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We have an exam procedure that we are evaluating (phrasing this in a medical sense, but I think it can be more general): a group of people are examined, some are found to have a physical condition that requires more invasive tests. Those that are not found to have this condition are re-examined some time later. At the second exam, if the condition is discovered, the more invasive tests are performed. If not, the person is no longer examined for this condition.

We feel that the second exam is pretty much unnecessary, and if so, we'd like to eliminate it due to costs of various sorts.

To show this statistically, we were thinking of performing an equivalence test between the two exam results for the people in the group that did not have the condition in the first exam, hypothesizing that with 95% certainty no more than X% of that group will have the condition in the second exam.

Is this the right way to think about this problem? If not, suggestions would be appreciated.

Mike A.
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  • Maybe one sensible way. But if you get rid of the second-test, is everyone who failed on the first try then forever 'doomed'? – BruceET Sep 23 '19 at 16:08
  • Yes, forever 'doomed' in to be in the failure group, though, in reality, the passing case may be more detrimental than the failure case. – Mike A. Sep 23 '19 at 16:16
  • You may have 'anonomized' your situation so much that helpful statistical advice is impossible. – BruceET Sep 23 '19 at 16:24
  • I have de-anonomized it a bit and I hope that helps. – Mike A. Sep 23 '19 at 16:40
  • Why 95%? I think you'll need data to appropriately balance costs and benefits, rather than just assumptions. – Glen_b Sep 24 '19 at 03:38
  • Sure, assume we’ve analyzed the costs of the two errors and 95% is optimal choice. – Mike A. Sep 24 '19 at 03:42

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