Cox models with smooth functional effect of covariates measured with error

Journal of the American Statistical Association

Volumn 104, Issue 487, 2009, Pages 1144-1154

  Cheng, Yu Jen ^a   Crainiceanu, Ciprian M ^a  

^a JOHNS HOPKINS UNIVERSITY   (United States)

Author keywords

Measurement error; Smoothing; Survival analysis

Indexed keywords

EID: 70349764853     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/jasa.2009.tm08160     Document Type: Article

References (48)

1. Arjas, E., and Gasbarra, D. (1994), "Nonparametric Bayesian Inference From Right Censored Survival Data, Using Gibbs Sampler, " Statistica Sinica, 4, 505-524.
2. Augustin, T. (2004), "An Exact Corrected Log-Likelihood Function for Cox's Proportional Hazards Model Under Measurement Error and Some Extensions, " Scandinavian Journal of Statistics, 31, 43-50.
3. Berry, S., Carroll, R., and Ruppert, D. (2002), "Bayesian Smoothing and Regression Splines for Measurement Error Problems, " Journal of the American Statistical Association, 97, 160-169.
4. Carroll, R., Ruppert, D., Stefanski, L., and Crainiceanu, C. (2006), Measurement Error in Nonlinear Models, A Modern Perspective (2nd ed., New York: Chapman & Hall.
5. Clayton, D. (1991), "Models for the Analysis of Cohort and Case-Control Studies With Inaccurately Measured Exposures, " in Statistical Models for Longitudinal Studies of Health, New York: Oxford University Press.
6. Coresh, J., Astor, B., Greene, T., Eknoyan, G., and Levey, A. (2003), "Prevalence of Chronic Kidney Disease and Decreased Kidney Function in the Adult US Population: Third National Health and Nutrition Examination Survey, " American Journal of Kidney Diseases, 41, 1-12.
7. Coresh, J., Astor, B., McQuillan, G., Kusek, J., Greene, T., Van Lente, F., and Levey, A. (2002), "Calibration and Random Variation of the Serum Creatinine Assay as Critical Elements of Using Equations to Estimate Glomerular Filtration Rate, " American Journal of Kidney Diseases, 39, 920-929.
8. Cox, D. (1972), "Regression Models and Life Tables" (with discussion), Journal of the Royal Statistical Society, Ser. B, 34, 187-220.
9. (1975), "Partial Likelihood, " Biometrika, 62, 269-276.
10. Crainiceanu, C., Ruppert, D., Carroll, R., Joshi, A., and Goodner, B. (2007), "Spatially Adaptive Bayesian Penalized Splines With Heteroscedastic Errors, " Journal of Computational and Graphical Statistics, 16, 265-288.
11. Eilers, P., and Marx, B. (1996), "Flexible Smoothing Using B-Splines and Penalized Likelihood, " Statistical Science, 11, 89-121.
12. Gamerman, D. (1991), "Dynamic Bayesian Models for Survival Data, " Applied Statistics, 40, 63-79.
13. Geman, S., and Geman, D. (1984), "Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images, " IEEE Transactions on Pattern Analysis and Mechine Intelligence, 6, 721-741.
14. Gilks, W., and Wild, P. (1992), "Adaptive Rejection Sampling for Gibbs Sampling, " Applied Statistics, 41, 337-348.
15. Gray, R. J. (1992), "Flexible Methods for Analyzing Survival Data Using Splines, With Applications to Breast Cancer Prognosis, " Journal of the American Statistical Association, 87, 942-951.
16. (1994), "A Bayesian Analysis of Institutional Effects in a Multicenter Cancer Clinical Trial, " Biometrics, 50, 244-253.
17. Greene, W., and Cai, J. (2004), "Measurement Error in Covariates in the Marginal Hazards Model for Multivariate Failure Time Data, " Biometrics, 60, 987-996.
18. Hastie, T., and Tibshirani, R. (1990), Generalized Additive Models, London: Chapman & Hall.
19. Hennerfeind, A., Brezger, A., and Fahrmeir, L. (2006), "Geoadditive Survival Models, " Journal of the American Statistical Association, 101, 1065-1075.
20. Hsu, C., Kao, W., Coresh, J., Pankow, J., Marsh-Manzi, J., Boerwinkle, E., and Bray, M. (2005), "Apolipoprotein E and Progression of Chronic Kidney Disease, " Journal of the American Medical Association, 293 (23), 2892- 2899.
21. Hu, C., and Lin, D. (2004), "Semiparametric Failure Time Regression With Replicates of Mismeasured Covariates, " Journal of the American Statistical Association, 99, 105-118.
22. Hu, P., Tsiatis, A., and Davidian, M. (1998), "Estimating the Paramters of Cox Model When Covariate Variables Are Measured With Errors, " Biometrics, 54, 1407-1419.
