A multistate model for bivariate interval-censored failure time data

Biometrics

Volumn 64, Issue 4, 2008, Pages 1100-1109

  Cook, Richard J ^a   Zeng, Leilei ^b   Lee, Ker Ai ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

^b SIMON FRASER UNIVERSITY   (Canada)

Author keywords

Bivariate failure time; EM algorithm; Interval censoring; Markov model

Indexed keywords

MARKOV PROCESSES;

BIVARIATE; BIVARIATE FAILURE TIME; EXPECTATIONS MAXIMIZATION ALGORITHMS; FAILURE TIME; FAILURE TIME DATA; HISTORY DATA; INTERVAL CENSORING; LIFE HISTORY; MARKOV MODELING; MULTI-STATE MODEL;

MAXIMUM PRINCIPLE;

ALGORITHM; BLOOD; HUMAN IMMUNODEFICIENCY VIRUS; LIFE HISTORY; MARKOV CHAIN; NUMERICAL MODEL; OPTIMIZATION; RISK ASSESSMENT; SOFTWARE; VIRUS;

ALGORITHM; ANALYSIS OF VARIANCE; ARTICLE; CYTOMEGALOVIRUS; DATA ANALYSIS; HUMAN; HUMAN IMMUNODEFICIENCY VIRUS INFECTED PATIENT; LIFE HISTORY; PROBABILITY; RISK FACTOR; VIRUS SHEDDING;

CYTOMEGALOVIRUS;

EID: 56049092776     PISSN: 0006341X     EISSN: 15410420     Source Type: Journal    
DOI: 10.1111/j.1541-0420.2007.00978.x     Document Type: Article

References (39)

