Nonparametric estimation with recurrent event data

Journal of the American Statistical Association

Volumn 96, Issue 456, 2001, Pages 1299-1315

  Pena E A ^a   Strawderman, R L ^b   Hollander, M ^c  

^a UNIVERSITY OF SOUTH CAROLINA   (United States)

^b Department of Obstetrics Gynecology   (United States)

^c FLORIDA STATE UNIVERSITY   (United States)

Author keywords

Correlated recurrent times; EM algorithm; Frailty model; Informative censoring; Lexis diagram; Martingale; Sum quota sampling; Weak convergence

Indexed keywords

EID: 1542679214     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1198/016214501753381922     Document Type: Article

References (36)

1. Aalen, O., and Husebye, E. (1991), “Statistical Analysis of Repeated Events Forming Renewal Processes,” Statistics in Medicine, 10,1227-1240.
2. Andersen, P., Borgan, O., Gill, R., and Keiding, N. (1993), Statistical Models Based on Counting Processes, New York: Springer-Verlag.
3. Andersen, P., and Gill, R. (1982), “Cox’s Regression Model for Counting Processes: A Large Sample Study,” Annals of Statistics, 10, 1100-1120.
4. Brent, R. (1973), Algorithms for Minimization without Derivatives, New York: Prentice-Hall.
5. Cai, Z., and Roussas, G. (1998), “Kaplan-Meier Estimator under Association,” Journal of Multivariate Analysis, 67(2), 318-348.
6. Fleming, T., and Harrington, D. (1991), Counting Processes and Survival Analysis, New York: Wiley.
7. Gill, R. (1980), Nonparametric Estimation Based on Censored Observations of a Markov Renewal Process. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 53, 97-116.
8. Gill, R. (1983), “Discussion of Papers by Helland and Kurtz,” Bulletin of the International Statistical Institute, 50, 239-243.
9. Gill, R. D. (1981), “Testing with Replacement and the Product-Limit Estimator,” The Annals of Statistics, 9, 853-860.
10. Hall, W., and Wellner, J. (1980), “Confidence Bands for a Survival Curve from Censored Data,” Biometrika, 67, 133-143.
11. Heckman, J., and Singer, B. (1984), “A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data,” Econometrica, 52, 271-320.
12. Hollander, M., and Peña, E. (1989), “Families of Confidence Bands for the Survival Function under the General Random Censorship Model and the Koziol-Green Model,” Canadian Journal of Statistics, 17, 59-74.
13. Hu, J., and Lawless, J. (1996), “Estimation of Rate and Mean Functions from Truncated Recurrent Event Data,” Journal of the American Statistical Association, 91, 300-310.
14. Husebye, E., Skar, V., Aalen, O., and Osnes, M. (1990), “Digital Ambulatory Manometry of the Small Intestine in Healthy Adults: Estimation of the Variation within and between Individuals and Statistical Management of Aborted MMC Periods,” Digestive Diseases and Sciences, 35, 1057-1065.
15. Jacod, J. (1975), “Multivariate Point Processes: Predictable Projection, Radon-Nikodym Derivatives, Representation of Martingales,” Zeitschrift für Wahrscheinlichkeitstheorie Verwandte Gebiete, 31, 235-253.
16. Kalbfleisch, J. D., Lawless, J. F., and Robinson, J. A. (1991), “Methods for the Analysis and Prediction of Warranty Claims,” Technometrics, 33(3), 273-285.
17. Keiding, N., Andersen, C., and Fledelius, P. (1998), “The Cox Regression Model for Claims Data in Non-life Insurance,” Astin Bulletin, 28, 95-118.
18. Lawless, J., and Nadeau, C. (1995), “Some Simple Robust Methods for the Analysis of Recurrent Events,” Technometrics, 37(2), 158-168.
19. Lin, D., Wei, L., and Ying, Z. (1998), “Accelerated Failure Time Models for Counting Processes,” Biometrika, 85(3), 605-618.
20. McClean, S., and Devine, C. (1995), “A Nonparametric Maximum Likelihood Estimator for Incomplete Renewal Data,” Biometrika, 82(4), 791-803.
21. Murphy, S. (1995), “Asymptotic Theory for the Frailty Model,” The Annals of Statistics, 23, 182-198.
22. Nair, V. (1984), “Confidence Bands for Survival Functions with Censored Data: A Comparative Study,” Technometrics, 26, 265-275.
23. Nielsen, G., Gill, R., Andersen, P., and Sorensen, T. (1992), “A Counting Process Approach to Maximum Likelihood Estimation in Frailty Models,” Scandinavian Journal of Statistics, 19, 25-43.
24. Oakes, D. (1989), “Bivariate Survival Models Induced by Frailties,” Journal of the American Statistical Association, 84, 487-493.
25. Oakes, D. (1991). “Frailty Models for Multiple Event Times,” in Survival Analysis: State of the Art, eds. J. P. Klein and P. K. Goel, Dordrecht: Kluwer, pp. 371-379.
26. Parner, E. (1998), “Asymptotic Theory for the Correlated Gamma Frailty Model,” Annals of Statistics, 26, 183-214.
27. Peña, E., Strawderman, R., and Hollander, M. (2000), “A Weak Convergence Result Relevant in Recurrent Models,” Recent Advances in Reliability Theory (Bordeaux 2000), eds. N. Limnios and M. Nikulin, Boston: Birkhäuser, pp. 493-515.
28. Peña, E., Strawderman, R., and Hollander, M. (2001), “Nonparametric Estimation with Recurrent Event Data,” Technical Report No. 204, Department of Statistics, University of South Carolina. Also available as a technical report from the Department of Biometrics and Statistics, Cornell University, and from the Department of Statistics, Florida State University.
29. Prentice, R., Williams, B., and Peterson, A. (1981), “On the Regression Analysis of Multivariate Failure Time Data,” Biometrika, 68, 373-379.
30. Resnick, S. (1994), Adventures in Stochastic Processes, Boston: Birkhäuser.
31. Sellke, T. (1988), “Weak Convergence of the Aalen Estimator for a Censored Renewal Process,” in Statistical Decision Theory and Related Topics IV, (eds. S. Gupta and J. Berger), New York: Springer-Verlag, Vol. 2, 183-194.
32. Soon, G., and Woodroofe, M. (1996), “Nonparametric Estimation and Consistency for Renewal Processes,” Journal of Statistical Planning and Inference, 53, 171-195.
33. Vardi, Y. (1982a), “Nonparametric Estimation in the Presence of Length Bias,” The Annals of Statistics, 10, 616-620.
34. Vardi, Y. (1982b), “Nonparametric Estimation in Renewal Processes,” The Annals of Statistics, 10, 772-785.
35. Vaupel, J. (1990), “Kindred Lifetimes: Frailty Models in Population Genetics,” in Convergent Issues in Genetics and Demography, eds. J. Adams, D. A. Lam, A. I. Herman, and P. E. Smouse, London: Oxford University Press, pp. 156-170.
36. Wang, M. C., and Chang, S. H. (1999), “Nonparametric Estimation of a Recurrent Survival Function,” Journal of the American Statistical Association, 94, 146-153.