Statistica Sinica 22 (2012), 1427-1456

doi:http://dx.doi.org/10.5705/ss.2010.167

A DIRECT SEMIPARAMETRIC RECEIVER OPERATING

CHARACTERISTIC CURVE REGRESSION WITH

UNKNOWN LINK AND BASELINE FUNCTIONS

Huazhen Lin$^1$, Xiao-Hua Zhou$^{2,3,4}$ and Gang Li$^5$

$^1$Southwestern University of Finance and Economics,

$^2$HSR$\&$D Center of Excellence, $^3$University of Washington,

$^4$Peking University and $^5$University of California at Los Angeles

Abstract: In this article, we study a direct receiver operating characteristic (ROC) curve regression model with completely unknown link and baseline functions. A semiparametric procedure is proposed to estimate both the parametric and nonparametric components of the model. The resulting parameter estimates and ROC curve estimates are shown to be consistent and asymptotically normal with a $n^{-1/2}$ convergence rate. With arbitrary link and baseline functions, our model is more robust than existing direct ROC regression models that require either complete or partially complete specification of the link and baseline functions. Moreover, the robustness of our new method is gained at little cost to efficiency, as evidenced by the parametric convergence rate of our estimators and by the simulation study. An illustrative example is given using a hearing test data set.

Key words and phrases: Diagnostic tests, kernel smoothing, nonparametric, ROC regression, transformation models.