title: Relationship between Brier score and area under the binormal ROC curve.
abstract: 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.
authors.affiliation: 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
authors.forename: Mitsuru
authors.initials: M
authors.lastname: Ikeda
authors.forename: Takeo
authors.initials: T
authors.lastname: Ishigaki
authors.forename: Kazunobu
authors.initials: K
authors.lastname: Yamauchi
mesh_terms: D003627:Data Interpretation, Statistical; D003658:Decision Making, Computer-Assisted; D015233:Models, Statistical; D011237:Predictive Value of Tests; D011336:Probability