23. Huang, Y., and Wang, C. (2000), "Cox Regression With Accurate Covariates Unascertainable: A Nonparametric Correction Approach, " Journal of the American Statistical Association, 96, 1469-1482.
24. Ibrahim, J., Chen, M.-H., and Sinha, D. (2001), Bayesian Survival Analysis, New York: Springer-Verlag.
25. Investigators, A. (1989), "The Atherosclerosis Risk in Communities (ARIC) Study: Design and Objectives, " American Journal of Epidemiology, 129, 689-702.
26. Kauermann, G., Xu, R., and Vaida, F. (2008), "Stacked Laplace-EM Algorithm for Duration Models With Time-Varying and Random Effects, " Computational Statistics and Data Analysis, 52 (5), 2514-2528.
27. Kottgen, A., Russell, S., Loehr, L., Crainiceanu, C., Rosamond, W., Chang, P. P., Chambless, L., and Coresh, J. (2007), "Reduced Kidney Function as a Risk Factor for Incident Heart Failure: The Atherosclerosis Risk in Communities (ARIC) Study, " Journal of the American Society of Nephrology, 18, 1307-1315. (Pubitemid 46536917)
28. Lang, S., and Brezger, A. (2004), "Bayesian P-Splines, " Journal of Computational and Graphical Statistics, 13, 181-212.
29. Leonard, T. (1978), "Density Estimation, Stochastic Processes and Prior Information, " Journal of the Royal Statistical Society, Ser. B, 40, 113-146.
30. Li, Y., and Lin, X. (2003), "Functional Inference in Frailty Models for Clustered Survival Data Using the Simex Approach, " Journal of the American Statistical Association, 98, 191-203.
31. Li, Y., and Ryan, L. (2006), "Inference on Survival Data With Covariate Measurement Error an Imputation-Based Approach, " Scandinavian Journal of Statistics, 33, 169-190.
32. Mallick, B., Hoffman, F., and Carroll, R. (2002), "Semiparametric Regression ModellingWith Mixtures of Berkson and Classical Error, With Application to Fallout From the Nevada Test Site, " Biometrics, 58, 13-20.
33. Miller, R. (1998), Survival Analysis, New York: Wiley.
34. Nakamura, T. (1992), "Proportional Hazards Models With Covariates Subject to Measurement Error, " Biometrics, 48, 829-838.
35. National Kidney Foundation (2002), "K/DOQI Clinical Practice Guidelines for Chronic Kidney Disease: Evaluation, Classification and Stratification, " American Journal of Kidney Disease, 39 (1), S1-S266.
36. Pepe, M., Self, S., and Prentice, R. (1989), "Further Results in Covariate Measurement Errors in Cohort Studies With Time to Response Data, " Statistics in Medicine, 8, 1167-1178.
37. Prentice, R. (1982), "Covariate Measurement Errors and Parameter Estimation in a Failure Time Regression Model, " Biometrika, 69, 331-342.
38. Ruppert, D., Wand, M., and Carroll, R. (2003), Semiparametric Regression, Cambridge: Cambridge University Press.
39. Sleeper, L. A., and Harrington, D. P. (1990), "Regression Splines in the Cox Model With Application to Covariate Effects in Liver Disease, " Journal of the American Statistical Association, 85, 941-948.
40. Song, X., and Huang, Y. (2005), "On Corrected Score Approach for Proportional Hazards Model With Covariate Measurement Error, " Biometrics, 61, 702-714.
41. Staudenmayer, J., and Ruppert, D. (2004), "Local Polynomial Regression and Simulation-Extrapolation, " Journal of the Royal Statistical Society, Ser. B, 66, 17-30.
42. Stefanski, L. (1989), "Unbiased Estimation of a Nonlinear Function of a Normal Mean With Application to Measurement Error Models, " Communications in Statistics, Ser. A, 18, 4335-4358.
43. Stevens, L., Coresh, J., Greene, T., and Levey, A. (2006), "Assessing Kidney Function-Measured and Estimated Glomerular Filtration Rate, " New England Journal of Medicine, 354 (23), 2473-2483. (Pubitemid 43855050)
44. Tadesse, M., Ibrahim, J., Gentleman, R., Chiaretti, S., Ritz, J., and Foa, R. (2005), "Bayesian Error-in Variable Survival Model for the Analysis of GeneChip Arrays, " Biometrics, 61, 488-497.
45. Tsiatis, A., and Davidian, M. (2001), "A Semiparametric Estimator for the Proportional Hazards Model With Longitudinal Covariates Measured With Error, " Biometrika, 88, 447-458.
46. Wang, C., Hsu, L., Feng, Z., and Prentice, R. (1997), "Regression Calibration in Failure Time Regression, " Biometrics, 53, 131-145.
47. Zhou, H., and Pepe, M. (1995), "Auxiliary Covariate Data in Failure Time Regression, " Biometrika, 82, 139-149.
48. Zhou, H., and Wang, C. (2000), "Failure Time Regression With Continuous Covariates Measured With Error, " Journal of the Royal Statistical Society, Ser. B, 62, 657-665.