A goodness-of-fit test for generalised conditional linear models under left truncation and right censoring

Journal of Nonparametric Statistics

Volumn 22, Issue 5, 2010, Pages 547-566

  Teodorescu, Bianca ^a   van Keilegom, Ingrid ^a  

^a UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Additive hazards model; Bootstrap; Goodness of fit; Least squares estimator; Proportional hazards model; Semiparametric regression; Survival analysis; Time varying coefficients

Indexed keywords

EID: 77954293525     PISSN: 10485252     EISSN: 10290311     Source Type: Journal    
DOI: 10.1080/10485250903302788     Document Type: Article

References (40)

1. Aalen, O.O. (1980), 'A Model for Non-parametric Regression Analysis of Counting Processes', in Lecture Notes on Mathematical Statistics and Probability, 2, eds. W. Klonecki, A. Kozek, and J. Rosiski, NewYork: Springer-Verlag, pp.1-25.
2. Aalen, O.O. (1993), 'Further Results on the Nonparametric Linear Regression Model in Survival Analysis', Statistics in Medicine, 12, 1569-1588.
3. Akritas, M.G. (1996), 'On the Use of Nonparametric Regression Techniques for Fitting Parametric Regression Models', Biometrics, 52, 1342-1362.
4. Andersen, P.K. (1982), 'Testing Goodness of Fit of Cox's Regression and Life Model', Biometrics, 38, 67-77.
5. Arjas, E. (1988), 'A Graphical Method for Assessing Goodness of Fit in Cox's Proportional Hazards Model', Journal of the American Statistical Association, 83, 204-212.
6. Cai, Z., and Sun, Y. (2003), 'Local Linear Estimation for Time-Dependent Coefficients in Cox's Regression Models', Scandinavian Journal of Statistics, 30, 93-111.
7. Cao, R., and González-Manteiga, W. (2008), 'Goodness-of-Fit Tests for Conditional Models Under Censoring and Truncation', Journal of Econometrics, 143, 166-190.
8. Chen, Y.Q. (2001), 'Accelerated Hazards Regression Model and its Adequacy for Censored Survival Data', Biometrics, 57,853-860.
9. Dabrowska, D. (1989), 'Uniform Consistency of the Kernel Conditional Kaplan-Meier Estimate', Annals of Statistics, 17,1157-1167.
10. De Jong, P. (1987), 'A Central Limit Theorem for Generalized Quadratic Forms', Probability Theory and Related Fields, 75,261-277.
11. Gill, R.D., and Schumacher, M. (1987), 'A Simple Test of the Proportional Hazards Assumption', Biometrika, 74, 289-300.
12. González-Manteiga, W., and Cao, R. (1993), 'Testing the Hypothesis of a General Linear Model using Nonparametric Regression Estimation', Test, 2, 161-188.
13. Grigoletto, M., and Akritas, M.G. (1999), 'Analysis of Covariance with Incomplete Data via Semiparametric Model Transformations', Biometrics, 55, 1177-1187.
14. Härdle, W., and Mammen, E. (1993), 'Comparing NonparametricVersus Parametric Regression Fits', Annals of Statistics, 21,1926-1947.
15. Huffer, F.W., and McKeague, I.W. (1991), 'Weighted Least Squares Estimation forAalen'sAdditive Risk Model', Journal of the American Statistical Association, 86, 114-129.
16. Iglesias-Pérez, C., and González-Manteiga, W. (1999), 'Strong Representation of a Generalized Product-Limit Estimator for Truncated and Censored Data with Some Applications', Journal of Nonparametric Statistics, 10, 213-244.
17. Iglesias-Pérez, C., and González-Manteiga, W. (2003), 'Bootstrap for the Conditional Distribution Function with Truncated and Censored Data', The Annals of the Institute of Statistical Mathematics, 55, 331-357.
18. Jung, S.H. (1996), 'Regression Analysis for Long-term Survival Rate', Biometrika, 83, 227-232.
19. Kaplan, E.L., and Meier, P. (1958), 'Nonparametric Estimation from Incomplete Observations', Journal of the American Statistical Association, 53, 457-481.