1. Aalen, O. O., Borgan, O., and Fekjaer, H. (2001). Covariate adjustment of event histories estimated with Markov chains: The additive approach. Biometrics 57, 993 1001.
2. Andersen, P. K., Borgan, O., Gill, R. D., and Keiding, N. (1993). Statistical Models Based on Counting Processes. New York : Springer-Verlag.
3. Bellamy, S. L., Li, Y., Ryan, L. M., Lipsitz, S., Canner, M., and Wright, R. (2004). Analysis of clustered and interval-censored data from a community-based study in asthma. Statistics in Medicine 23, 3607 3621.
4. Betensky, R. A. and Finkelstein, D. M. (1999a). A non-parametric maximum likelihood estimator for bivariate interval censored data. Statistics in Medicine 18, 3089 3100.
5. Betensky, R. A. and Finkelstein, D. M. (1999b). An extension of Kendall's coefficient of concordance to bivariate interval censored data. Statistics in Medicine 18, 3101 3109.
6. Betensky, R. A. and Finkelstein, D. (2002). Testing for dependence between failure time and visit compliance with interval-censored data. Biometrics 58, 58 63.
7. Betensky, R. A., Lindsey, J. C., Ryan, L. M., and Wand, M. P. (1999). Local EM estimation of the hazard function for interval-censored data. Biometrics 55, 238 245.
8. Betensky, R. A., Lindsey, J. C., Ryan, L. M., and Wand, M. P. (2002). A local likelihood proportional hazards model for interval censored data. Statistics in Medicine 21, 263 275.
9. Chen, B. E., Cook, R. J., Lawless, J. F., and Zhan, M. (2005). Statistical methods for multivariate interval-censored recurrent events. Statistics in Medicine 24, 671 691.
10. Cook, R. J. and Lawless, J. F. (2007). The Statistical Analysis of Recurrent Events. New York : Springer.
11. Cox, D. R. and Miller, H. D. (1977). Theory of Stochastic Processes. London : Chapman & Hall.
12. Datta, S. and Satten, G. A. (2001). Validity of the Aalen-Johansen estimators of stage occupation probabilities and Nelson-Aalen estimators of integrated transition hazards for non-Markov models. Statistics and Probability Letters 55, 403 411.
13. Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B 39, 1 38.
14. Finkelstein, D. (1986). A proportional hazards model for interval-censored failure time data. Biometrics 42, 845 854.
15. Friedman, M. (1982). Piecewise exponential models for survival data with covariates. Annals of Statistics 10, 101 113.
16. Gentleman, R. and Vandal, A. (2001). Computational algorithms for censored-data problems using intersection graphs. Journal of Computational and Graphical Statistics 10, 403 421.
17. Gentleman, R. and Vandal, A. (2002). Nonparametric estimation of the bivariate CDF for arbitrarily censored data. Canadian Journal of Statistics 30, 557 571.
18. Goggins, W. B. and Finkelstein, D. M. (2000). A proportional hazards model for multivariate interval-censored failure time data. Biometrics 56, 940 943.
19. Goggins, W. B., Finkelstein, D. M., and Zaslavsky, A. M. (1999). Applying the Cox proportional hazards model when the change time of a binary time-varying covariate is interval censored. Biometrics 55, 445 451.
20. Grüger, J., Kay, R., and Schumacher, M. (1991). The validity of inferences based on incomplete observations in disease state models. Biometrics 47, 595 605.
21. Hougaard, P. (2000). Analysis of Multivariate Survival Data. New York : Springer.
22. Jamshidian, M. and Jennrich, R. (2000). Standard errors for EM estimation. Journal of the Royal Statistical Society, Series B 62, 257 270.
23. Joe, H. (1997). Multivariate Models and Multivariate Dependence Concepts. New York : Chapman & Hall.
24. 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.
25. Kalbfleisch, J. D. and Lawless, J. F. (1989). Some statistical methods for panel life history data. Proceedings of the Statistics Canada Symposium on Analysis of Data in Time. Statistics Canada.
26. Kim, M. Y. and Xue, X. (2002). The analysis of multivariate interval-censored survival data. Statistics in Medicine 21, 3715 3726.
27. Lawless, J. F. and Zhan, M. (1998). Analysis of interval-grouped recurrent-event data using piecewise constant rate functions. The Canadian Journal of Statistics 26, 549 565.
28. Liang, K. Y. and Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika 73, 13 22.
29. Lindsey, J. C. and Ryan, L. M. (1993). A three-state multiplicative model for rodent tumorigenicity experiments. Applied Statistics 42, 283 300.
30. Lindsey, J. C. and Ryan, L. M. (1998). Tutorial in biostatistics: Methods for interval-censored data. Statistics in Medicine 17, 219 238.
31. Loader, C. R. (1996). Local likelihood density estimation. The Annals of Statistics 24, 1602 1618.
32. Louis, T. (1982). Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, Series B (Methodological) 44, 226 233.
33. Meng, X. and Rubin, D. (1991). Using EM to obtain asymptotic variance-covariance matrices: The SEM algorithm. Journal of the American Statistical Association 86, 899 909.
34. Riggs, B. L., Hodgson, S. F., O'Fallon, W. M., Chao, E. Y., Wahner, H. W., Muhs, J. M., Cedel, S. L., and Melton, L. J. (1990). Effect of fluoride treatment on the fracture rate in postmenopausal women with osteoporosis. New England Journal of Medicine 322, 802 809.
35. Shih, J. H. and Louis, T. A. (1995). Inferences on the association parameter in copula models for bivariate survival data. Biometrics 51, 1384 1399.
36. Sun, J. (2006). The Statistical Analysis of Interval-Censored Failure Time Data. New York : Springer.
37. Turnbull, B. W. (1976). The empirical distribution function with arbitrarily grouped, censored and truncated data. Journal of the Royal Statistical Society, Series B 38, 290 295.
38. Warkentin, T. E., Cook, R. J., Marder, V. J., Sheppard, J. A., Moore, J. C., Eriksson, B. I., Greinacher, A., and Kelton, J. G. (2005). Anti-platelet factor 4/heparin antibodies in orthopedic surgery patients receiving antithrombotic prophylaxis with fondaparinux or enoxaparin. Blood 12, 3791 3796.
39. Wei, L. J., Lin, D. Y., and Weissfeld, L. (1989). Regression analysis of multivariate incomplete failure time data by modeling marginal distributions. Journal of the American Statistical Association 84, 1065 1073.