Nonparametric estimation of stage occupation probabilities in a multistage model with current status data

Biometrics

Volumn 62, Issue 3, 2006, Pages 829-837

  Datta, Somnath ^a   Sundaram, Rajeshwari ^b  

^a UNIVERSITY OF LOUISVILLE   (United States)

^b UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE   (United States)

Author keywords

Current status data; Markov chain; Multistage models; Nonparametric regression; PAV; Stage occupation probabilities; Transition probabilities

Indexed keywords

EMPLOYMENT; MARKOV PROCESSES; TREES (MATHEMATICS);

CURRENT-STATUS DATUM; MULTI STAGE MODELING; NON-PARAMETRIC ESTIMATIONS; NON-PARAMETRIC REGRESSION; OCCUPATION PROBABILITY; PAV; STAGE OCCUPATION PROBABILITY; SURVIVAL DATA; TRANSITION PROBABILITIES; TRANSITION TIME;

SAMPLING;

EMPIRICAL ANALYSIS; MARKOV CHAIN; MULTIVARIATE ANALYSIS; PARAMETERIZATION; PROBABILITY; REGRESSION ANALYSIS; SIMULATION; SURVIVAL;

ARTICLE; CALCULATION; CARDIOVASCULAR DISEASE; MATHEMATICAL MODEL; MEDICAL RESEARCH; OCCUPATION;

EID: 33748783054     PISSN: 0006341X     EISSN: 15410420     Source Type: Journal    
DOI: 10.1111/j.1541-0420.2006.00529.x     Document Type: Article

References (31)

1. Aalen, O. O. (1976). Nonparametric inference in connection with multiple decrement models. Scandinavian Journal of Statistics 3, 15-27.
2. Aalen, O. O. (1978). Nonparametric inference for a family of counting processes. Annals of Statistics 6, 701-726.
3. Aalen, O. O. and Johansen, S. (1978). An empirical transition matrix for nonhomogeneous Markov chains based on censored observations. Scandinavian Journal of Statistics 5, 141-150.
4. Aalen, O. O., Borgan, Ø., and Fekjær, H. (2001). Covariate adjustment of event histories estimated from Markov chains: The additive approach. Biometrics 57, 993-1001.
5. Andersen, P. K. (1988). Multistate models in survival analysis: A study of nephropathy and mortality in diabetes. Statistics in Medicine 7, 939-944.
6. Andersen, P. K., Hansen, L. S., and Keiding, N. (1991). Assessing the influence of reversible disease indicators on survival. Statistics in Medicine 10, 1061-1067.
7. Andersen, P. K., Borgan, Ø., Gill, R. D., and Keiding, N. (1993). Statistical Models Based on Counting Processes. New York: Springer-Verlag.
8. Banerjee, M. and Wellner, J. A. (2005). Confidence intervals for current status data. Scandinavian Journal of Statistics 32, 405-424.
9. Barlow, R. E., Bartholomew, J. M., Bremner, J. M., and Brunk, H. D. (1972). Statistical Inference under Order Restrictions. New York: Wiley.
10. Datta, S. and Satten, G. A. (2001). Validity of the Aalen-Johansen estimators of stage occupation probabilities and integrated transition hazards for non-Markov models. Statistics and Probability Letters 55, 403-411.
11. Datta, S. and Satten, G. A. (2002). Estimation of integrated transition hazards and stage occupation probabilities for non-Markov systems under dependent censoring. Biometrics 58, 792-802.
12. Dewanji, A. D. and Kalbfleisch, J. D. (1986). Nonparametric methods for survival/sacrifice experiments. Biometrics 42, 325-341.
13. Ding, A. A. and Wang, W. (2004). Testing independence for bivariate current status data. Journal of the American Statistical Association 99, 145-155.
14. Dinse, G. E. (1988). Estimating tumor incidence rates in animal carcinogenicity experiments. Biometrics 44, 405-415.
15. Frydman, H. (1995). Nonparametric estimation of a Markov 'illness-death' process from interval-censored observations, with application to diabetes survival data. Biometrika 82, 773-789.
16. Gentleman, R. and Geyer, C. J. (1994). Maximum likelihood for interval censored data: Consistency and computation. Biometrika 81, 618-623.
17. Härdle, W. (1990). Applied Nonparametric Regression. Cambridge, U.K.: Cambridge University Press.
18. Huang, J. and Wellner, J. A. (1997). Interval censored survival data: A review of recent progress. In Proceedings of the First Seattle Symposium in Biostatistics: Survival Analysis, D. Lin and T. Fleming (eds), 123-169. New York: Springer.
19. Hudgens, M. G., Satten, G. A., and Longini, I. M., Jr. (2001). Nonparametric maximum likelihood estimation for competing risk survival data subject to interval censoring and truncation. Biometrics 57, 74-80.
20. Jewell, N. P., van der Laan, M. J., and Henneman, T. (2003). Nonparametric estimation from current status data with competing risks. Biometrika 90, 183-197.
21. Kalbfleisch, J. D. and Lawless, J. F. (1985). The analysis of panel data under a Markov assumption. Journal of the American Statistical Association 80, 863-871.
22. Kay, R. (1986). A Markov model for analyzing cancer markers and disease states in survival studies. Biometrics 42, 855-865.
23. Klein, J. P., Klotz, J. H., and Grever, M. R. (1984). A biological marker model for predicting disease transitions. Biometrics 40, 927-936.
24. Li, G. and Datta, S. (2001). A bootstrap approach to nonparametric regression for right censored data. Annals of the Institute of Statistical Mathematics 53, 708-729.
25. Mammen, E. (1991). Estimating a smooth monotone regression function. Annals of Statistics 19, 724-740.
26. Mukerjee, H. (1988). Monotone nonparametric regression. Annals of Statistics 16, 741-750.
27. Nadaraya, E. (1964). On estimating regression. Theory of Probability and Its Applications 9, 141-142.
28. Shao, J. and Tu, D. (1995). The Jackknife and Bootstrap. New York: Springer.
29. Wand, M. P. and Jones, M. C. (1995). Kernel Smoothing. London: Chapman and Hall.
30. Wang, W. and Ding, A. A. (2000). On assessing the association for bivariate current status data. Biometrika 87, 879-893.
31. Watson, G. (1964). Smooth regression analysis. Sankhya, Series A 26, 302-305.