Sieve maximum likelihood estimation for regression models with covariates missing at random

Journal of the American Statistical Association

Volumn 102, Issue 480, 2007, Pages 1309-1317

  Chen, Qingxia ^a   Zeng, Donglin ^b   Ibrahim, Joseph G ^b  

^a VANDERBILT UNIVERSITY   (United States)

^b University of North Carolina at Chapel Hill   (United States)

Author keywords

B spline; Generalized linear model; Missing covariates; Model misspecification; Semiparametric efficiency

Indexed keywords

EID: 38349073376     PISSN: 01621459     EISSN: None     Source Type: Journal    
DOI: 10.1198/016214507000001058     Document Type: Article

References (37)

1. Adams, R. A. (1975), Sobolev Spaces, New York: Academic Press.
2. Breslow, N. E., and Holubkov, R. (1997), "Maximum Likelihood Estimation of Logistic Regression Parameters Under Two-Phase, Outcome-Dependent Sampling," Journal of the Royal Statistical Society, Ser. B, 59, 447-461.
3. Chatterjee, N., Chen, Y. H., and Breslow, N. E. (2003), "A Pseudoscore Estimator for Regression Problems With Two-Phase Sampling," Journal of the American Statistical Association, 98, 158-168.
4. Chen, H. Y. (2002), "Double-Semiparametric Method for Missing Covariates in Cox Regression," Journal of the American Statistical Association, 97, 565-576.
5. _ (2004), "Nonparametric and Semiparametric Models for Missing Covariates in Parametric Regression," Journal of the American Statistical Association, 99, 1176-1189.
6. Chen, H. Y., and Little, R. J. (1999), "Proportional Hazards Regression With Missing Covariates," Journal of the American Statistical Association, 94, 896-908.
7. Chen, M.-H., and Ibrahim, J. G. (2001), "Maximum Likelihood Methods for Cure Rate Models With Missing Covariates," Biometrics, 57, 43-52.
8. Chen, Q., and Ibrahim, J. G. (2006), "Semiparametric Models for Missing Covariate and Response Data in Regression Models," Biometrics, 62, 177-184.
9. Debnath, L., and Mikusinski, P. (1990), Introduction to Hilbert Spaces With Applications, San Diego: Academic Press.
10. Falkson, G., Cnaan, A., and Simson, I. W. (1990), "A Randomized Phase II Study of Acivicin and 4-Deoxydoxorubicin in Patients With Hepatocellular Carcinoma in an Eastern Cooperative Oncology Group Study," American Journal of Clinical Oncology, 13, 510-515.
11. Falkson, G., Lipsitz, S., Borden, E., Simson, I. W., and Haller, D. (1995), "A ECOG Randomized Phase II Study of Beta Interferon and Menogoril," American Journal of Clinical Oncology, 18, 287-292.
12. Ibrahim, J. G., Chen, M. H., Lipsitz, S. R., and Herring, A. H. (2005), "Missing-Data Methods for Generalized Linear Models: A Comparative Review," Journal of the American Statistical Association, 100, 332-346.
13. Ibrahim, J. G., Lipsitz, S. R., and Chen, M. H. (1999), "Missing Covariates in Generalized Linear Models When the Missing Data Mechanism Is Nonignorable," Journal of the Royal Statistical Society, Ser. B, 61, 173-190.
14. Lawless, J. F., Kalbfleisch, J. D., and Wild, C. J. (1999), "Semiparametric Methods for Response-Selective and Missing-Data Problems in Regression," Journal of the Royal Statistical Society, Ser. B, 61, 413-438.
15. Lipsitz, S. R., Ibrahim, J. G., and Zhao, L. (1999), "A Weighted Estimating Equation for Missing Covariate Data With Properties Similar to Maximum Likelihood," Journal of the American Statistical Association, 94, 1147-1160.
16. Little, R. J. A. (1992), "Regression With Missing X's: A Review," Journal of the American Statistical Association, 87, 1127-1137.
17. Little, R. J. A., and Rubin, D. B. (2002), Statistical Analysis With Missing Data, (2nd ed.), New Jersey: Wiley.
18. Murphy, S. A., and van der Vaart, A. W. (1997), "Semiparametric Likelihood Ratio Inference," The Annals of Statistics, 25, 1471-1509.
19. _ (2000), "On Profile Likelihood" (with discussion), Journal of the American Statistical Association, 95, 449-465.
20. Paik, M. C. (1996), "Quasi-Likelihood Regression Models With Missing Covariates," Biometrika, 83, 825-834.
21. Pepe, M. S., and Fleming, T. R. (1991), "A Nonparametric Method for Dealing With Mismeasured Covariate Data," Journal of the American Statistical Association, 86, 108-113.
22. Powell, M. J. D. (1988), "A Tolerant Algorithm for Linearly Constrained Optimizations Calculations," DAMTP Report NA17, University of Cambridge, U.K.
23. Reilly, M., and Pepe, M. S. (1995), "A Mean Score Method for Missing and Auxiliary Covariate Data in Regression Models," Biometrika, 82, 299-314.
24. Robins, J. M., Hsieh, F., and Newey, W. (1995), "Semiparametric Estimation of a Conditional Density With Missing or Mismeasured Covariates," Journal of the Royal Statistical Society, Ser. B, 57, 409-424.
25. Robins, J. M., Rotnitzky, A., and Zhao, L. (1994), "Estimation of Regression Coefficients When Some Regressors Are Not Always Observed," Journal of the American Statistical Association, 89, 846-866.
26. Rubin, D. B. (1976), "Inference and Missing Data," Biometrika, 63, 581-592.
27. Schumaker, L. (1981), Spline Functions: Basic Theory, New York: Wiley-Interscience.
28. Scott, A. J., and Wild, C. J. (1997), "Fitting Regression Models to Case-Control Data by the Maximum Likelihood Method," Biometrika, 84, 57-71.
29. _ (2001), "Maximum Likelihood for Generalised Case-Control Studies," Journal of Statistical Planning and Inference, 96, 3-27.
30. _ (2002), "On the Robustness of Weighted Methods for Fitting Models to Case-Control Data," Journal of the Royal Statistical Society, 64, 207-219.
31. Shen, X. (1997), "On Methods of Sieves and Penalization," The Annals of Statistics, 25, 2555-2591.
32. Smith, P. L. (1979), "Splines as a Useful and Convenient Statistical Tool," The Annals of Statistics, 33, 57-62.
33. van der Laan, M. J., and Robins, J. M. (2003), Unified Methods for Censored Longitudinal Data and Causality, New York: Springer-Verlag.
34. van der Vaart, A. W. (1998), Asymptotic Statistics, Cambridge, U.K.: Cambridge University Press.
35. Zeng, D. (2005), "Likelihood Approach for Marginal Proportional Hazards Regression in the Presence of Dependent Censoring," The Annals of Statistics, 33, 501-521.
36. Zhao, L., and Lipsitz, S. (1992), "Designs and Analysis of Two-Stage Studies," Statistics in Medicine, 11, 769-782.
37. Zhou, H. B., and Pepe, M. S. (1995), "Auxiliary Covariate Data in Failure Time Regression," Biometrika, 82, 139-149.