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I'm comparing a bunch of SARS-CoV2 rapid antigen tests:

Table Source

Columns 4 and 6 list the values for sensitivity and limit of detection (LOD). How come that a test with a several times lower limit of detection can have a worse sensitivity?

As an example, consider tests #2 and #4:

#2 - Sensitivity: 97.7% - Limit of detection: 2.0*10^2.4 = 502 TCID50/ml

#4 - Sensitivity: 91.4% - Limit of detection: 2.5*10^1.8 = 158 TCID50/ml

Shouldn't these values correlate, i.e. the more sensitive a test is the smaller the amount it is still able to detect?

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Not necessarily. Sensitivity and specificity are decision criterion-based measures. They are not actually separable from another, they are a consequence of choosing a threshold at which to say "the test reports positive" or "the test reports negative", a consequence of this binary result. As such they are weighed against each other. You can always make a test with 100% sensitivity as long as you always report "Yes". You can always make a test with 100% specificity as long as you always report "No".

Similarly, you can define what it means to have reached a limit of detection, but this need not be the same trade-off as the one you use for sensitivity and specificity. For example, you might declare this as the point where your readout is "significantly greater" than baseline in a collection of known positives vs known negatives. But if you set your decision threshold right at that level of detection, you may still have, let's say, only 50% specificity at that level and accept too many false-positives, so you set a different decision criteria.

They are apples and oranges, there is no reason they need to correspond.

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  • $\begingroup$ Thanks for your answer! So which value is more indicative for the quality of the test? Say, I have two tests with the same sensitivity, but one has a much lower LOD - or - two tests with similar LOD, but one has a higher sensitivity (all other parameters being similar, incl. specificity). How to make a decision? $\endgroup$
    – david
    Jan 8, 2021 at 19:28
  • $\begingroup$ @david There isn't enough information to make that decision. Probably all of the tests on your list are statistically equivalent, unless there are substantial discrepancies in how they were evaluated. For example, you could get an artificially high sensitivity if you tested only very saturated target samples. You would need much more extensive real-world evaluation than I am aware of anyone having on hand as of yet. $\endgroup$
    – Bryan Krause
    Jan 8, 2021 at 19:31
  • $\begingroup$ Also, making a test report always "Yes" doesn't make it 100% sensitive if it gives false positives most of the time, does it? Sensitivity measures the true positives, so one cannot simply "tweak" the reported sensitivity by relaxing specificity, right? Example: If my test reports "Yes" every time it encounters aqueous oxygen, this doesn't make it 100% sensitive (it could very well be 0% sensitive by completely failing to detect the antigen in a deoxygenated solution). $\endgroup$
    – david
    Jan 8, 2021 at 19:33
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    $\begingroup$ @david Sensitivity is "true positives"/"actual positives". If you always report Yes, you will have 100% sensitivity: you report every actual positive as true positive. You will also report a lot of Yes when it is an "actual negative", but this doesn't hurt your sensitivity, it hurts your specificity. A test that always says "Yes" has 100% sensitivity and 0% specificity. You're right that this isn't a very good test, but just knowing sensitivity doesn't help much with that. $\endgroup$
    – Bryan Krause
    Jan 8, 2021 at 19:37
  • $\begingroup$ Are you using "true" and "actual" as synonyms or are you saying that sensitivity = true pos./actual pos.? $\endgroup$
    – david
    Jan 9, 2021 at 14:18

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