Relationship between Brier score and area under the binormal ROC curve.
If we consider the Brier score (B) in the context of the signal detection theory and assume that it makes sense to consider the existence of B as a parameter for the population (let B be this B), and if we assume that the calibration in the observer's probability estimate is perfect, we find that there is a theoretical relationship between B and the area under the binormal receiver operating characteristic (ROC) curve, A(Z). We have derived this theoretical functional relationship between B and A(Z), by using the parameter a and b in the binormal ROC model and the prior probability of signal events (alpha); here, the two underlying normal distributions are N and N; and, a= and b=. We empirically found that, if parameters b and alpha are constant, B values in relation to given A(Z) values monotonically decrease as A(Z) values increase, and these relationship curves have monotonically decreasing slopes.
Ikeda
Mitsuru
M
Department of Medical Information and Medical Records, Nagoya University Hospital, 65, Tsurumai-cho, Showa-ku, Nagoya 466-8560, Japan. a40495a@nucc.cc.nagoya-u.ac.jp
Ishigaki
Takeo
T
Yamauchi
Kazunobu
K
D003627:Data Interpretation, Statistical; D003658:Decision Making, Computer-Assisted; D015233:Models, Statistical; D011237:Predictive Value of Tests; D011336:Probability