A functional method for the conditional logistic regression with errors-in-covariates

References

• Armstrong , B. G. , Whittemore , A. S. and Howe , G. R. 1989 . Analysis of Case–Control Data with Covariate Measurement Error: Application to Diet and Colon Cancer . Statistics in Medicine , 8 : 1151 – 1163 .
   PubMed Web of Science ®Google Scholar
• Bosley , D. L. 1996 . A Technique for the Numerical Verification of Asymptotic Expansions . SIAM Review , 38 : 128 – 135 .
   Web of Science ®Google Scholar
• Breslow , N. E. and Cain , K. C. 1988 . Logistic Regression for Two-Stage Case-Control Data . Biometrika , 75 : 11 – 20 .
   Web of Science ®Google Scholar
• Breslow , N. E. and Day , N. E. 1980 . Statistical Methods in Cancer Research , Vol. 1 , Lyon , , France : International Agency for Research on Cancer .
   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
• Buzas , J. S. and Stefanski , L. A. 1996 . A Note on Corrected Score Estimation . Statistics and Probability Letters , 28 : 1 – 8 .
   Web of Science ®Google Scholar
• Carroll , R. J. , Ruppert , D. , Stepanski , L. A. and Crainiceanu , C. 2006 . Measurement Error in Nonlinear Models: A Modern Perspective , 2 , New York : Chapman & Hall .
   Google Scholar
• Cheng , K. F. and Hsueh , H. M. 2003 . Estimation of a Logistic Regression Model with Mismeasured Observations . Statistica Sinica , 13 : 111 – 127 .
   Web of Science ®Google Scholar
• Field , C. A. and Welsh , A. H. 2007 . Bootsrapping Clustered Data . Journal of the Royal Statistical Society, Series B , 69 : 369 – 390 .
   Google Scholar
• Forbes , A. B. and Santner , T. J. 1995 . Estimators of Odds Ratio Regression Parameters in Matched Case–Control Studies with Covariate Measurement Error . Journal of the American Statistical Association , 90 : 1075 – 1084 .
   Web of Science ®Google Scholar
• Foutz , R. V. 1977 . On the Unique Consistent Solution to the Likelihood Equations . Journal of the American Statistical Association , 72 : 147 – 148 .
   Web of Science ®Google Scholar
• Guolo , A. 2008 . A Flexible Approach to Measurement Error Correction in Case Control Studies . Biometrics , 64 : 1207 – 1214 .
   Web of Science ®Google Scholar
• Guolo , A. and Brazzale , A. R. 2008 . A Simulation-Based Comparison of Techniques to Correct for Measurement Error in Matched Case–Control Studies . Statistics in Medicine , 27 : 3755 – 3775 .
   Web of Science ®Google Scholar
• Huang , Y. and Wang , C. Y. 2000 . Cox Regression with Accurate Covariates Unascertainable: A Nonparametric-Correction Approach . Journal of the American Statistical Association , 95 : 1209 – 1219 .
   Web of Science ®Google Scholar
• Huang , Y. and Wang , C. Y. 2001 . Consistent Functional Methods for Logistic Regression with Errors in Covariates . Journal of the American Statistical Association , 96 : 1469 – 1482 .
   Web of Science ®Google Scholar
• McShane , L. M. , Midthune , D. N. , Dorgan , J. F. , Freedman , L. S. and Carroll , R. J. 2001 . Covariate Measurement Error Adjustment for Matched Case–Control Studies . Biometrics , 57 : 62 – 73 .
   Web of Science ®Google Scholar
• Rabe-Hesketh , S. , Pickles , A. and Skrondal , A. 2003 . Correcting for Covariate Measurement Error in Logistic Regression Using Nonparametric Maximum Likelihood Estimation . Statistical Modelling , 3 : 215 – 232 .
   Web of Science ®Google Scholar
• Reilly , M. and Pepe , M. S. 1995 . A Mean Score Method for Missing and Auxiliary Covariate Data in Regression Models . Biometrika , 82 : 299 – 314 .
   Web of Science ®Google Scholar
• Schatzkin , A. , Subar , A. F. , Thompson , F. E. , Harlan , L. C. , Tangrea , J. , Hollenbeck , A. R. , Hurwitz , P. E. , Coyle , L. S.N.M.D.S. , Freedman , L. S. , Brown , C. C. , Midthune , D. and Kipnis , V. 2001 . Design and Serendipity in Establishing a Large Cohort with Wide Dietary Intake Distributions . American Journal of Epidemiology , 154 : 1119 – 1125 .
   PubMed Web of Science ®Google Scholar
• Sinha , S. , Mallick , B. K. , Kipnis , V. and Carroll , R. J. 2010 . Semiparametric Bayesian Analysis of Nutritional Epidemiology Data in the Presence of Measurement Error . Biometrics , 66 : 444 – 454 .
   Web of Science ®Google Scholar
• Stefanski , L. A. and Carroll , R. J. 1987 . Conditional Scores and Optimal Scores for Generalized Linear Measurement-Error Models . Biometrika , 74 : 703 – 716 .
   Web of Science ®Google Scholar
• Sugar , E. A. , Wang , C.-Y. and Prentice , R. L. 2007 . Logistic Regression with Exposure Biomarkers and Flexible Measurement Error . Biometrics , 63 : 143 – 151 .
   PubMed Web of Science ®Google Scholar
• van der Vaart , A. W. 1998 . Asymptotic Statistics , Cambridge , , UK : Cambridge University Press .
   Google Scholar
• Wang , C. Y. and Wang , S. 1997 . Semiparametric Methods in Logistic Regression with Measurement Error . Statistica Sinica , 7 : 1103 – 1120 .
   Web of Science ®Google Scholar