| I agree with you, also the bogus argument of "since most people are HIV free..." assumes direct testing instead of pooled testing (using modern information theoretic optimized pooled testing). A bit of data is most informative if the entropy is 1 bit as well. A signal that is true most of the time, or a different signal that is false most of the time is less informative. Use pooled testing such that the result is true or false half of the time. Had information theoretically justified pooled testing been applied from the start, then: * 1) control-testing the testing contractors would have been straightforward and passing 10 control samples by chance would have a likelihood of 1 over 1024. * 2) it would have made obvious that saving money on control-testing the contractors would hardly save any money * 3) even in the bad scenario that control testing was skipped, the issue of contractors cheating would have surfaced much faster, since combining the pooled tests to identify which patient tests positive would constantly result in mysteries, meaning control-testing needs to be enabled, not the mathematics of pooled testing brought in doubt. * 4) testing pharma industry hates pooled testing, as it means technological competition instead of sales growth by abusing the naive but false "common sense" that you need as many tests as patients tested. on a side note: assuming tests with different operating point on the RoC curves (having different false positive vs false negative ratios) have different prices, do we know if the operators blatantly provided fabricated results, or if they blatantly ignored basic mathematics and thought the more expensive tests could be substituted by the cheaper ones even if intended for a different purpose? consider a test designed for telling a patient that we diagnosed HIV, and then consider a test designed for screening an organ to be inserted into a patient. do you think they should both use the same test? or do you think it wiser to have the diagnosis test have lower false positive rates, and the organ screening test to have lower false negative rates? |