≈ 1 : 135 or 0.7 % post-test probability of nevertheless really having Covid-19.
I.e. up to maybe 1 false negative case.
Update: I've updated the linked answer since I've meanwhile found more detailed data on the actual validation performed for several tests. Most of them used more than the minimum required sample size, but it's not that 1000s of validation samples were run. (The infamous CDC test got emergency approval after only 13 positive validation cases, though, so even less. But that was beginning of Feb, and they may not have had more test samples available at that time)
If we want to calculate with expected instead of worst-possible performance for e.g. the Thermo Fisher test, LR+ and LR- would be 61 and 1/61, respectively.
PPV would then have been 90 % (7 false positives) and NPV 0.25 % (0 false negatives).
The published numbers probably based on the PCR test. About the PCR I has found some information few time ago.
At first it is to consider that there is only a certain period in which a sample from a certain area shows results in the PCR. For throat swab samples was found that it can take 4 to 8 days for an existing infection to be displayed with PCR. The time period in which the test remains positive is limited to 4 to 15 days, although the disease continued to develop. Now nasal samples are recommended before taking a throat swab, but there will also be a suitable period for sampling.
In expansion, how accurate are the PCR tests in the period in which the tests should reliable be positive. There is a study in which PCR tests were carried out daily. There is shown that inside of period with positive results, some tests produced a negative result. The days only from first day with a positive result to the last day with a positive result gives a total period of 84 days over all patients. During this time, also 11 tests with negative results were produced. This gives a value of 13.7% negative test results, even though the patient was infected with COVID-19.
It must be noted that PCR testing is not a simple yes/no test. The result first depends whether a sufficient number of viruses is obtained.
Here is described that for a number of 484 copies of SARS-CoV-2 RNA per milliliter some PCR test products detect SARS-CoV-2 with 100% but one other of the approved products detects 0% of virus.
So there is not the one accuracy. It is to be asked which type of test kit was used by which manufacturer, who took how the sample, etc. Every single item can significantly impact the accuracy of a test.