Cox Regression with Accurate Covariates Unascertainable: A Nonparametric-Correction Approach

References

• Andersen , P. K. , Borgan , O. , Gill , R. D. and Keiding , N. 1993 . Statistical Models Based on Counting Processes , New York : Springer-Verlag .
   Google Scholar
• Andersen , P. K. and Gill , R. D. 1982 . “Cox's Regression Model for Counting Processes: A Large Sample Study” . The Annals of Statistics , 10 : 1100 – 1120 .
   Web of Science ®Google Scholar
• Begun , J. B. , Hall , W. J. , Huang , W. M. and Wellner , J. A. 1983 . “Information and Asymptotic Efficiency in Parametric-Nonparametric Models” . The Annals of Statistics , 11 : 432 – 452 .
   Web of Science ®Google Scholar
• Breslow , N. E. 1974 . “Covariance Analysis of Censored Survival Data” . Biometrics , 30 : 89 – 99 .
   PubMed Web of Science ®Google Scholar
• Buzas , J. S. 1998 . “Unbiased Scores in Proportional Hazards Regression With Covariate Measurement Error” . Journal of Statistical Planning and Inference , 67 : 247 – 257 .
   Web of Science ®Google Scholar
• Carroll , R. J. , Ruppert , D. and Stefanski , L. A. 1995 . Measurement Error in Nonlinear Models , London : Chapman and Hall .
   Google Scholar
• Cox , D. R. 1972 . “Regression Models and Life Tables (with Discussion)” . Journal of the Royal Statistical Society , 34 : 187 – 220 . Ser. B
   Google Scholar
• Cox , D. R. 1975 . “Partial Likelihood” . Biometrika , 62 : 269 – 279 .
   Web of Science ®Google Scholar
• Gill , R. D. 1989 . “Non- and Semi-parametric Maximum Likelihood Estimators and the Von Mises Method–I” . Scandinavian Journal of Statistics , 16 : 97 – 128 .
   Web of Science ®Google Scholar
• Hammer , S. M. , Katzenstein , D. A. , Hughes , M. D. , Gundacker , H. , Schooley , R. T. , Haubrich , R. H. , Henry , W. K. , Lederman , M. M. , Phair , J. P. , Niu , M. , Hirsch , M. S. and Merigan , T. C. 1996 . “A Trial Comparing Nucleoside Monotherapy With Combination Therapy in HIV-Infected Adults With CD4 Cell Counts from 200 to 500 per Cubic Millimeter” . The New England Journal of Medicine , 335 : 1081 – 1090 .
   PubMed Web of Science ®Google Scholar
• Hu , P. , Tsiatis , A. A. and Davidian , M. 1998 . “Estimating the Parameters in the Cox Model When Covariate Variables Are Measured With Error” . Biometrics , 54 : 1407 – 1419 .
   PubMed Web of Science ®Google Scholar
• Huang , Y. and Wang , C. Y. 1999 . “Nonparametric Correction to Errors in Covariates,” , Seattle : Fred Hutchinson Cancer Research Center . Technical Report
   Google Scholar
• Hughes , M. D. 1993 . “Regression Dilution in the Proportional Hazards Model” . Biometrics , 49 : 1056 – 1066 .
   PubMed Web of Science ®Google Scholar
• Kong , F. H. and Gu , M. 1999 . “Consistent Estimation in Cox Proportional Hazards Model With Covariate Measurement Errors” . Statistica Sinica , 9 : 953 – 969 .
   Web of Science ®Google Scholar
• Lin , D. Y. 1991 . “Goodness-of-Fit Analysis for the Cox Regression Model Based on a Class of Parameter Estimators” . Journal of the American Statistical Association , 86 : 725 – 728 .
   Web of Science ®Google Scholar
• Lin , D. Y. and Wei , L. J. 1989 . “The Robust Inference for the Cox Proportional Hazards Model” . Journal of the American Statistical Association , 84 : 1074 – 1078 .
   Web of Science ®Google Scholar
• Lin , D. Y. and Ying , Z. 1993 . “Cox Regression With Incomplete Covariate Measurements” . Journal of the American Statistical Association , 88 : 1341 – 1349 .
   Web of Science ®Google Scholar
• Nakamura , T. 1990 . “Corrected Score Function for Errors in Variables Models: Methodology and Application to Generalized Linear Models” . Biometrika , 77 : 127 – 137 .
   Web of Science ®Google Scholar
• Nakamura , T. 1992 . “Proportional Hazards Model With Covariates Subject to Measurement Error” . Biometrics , 48 : 829 – 838 .
   PubMed Web of Science ®Google Scholar
• Prentice , R. L. 1982 . “Covariate Measurement Errors and Parameter Estimation in a Failure Time Regression Model” . Biometrika , 69 : 331 – 342 .
   Web of Science ®Google Scholar
• Prentice , R. L. 1986 . “A Case-Cohort Design for Epidemiologic Cohort Studies and Disease Prevention Trials” . Biometrika , 73 : 1 – 11 .
   Web of Science ®Google Scholar
• Prentice , R. L. , Williams , B. J. and Peterson , A. V. 1981 . “On the Regression Analysis of Multivariate Failure Time Data” . Biometrika , 68 : 373 – 379 .
   Web of Science ®Google Scholar
• Stefanski , L. A. 1989 . “Unbiased Estimation of a Nonlinear Function of a Normal Mean With Application to Measurement Error Models” . Communications in Statistics , 18 : 4335 – 4358 . Ser. A
   Google Scholar
• Tsiatis , A. A. 1981 . “A Large Sample Study of Cox's Regression Model” . The Annals of Statistics , 9 : 93 – 108 .
   Web of Science ®Google Scholar
• Wang , C. Y. , Hsu , L. , Feng , Z. D. and Prentice , R. L. 1997 . “Regression Calibration in Failure Time Regression” . Biometrics , 53 : 131 – 145 .
   PubMed Web of Science ®Google Scholar
• Wei , L. J. , Lin , D. Y. and Weissfeld , L. 1989 . “Regression Analysis of Multivariate Incomplete Failure Time Data by Modeling Marginal Distributions” . Journal of the American Statistical Association , 84 : 1065 – 1073 .
   Web of Science ®Google Scholar
• Zhong , M. , Sen , P. K. and Cai , J. “Cox Regression Model With Mismeasured Covariates or Missing Covariate,” . ASA Proceedings of the Biometrics Section . pp. 323 – 328 .
   Google Scholar
• Zhou , H. and Pepe , M. S. 1995 . “Auxiliary Covariate Data in Failure Time Regression Analysis” . Biometrika , 82 : 139 – 149 .
   Web of Science ®Google Scholar