Med Decis Making - Constructing proper ROCs from ordinal response data using weighted power functions.


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CKGROUND: Receiver operating characteristic (ROC) analysis is the standard method for describing the accuracy of diagnostic systems where the decision task involves distinguishing between 2 mutually exclusive possibilities. The popular binormal curve-fitting model usually produces ROCs that are improper in that they do not have the ever-decreasing slope required by signal detection theory. Not infrequently, binormal ROCs have visible hooks that falsely imply worse-than-chance diagnostic differentiation where the curve lies below the no-information diagonal. In this article, we present and evaluate a 2-parameter, weighted power function (WPF) model that always results in a proper ROC curve with a positive, monotonically decreasing slope.METHODS: We used a computer simulation study to compare results from binormal and WPF models.RESULTS: The WPF model produces ROC curves that are less biased and closer to the true values than are curves obtained using the binormal model. The better performance of the WPF model follows from its design constraint as a necessarily proper ROC.CONCLUSIONS: The WPF model fits a broader variety of data sets than previously published power function models while maintaining straightforward relationships among the original decision variable, specific operating points, ROC curve contours, and model parameters. Compared with other proper ROC models, the WPF model is distinctive in its simplicity, and it avoids the flaws of the conventional binormal ROC model.

Resumo Limpo

ckground receiv oper characterist roc analysi standard method describ accuraci diagnost system decis task involv distinguish mutual exclus possibl popular binorm curvefit model usual produc roc improp everdecreas slope requir signal detect theori infrequ binorm roc visibl hook fals impli worsethanch diagnost differenti curv lie noinform diagon articl present evalu paramet weight power function wpf model alway result proper roc curv posit monoton decreas slopemethod use comput simul studi compar result binorm wpf modelsresult wpf model produc roc curv less bias closer true valu curv obtain use binorm model better perform wpf model follow design constraint necessarili proper rocconclus wpf model fit broader varieti data set previous publish power function model maintain straightforward relationship among origin decis variabl specif oper point roc curv contour model paramet compar proper roc model wpf model distinct simplic avoid flaw convent binorm roc model

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