Proportional Hazards Model With Covariate Measurement Error and Instrumental Variables

REFERENCES

• Andersen, P.K., 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
• Carroll, R.J., Ruppert, D., Crainiceanu, C.M., Tosteson, T.D., Karagas, R.M. (2004), Nonlinear and Nonparametric Regression and Instrumental Variables, Journal of the American Statistical Association, 99, 736–750.
   Web of Science ®Google Scholar
• Carroll, R.J., Ruppert, D., Stefanski, L.A., and Crainiceanu, C.M. (2006), Measurement Error in Nonlinear Models, New York: Chapman & Hall/CRC.
   Google Scholar
• Cragg, J.G. (1983), More Efficient Estimation in the Presence of Heteroskedasticity of Unknown Form, Econometrica, 51, 751–763.
   Web of Science ®Google Scholar
• Dafni, U.G., Tsiatis, A.A. (1998), Evaluating Surrogate Markers of Clinical Outcome Measured With Error, Biometrics, 54, 1445–1462.
   PubMed Web of Science ®Google Scholar
• Davidian, M., Gallant, A.R. (1993), The Nonlinear Mixed Effects Model With a Smooth Random Effects Density, Biometrika, 80, 475–488.
   Web of Science ®Google Scholar
• Hammer, S.M., Katezstein, D.A., Hughes, M.D., Gundaker, H., Schooley, R.T., Haubrich, R.H., Henry, W.K., Lederman, M.M., Phair, J.P., Niu, M., Hirsch, M.S., 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, New England Journal of Medicine, 335, 1081–1089.
   PubMed Web of Science ®Google Scholar
• Hansen, L.P. (1982), Large Sample Properties of Generalized Method of Moments Estimators, Econometrica, 50, 1029–1054.
   Web of Science ®Google Scholar
• Hu, C., Lin, D.Y. (2002), Cox Regression With Covariate Measurement Error, Scandinavian Journal of Statistics, 29, 637–655.
   Web of Science ®Google Scholar
• Huang, Y., 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
• ——— (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
• ——— (2006), Errors-In-Covariates Effect on Estimating Functions: Additivity in Limit and Nonparametric Correction, Statistica Sinica, 16, 861–881.
   Google Scholar
• Liao, X., Zucker, D.M., Li, Y., Speigelman, D. (2011), Survival Analysis with Error-Prone Time-Varying Covariates: A Risk Set Calibration Approach, Biometrics, 67, 50–58.
   PubMed 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
• Newey, W. (1988), Adaptive Estimation of Regression Models via Moment Restrictions, Journal of Econometrics, 38, 301–339.
   Web of Science ®Google Scholar
• Newey, W., and McFadden, D. (1994), “Large Sample Estimation and Hypothesis Testing,” Handbook of Econometrics, Chapter 36, Amsterdam, The Netherlands: Elsevier Science.
   Google Scholar
• Prentice, R. (1982), Covariate Measurement Errors and Parameter Estimates in a Failure Time Regression Model, Biometrika, 69, 331–342.
   Web of Science ®Google Scholar
• Song, X., Davidian, M., Tsiatis, A.A. (2002a), A Semiparametric Likelihood Approach to Joint Modeling of Longitudinal and Time-to-Event Data, Biometrics, 58, 742–753.
   PubMed Web of Science ®Google Scholar
• ——— (2002b), An Estimator for the Proportional Hazards Model With Multiple Longitudinal Covariates Measured With Error, Biostatistics, 3, 511–528.
   PubMedGoogle Scholar
• Song, X., Huang, Y. (2005), On Corrected Score Approach for Proportional Hazards Model With Covariate Measurement Error, Biometrics, 61, 702–714.
   PubMed Web of Science ®Google Scholar
• Song, X., Wang, C.Y. (2008), Semiparametric Approaches for Joint Modeling of Longitudinal and Survival Data with Time Varying Coefficients, Statistica Sinica, 27, 3178–3190.
   Google Scholar
• Stock, J.H., and Watson, W.W. (2010), Introduction to Econometrics, New-York: Addison-Wesley.
   Google Scholar
• Stock, J.H., Wright, J.H. (2000), GMM With Weak Identification, Econometrica, 68, 1055–1096.
   Web of Science ®Google Scholar
• Tapsoba, J.D., Lee, S.M., Wang, C.Y. (2011), Joint Modeling of Survival Time and Longitudinal Data With Subject-Specific Change Points in The Covariates, Statistics in Medicine, 30, 232–249.
   PubMed Web of Science ®Google Scholar
• Tsiatis, A.A., Davidian, M. (2001), A Semiparametric Estimator for the Proportional Hazards Model With Longitudinal Covariates Measured With Error, Biometrika, 88, 447–458.
   Web of Science ®Google Scholar
• Wang, C.Y. (2006), Corrected Score Estimator for Joint Modeling of Longitudinal and Failure Time Data, Statistica Sinica, 16, 235–353.
   Web of Science ®Google Scholar
• ——— (2008), Non-parametric Maximum Likelihood Estimation for Cox Regression With Subject-Specific Measurement Error, Scandinavian Journal of Statistics, 35, 613–628.
   Google Scholar
• Wang, C.Y., Hsu, L., Feng, Z.D., Prentice, R.L. (1997), Regression Calibration in Failure Time Regression, Biometrics, 53, 131–145.
   PubMed Web of Science ®Google Scholar
• Wulfsohn, M.S., Tsiatis, A.A. (1997), A Joint Model for Survival and Longitudinal Data Measured With Error, Biometrics, 53, 330–339.
   PubMed Web of Science ®Google Scholar