Nonparametric inference for competing risks current status data with continuous, discrete or grouped observation times

Biometrika

Volumn 98, Issue 2, 2011, Pages 325-340

  Maathuis, M H ^a   Hudgens, M G ^b  

^a ETH ZURICH   (Switzerland)

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

Author keywords

Competing risk; Confidence interval; Current status data; Interval censoring; Nonparametric maximum likelihood estimator; Survival analysis

Indexed keywords

HUMAN IMMUNODEFICIENCY VIRUS;

EID: 79957841704     PISSN: 00063444     EISSN: 14643510     Source Type: Journal    
DOI: 10.1093/biomet/asq083     Document Type: Article

References (23)

1. AYER, M., BRUNK, H. D., EWING, G. M., REID, W. T. & SILVERMAN, E. (1955). An empirical distribution function for sampling with incomplete information. Ann. Math. Statist. 26, 641-47.
2. BANERJEE, M. & WELLNER, J. A. (2001). Likelihood ratio tests for monotone functions. Ann. Statist. 29, 1699-732.
3. BANERJEE, M. & WELLNER, J. A. (2005). Confidence intervals for current status data. Scand. J. Statist. 32, 405-24. (Pubitemid 41251535)
4. GENTLEMAN, R. & VANDAL, A. C. (2002). Nonparametric estimation of the bivariate CDF for arbitrarily censored data. Can. J. Statist. 30, 557-72.
5. GROENEBOOM, P., JONGBLOED, G. & WELLNER, J. A. (2008a). The support reduction algorithm for computing nonparametric function estimates in mixture models. Scand. J. Statist. 35, 385-99.
6. GROENEBOOM, P.,MAATHUIS, M. H.&WELLNER, J. A. (2008b). Current status data with competing risks: Consistency and rates of convergence of the MLE. Ann. Statist. 36, 1031-63.
7. GROENEBOOM, P., MAATHUIS, M. H. & WELLNER, J. A. (2008c). Current status data with competing risks: Limiting distribution of the MLE. Ann. Statist. 36, 1064-89.
8. GROENEBOOM, P.&WELLNER, J. A. (2001). Computing Chernoff 's distribution. J. Comp. Graph. Statist. 10, 388-400.
9. HUDGENS, M. G., SATTEN, G. A. & LONGINI, I. M. (2001). Nonparametric maximum likelihood estimation for competing risks survival data subject to interval censoring and truncation. Biometrics 57, 74-80. (Pubitemid 32200139)
10. JEWELL, N. P. & KALBFLEISCH, J. D. (2004). Maximum likelihood estimation of ordered multinomial parameters. Biostatistics 5, 291-306. (Pubitemid 41180230)
11. JEWELL, N. P., VAN DER LAAN, M. J. & HENNEMAN, T. (2003). Nonparametric estimation from current status data with competing risks. Biometrika 90, 183-97. (Pubitemid 39047190)
12. KITAYAPORN, D., VANICHSENI, S., MASTRO, T. D., RAKTHAM, S., VANIYAPONGS, T., DES JARLAIS, D. C.,WASI, C., YOUNG, N. L., SUJARITA, S., HEYWARD, W. L. & ESPARZA, J. (1998). Infection with HIV 1 subtypes B and E in injecting drug users screened for enrollment into a prospective cohort in Bangkok, Thailand. J. Acq. Immun. Defic. Synd. Hum. Retrovir. 19, 289-95.
13. KOSOROK, M. R. (2008). Bootstrapping theGrenander estimator. In Beyond Parametrics in Interdisciplinary Research: Festschrift in Honor of Professor Pranab K. Sen, 282-292. Institute of Mathematics and Statistics Collection 2. Ed. N. Balakrishnan, E. A. Peña andM. J. Silvapulle. IMS Collections. Beachwood, OH: Institute of Mathematics and Statistics.
14. KRAILO, M. D. & PIKE, M. C. (1983). Estimation of the distribution of age at natural menopause from prevalence data. Am. J. Epidemiol. 117, 356-62.
15. MAATHUIS, M. H. (2005). Reduction algorithm for theMLE for the distribution function of bivariate interval censored data. J. Comp. Graph. Statist. 14, 352-62. (Pubitemid 40855810)
16. MACMAHON, B. & WORCESTOR, J. (1966). Age at menopause, United States 1960-1962. National Center for Health Statist. Vital Health Statist. 11, 161-73.
17. POLITIS, D. N. & ROMANO, J. P. (1994). Large sample confidence regions based on subsamples underminimal assumptions. Ann. Statist. 22, 2031-50.
18. SEN, B., BANERJEE, M. & WOODROOFE, M. (2010). Inconsistency of the bootstrap: The Grenander estimator. Ann. Statist. 38, 1953-77.
19. VAN DER VAART, A. W. (1998). Asymptotic Statistics. Cambridge Series in Statistical and Probabilistic Mathematics. Cambridge: Cambridge University Press.
20. VANICHSENI, S., KITAYAPORN, D., MASTRO, T. D., MOCK, P. A., RAKTHAM, S., DES JARLAIS, D. C., SUJARITA, S., SRISUWANVILAI, L., YOUNG, N. L.,WASI, C., SUBBARAO, S., HEYWARD, W. L., ESPARZA, J. & CHOOPANYA, K. (2001). Continued high HIV-1 incidence in a vaccine trial preparatory cohort of injection drug users in Bangkok, Thailand. AIDS 15, 397-405. (Pubitemid 32163826)
21. WOODROOFE, M. & ZHANG, R. (1999). Isotonic estimation for grouped data. Statist. Prob. Lett. 45, 41-7.
22. YU, Q., SCHICK, A., LI, L. & WONG, G. Y. C. (1998). Asymptotic properties of the GMLE in the case 1 intervalcensorship model with discrete inspection times. Can. J. Statist. 26, 619-27. (Pubitemid 128187231)
23. ZHANG, R.,KIM, J. & WOODROOFE, M. (2001). Asymptotic analysis of isotonic estimation for grouped data. J. Statist. Plan. Infer. 98, 107-17. (Pubitemid 33619453)