臺灣博碩士論文加值系統

Receiver operating characteristic (ROC) curve is a technique　for evaluate screening or diagnostic tests with not binary test　results.
ROC regression analysis provides a method to evaluate
covariate effects which may infuence the test accuracy.
In　ROC regression analysis, if we perturb one case in data, the ROC　regression estimators estimated by using perturbed data may be more　different than by complete data.
The character of estimators may be　determined by this case while most of the data is essentially　ignored. Therefore, we have interests in studying the influence of unusual observations in ROC regression analysis.
The perturbation theory provides a useful tool in sensitivity analysis.
In this thesis, we develop single-perturbation influence functions to detect the influential points for ROC regression.
A simulated data and a real data are provided to illustrate the applications of our approach.

1 Introduction 1
2 ROC regression and estimation method 3
2.1 ROC Regression.........................................3
2.2 Quasi-likelihood Estimation............................4
3 Influence Function for ROC Regression 6
3.1 Influence Function.....................................6
3.2 The Influence Function for Mean Parameter..............6
3.3 The Influence Function for ROC Regression..............9
3.4 Empirical Influence Function...........................11
3.5 Sample Influence Function for Mean Parameter...........12
3.6 Cut Points Selection for Influence Function............12
4 Example 13
4.1 A Simulated Data.......................................13
4.2 Application to Radiology Data..........................17
5 Conclusion 23
References 31
Appendix 33

Andrews, D. F. (1972), Plots of high-dimensional data, Biometrics, 28, 125-136.
Cook, R. D. and Weisberg, S. (1980), Characterizations of an empirical influence function for detecting influential cases in regression, Technometrics, 22, 495-508.
Devlin, S. J., Gnanadesikan, R., and Kettenring, J. R. (1975), Robuest estimation and outlier detection with correlation coefficients, Biometrika, 62, 531-546.
Hampel, F. (1968), Contributions tothe theory of robust estimation. Unpublished Ph.D. dissertation, Univ. of California, Berkeley.
Hampel, F. (1974), The influence curve and its role in estimation, Journal of the American Statistical Association, 69, 383-393.
Hinkley, D. V. (1977), Jackknifing in unbalanced situations, Technometrics, 19, 285-292.
Margaret Sullivan Pepe (1998), Three approaches to regression analysis of
receiver operating characteristic curves for continuous test results,
Biometrika, 54, 124-135.
McCullagh, P. and Nelder, J. A. (1983), Quasi-likelihood functions, Annals of Statistics, 11, 59-67.
Muller, C., Wassermann, H. J., Erlank, P., Klopper, J. F., Morkel, H. R. & Ellmann, A. (1989),
Optimization of density and contrast yielded by multiformat photographic imagers used for scintigraphy, Phys. Med. Biol., 34, 473-481.
N. Reid and H. Crepeau (1985), Influence functions for proportional
hazards regression, Biometrika, 72, 1-9.
Pregibon, D. (1979), Data analysis methods for generalized linear models.
Unpublished Ph.D. dissertation, University of Toronto.
Pregibon, D. (1981), Logistic regression diagnostics, Ann. Statist., 9, 705-724.
Reeds, J. A. (1976), On the definition of von Mises functionals. Unpublished Ph.D. dissertation, Harvard University, Dept. of Statistics.
Thompson, M. L. $&$ Zucchini, W. (1989), On the statistical analysis of ROC curves, Statist. Med., 8, 1277-1290.
Tukey, J.M. (1977), Exploratory Data Analysis, Addison-Wesley.
von Mises, R. (1947), On the asymptotic distribution of differentiable statistical functions, Ann. Math. Statist., 18, 309-348.
von Mises, R. (1964), Mathematical Theory of Probability and Statistics, Academic Press, New York.