[Clips] Read two biometrics, get worse results - how it works
dan at geer.org
dan at geer.org
Thu Oct 20 11:42:19 EDT 2005
RAH, et al.,
It is true that one can combine two diagnostic
tests to a worse effect than either alone, but
it is not a foredrawn conclusion. To take a
medical example, you screen first with a cheap
test that has low/no false negatives then for the
remaining positives you screen with a potentially
more expensive test that has low/no false positives.
There is a whole health policy & management
literature on this. I reproduce the barest
precis of same below, assuming the reader can
manage to view it in a fixed width font while
respecting my hard carriage returns as writ.
--dan
cheat sheet on terminology of medical diagnostic testing
_________________________________________________________________
\ the true situation
\
\ + -
+-------+-------+---
| | |
+ | a | b | a+b
what the | | |
diagnostic +-------+-------+---
test returns | | |
- | c | d | c+d
| | |
+-------+-------+---
| | |
| a+c | b+d | t
true positives
a = positive testers who have disease
true negatives
d = negative testers who are without disease
false positives
b = positive testers who are without disease
false negatives
c = negative testers who have disease
prevalence
(a+c)/t = fraction of population that has disease
sensitivity
a/(a+c) = what fraction of those with disease test positive
specificity
d/(b+d) = what fraction of those without disease test negative
predictive value positive
a/(a+b) = what fraction of positive tests have disease
predictive value negative
a/(a+b) = what fraction of negative tests are without disease
Notes:
Information retrieval people know sensitivity as "recall" and
predictive value positive as "precision."
Screening with a cheap test with high sensitivity then an expensive
test with high specificity is often the best (most cost effective)
strategy.
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