20. Kauermann, G. (2005), 'Penalized Spline Smoothing in Multivariable Survival Models with Varying Coefficients', Computational Statistics and Data Analysis, 49, 169-186.
21. Klein, J.P., and Moeschberger, M.L. (1997), Survival Analysis: Techniques for Censored and Truncated Data, NewYork: Springer.
22. Lambert, P., and Eilers, P.H.C. (2004), 'Bayesian Survival Models with Smooth Time-Varying Coefficients using Penalized Poisson Regression', Technical Report TR0435. http://www.stat.ucl.ac.be/publications.
23. Marzec, L., and Marzec, P. (1997), 'On Fitting Cox's Regression Model with Time-Dependent Coefficients', Biometrika, 84,901-908.
24. McKeague, I.W., and Sasieni, P.D. (1994), 'A Partly Parametric Additive Risk Model', Biometrika, 81, 501-514.
25. McKeague, I.W., and Utikal, K.J. (1990), 'Inference for a Nonlinear Counting Process Regression Model', Annals of Statistics, 18, 1172-1187.
26. Murphy, S.A. (1993), 'Testing for a Time Dependent Coefficient in Cox's Regression Model', Scandinavian Journal of Statistics, 20, 35-50.
27. Murphy, S. A., and Sen, P.K. (1991), 'Time-Dependent Coefficients in a Cox-Type Regression Model', Stochastic Processes and their Applications, 39, 153-180.
28. Nan, B., and Lin, X. (2003), 'A Varying-Coefficient Cox Model for the Effect of Age at a Marker Event on Age at Menopause'. http://www.bepress.com/umichbiostat/ paper16.
29. Parzen, M., and Lipsitz, S.R. (1999), 'A Global Goodness-of-Fit Statistic for Cox Regression Models', Biometrics, 55, 580-584.
30. Rossini, A.J., Wei, L.J., and Ying, Z. (1996), 'Checking Adequacy of the Semiparametric Location Shift Model with Censored Data', Lifetime Data Analysis, 2, 145-157.
31. Schoenfeld, D. (1980), 'Chi-squared Goodness-of-Fit Tests for the Proportional Hazards Regression Model', Biometrika, 67,145-153.
32. Silverman, B.W. (1978), 'Weak and Strong Uniform Consistency of the Kernel Estimate of a Density and its Derivatives', Annals of Statistics, 6, 177-184.
33. Subramanian, S. (2001), 'Parameter Estimation in Regression for Long-Term Survival Rate from Censored data', Journal of Statistical Planning and Inference, 99, 211-222.
34. Subramanian, S. (2004), 'Survival-Rate Regression using Kernel Conditional Kaplan-Meier Estimators', Journal of Statistical Planning and Inference, 123, 187-205.
35. Teodorescu, B. (2008), 'Generalized Conditional Linear Models with Time-Varying Coefficients under Left Truncation and Right Censoring', PhD thesis, Université catholique de Louvain, Belgium http://edoc.bib.ucl.ac.be:81/ETD-db/collection/available/BelnUcetd-12122008-014249/unrestricted/PhDthesis-BiancaTeodorescu.pdf.
36. Teodorescu, B., Van Keilegom, I., and Cao, R. (2009), 'Generalized Conditional Linear Models under Left Truncation and Right Censoring', The Annals of the Institute of Statistical Mathematics. http://dx.doi.org/10.1007/s10463-008-0187-z.
37. Tian, L., Zucker, D., and Wei, L.J. (2005), 'On the Cox Model with Time-Varying Regression Coefficients', Journal of the American Statistical Association, 100, 172-183.
38. Tsai, W.Y., Jewell, N.P., and Wang, M.C. (1987), 'A Note on the Product Limit Estimator under Right Censoring and Left Truncation', Biometrika, 74, 883-886.
39. Yang, S. (1998), 'Some Scale Estimators and Lack-of-Fit Tests for the Censored Two-Sample Accelerated Life Model', Biometrics, 54, 1040-1052.
40. Zucker, D.M., and Karr, A.F. (1990), 'Nonparametric Survival Analysis with Time-Dependent Covariate Effects: A Penalized Partial Likelihood Approach', Annals of Statistics, 18, 329-353.