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Problem:

After the EUA for SARS-CoV-2 tests, we have a diagnostic test that passes both of the following criteria:

All first five true-negative samples each produce a negative test result.

All first five true-positive samples each produce a positive test result.

We want to know, given these criteria, what is the maximum false-{positive, negative} rate per assay that can give chance alpha of passing results. This should be treated separately for f_P and f_N.

Put differently, we want to know how bad the error-rate of an EUA test can be compared to an FDA standard test in the different directions and still have chance alpha, e.g. 5%, of passing the above criteria.


Added variation, this is the reality

Test results (positive and negative) from unknown samples are confirmed by concordant results on a different EUA diagnostic test passing similar criteria with false-positives f_EUA2_P and false-negatives f_EUA2_N. Taking that into account, how does the above get worse.


Note: not inconceivable this could be recursed 2-3 times.

This is the reality we are dealing with, which is the current passing standard for EUA tests.

We also want to know what the maximum expected false positives and false negatives would be under this regime for different alpha.

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