Fig. (9) Mutual information between test results, disease status,
and pre-TP range. (A) Total mutual information MIT and its
components, the mutual information between test results and the
pre-TP range, MIR , and the mutual information between the test
results and disease status, MID , where the brackets indicate the
weighted average over all possible values of the pre-TP. These
three quantities are related by the sum MIT
= MIR
+ MID . Each
term can be further broken down into constituents, as illustrated in
B and C. (B) Components of the equation for the disease-state
related mutual information, MID . The component terms are the
change in uncertainty induced by positive and negative test results,
UD+ and UD , respectively. The disease-state related mutual
information is computed by adding these components together,
weighted by the probability of the corresponding test result,
denoted t+ for a positive result, and t- for a negative test result, i.e. MID=UD+UD+ . (C) Components of the equation for the
range-related mutual information, MIR . The comp onent terms are
the change in uncertainty (entropy) that results from positive and
negative test re sults, ΔUR-andΔUR+ , respectively. The mutual
information between the test result and unknown value of the pre-TP (i.e. the range-related mutual information) is computed by
adding these components toget her, weighted by the probabi lity o f
the corresponding test results, i.e. MIR = t+ΔUR+ + t-ΔUR- .