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Overview :
The entropy of a range of test results can provide insights
into the test's usefulness to diagnose a binary outcome.
If a given finding is a associated with a probability of a
binary outcome (presence or absence of a disease) then
entropy of the result = S =
= ((-1) * (probability) * LN(probability)) - ((1 -
(probability)) * LN(1 - (probability)))
If this is rearranged:
(-1) * S =
= LN(((1 - prob)^(1 - (prob))) * ((prob)^(prob)))
The entropy for a result is maximal when the probability is
0.5 and minimal when either the disease has been excluded (probability 0) or is
certain (probability 1).
Vollmer introduced the value (1 - S) which can be plotted vs
a laboratory result. The lower the value (the higher the entropy) the lower the
value of the information. A graphical plot of (1-S) against a range of test
values can identify ranges with limited or maximal diagnostic utility.
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