A DIRECT SEMIPARAMETRIC RECEIVER OPERATING CHARACTERISTIC CURVE REGRESSION WITH UNKNOWN LINK AND BASELINE FUNCTIONS.

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 non-parametric 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.

[1]  Z. Ying,et al.  Analysis of transformation models with censored data , 1995 .

[2]  C. Metz,et al.  Maximum likelihood estimation of receiver operating characteristic (ROC) curves from continuously-distributed data. , 1998, Statistics in medicine.

[3]  Margaret Sullivan Pepe,et al.  Distribution-free ROC analysis using binary regression techniques. , 2002, Biostatistics.

[4]  Jianqing Fan,et al.  Generalized Partially Linear Single-Index Models , 1997 .

[5]  Jianqing Fan,et al.  Local partial-likelihood estimation for lifetime data , 2006, math/0605511.

[6]  M. Pepe.  The Statistical Evaluation of Medical Tests for Classification and Prediction , 2003 .

[7]  W Zucchini,et al.  On the statistical analysis of ROC curves. , 1989, Statistics in medicine.

[8]  H. Müller,et al.  Kernel estimation of regression functions , 1979 .

[9]  Xiao-Hua Zhou,et al.  Statistical Methods in Diagnostic Medicine , 2002 .

[10]  C B Begg,et al.  A General Regression Methodology for ROC Curve Estimation , 1988, Medical decision making : an international journal of the Society for Medical Decision Making.

[11]  Margaret S. Pepe,et al.  A regression modelling framework for receiver operating characteristic curves in medical diagnostic testing , 1997 .

[12]  J. Hanley.  The Robustness of the "Binormal" Assumptions Used in Fitting ROC Curves , 1988, Medical decision making : an international journal of the Society for Medical Decision Making.

[13]  Margaret Sullivan Pepe,et al.  The Analysis of Placement Values for Evaluating Discriminatory Measures , 2004, Biometrics.

[14]  Hans-Georg Müller,et al.  Smooth Optimum Kernel Estimators of Densities, Regression Curves and Modes , 1984 .

[15]  Tianxi Cai,et al.  Semi-parametric ROC regression analysis with placement values. , 2004, Biostatistics.

[16]  H. Ramlau-Hansen.  Smoothing Counting Process Intensities by Means of Kernel Functions , 1983 .

[17]  W. Eddy.  Optimum Kernel Estimators of the Mode , 1980 .

[18]  Z. Ying,et al.  A resampling method based on pivotal estimating functions , 1994 .

[19]  L. J. Wei,et al.  On the Cox Model With Time-Varying Regression Coefficients , 2005 .

[20]  Jianming Ye,et al.  Nonparametric $n\sp {-1/2}$-consistent estimation for the general transformation models , 1997 .

[21]  Joel L. Horowitz,et al.  Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable , 1996 .

[22]  Huazhen Lin,et al.  Non‐parametric heteroscedastic transformation regression models for skewed data with an application to health care costs , 2008 .

[23]  Margaret S. Pepe,et al.  Semiparametric Receiver Operating Characteristic Analysis to Evaluate Biomarkers for Disease , 2002 .

[24]  P. Deheuvels.  Estimation non paramétrique de la densité par histogrammes généralisés , 1977 .